Honors Chemistry PDF - Phases of Matter

Honors Chemistry Phases of Matter (mostly GASES) Textbook HW: Chapter 11 Read and answer all ODD # questions 1-111 (56 total) – omit part b of number 109 I) Properties of the 3 States of Matter (mostly reminders) A. Entropy: Tendency for disorder Solid liquid...

Honors Chemistry Phases of Matter (mostly GASES) Textbook HW: Chapter 11 Read and answer all ODD # questions 1-111 (56 total) – omit part b of number 109 I) Properties of the 3 States of Matter (mostly reminders) A. Entropy: Tendency for disorder Solid liquid gas Least disordered most disordered Low entropy high entropy Entropy _____________ s→l l→g s→g Entropy______________ g→l l→s g→s B. Solids: -Particles are very close together -______________ shape because the particles are so closely packed together -_______________ volume because the particles are so closely packed together -solids have a high density and are relatively incompressible because the particles are so closely packed together -Particles _____________________ in fixed positions -____________________________ forces of attractions between particles as compared to the gas phase of the same substance -Solids have a very low rate of diffusion because of the strong attractive forces between the particles -Particles are arranged in an orderly, fixed, rigid, geometric pattern called a crystal lattice -_______________________ is the temperature at which a solid will turn to liquid= when the solid particles overcome the attractive forces holding them together -____________________________________ is the amount of heat needed to melt one gram of a solid -There are two categories of solids: crystalline and amorphous Amorphous solids are “solids without form” GLASS, plastic, gel, rubber Crystalline solids have the crystal lattice structure and are considered true solids There are four types of crystals: 1. Ionic crystals -have ionic bonding, are hard, have high melting points, and these solids do not conduct 2. Covalent NETWORK crystals -have covalent bonding, are a special exception to most covalently bonded solids, are very hard, have very high melting points, do not conduct, examples include diamond, silicon carbide (SiC), SiO2, and graphite 3. Metallic Crystals -have metallic bonding, are hard, have high melting points, DO conduct 4. Covalent MOLECULAR crystals -have covalent bonding, are soft, are poor (non)conductors, have low melting points, think of “SPLash into water” C. Liquids: -________________________ volume -________________________ shape: -take the shape of (but do not completely fill) the containers they are put in -particles are ______________________ than gas particles -particles have ____________________ attractive forces between particles than gases -have _____________________ attractive forces between particles than solids -particles ____________________ in fixed positions; liquid particles move past each other -have a ____________________entropy than gases -have a ____________________ entropy than solids -_________________________is the temperature at which a liquid will turn to gas -__________________________ is the amount of heat needed to turn one gram of a liquid into gas -volatile liquids are those that easily evaporate and therefore have weak IMF. Don’t distill these! -more ordered than gases because of the stronger forces of attractions between particles and lower mobility of the particles -relatively high density and low compressibility because particles are SO much closer than in gas phase -can diffuse because liquid particles are in constant, random motion. BUT diffusion in liquids is slower than in gases. Increasing the temperature of a liquid ___________ the rate of diffusion = __________ -Brownian Movement is the zig-zagged path of liquid molecules as seen under a microscope -Viscosity: the resistance to motion between particles of a liquid whenever they move past each other Stronger attractive forces = higher viscosity Weaker attractive forces = lower viscosity Increasing temp leads to particles moving faster and having less resistance (lower viscosity) Decreasing temp leads to particles moving slower having more resistance (higher viscosity) -Surface Tension: a property that results from the imbalance of forces at the surface of a liquid -Particles in the middle of a liquid have attractive forces in all directions -particles at the surface of a liquid do not have attractions to any particles above (bc there are no liquid particles above them). This is the imbalance. Strong attractive forces between particles = high surface tension Weak attractive forces between particles = low surface tension -beading of raindrops -Capillary action: the attraction of the surface of a liquid to the surface of a solid Stronger forces of attraction = more capillary action Weaker forces of attraction = less capillary action -paper chromatography -formation of a meniscus D. Gases: much more info on the way!!! 2 E. Changes of State: S l g -melting, freezing, boiling, condensing, subliming (CO2 and I2), deposing F. Phase Equilibrium: -when the RATE of one phase change is equal to the RATE of the opposing phase change -there is no change in the amount of either phase -some occur at a specific temperatures – in a closed container -DYNAMIC equilibrium: the particles are moving! -s→l l→g s→g G. Equilibrium Vapor Pressure: -the pressure that a vapor exerts on a liquid -If the temperature is increased, then the vapor pressure will increase because more liquid particles will have sufficient KE to escape the surface and turn into a gas. -More gas particles pushing down on the surface of a liquid = higher vapor pressure -Every liquid has its own unique vapor pressure at a given temp ONLY TEMPERATURE HAS AN EFFECT ON VAPOR PRESSURE (direct relationship) There is NO relationship between volume and vapor pressure -stronger forces of attractions between particles = lower VP -weaker forces of attractions between particles = higher VP Vapor pressure- temperature relationship can be given via graph or chart: Table H: As considered from left to right the IMFs get stronger. For the same pressure, the boiling point gets higher as you move towards the right. RED ROVER: the stronger the IMFs the higher the BP. 3 Evaporation: liquid turning to gas at the SURFACE of the liquid Boiling: liquid turning to gas throughout the entire sample (not just at the surface) Boiling Point: temp at which boiling occurs **This is dependent on air pressure** NORMAL boiling point: the temperature at which a substance boils when air pressure is standard pressure Boiling occurs when vapor pressure = air pressure o if air pressure is lowered, a liquid will boil at a lower temperature o if air pressure is raised, a liquid will boil at a higher temperature Examples: 1) The vapor pressure of water at 100 C is 101.3 kPa (see table H or VP chart) Boiling occurs when VP=air pressure. So, if air pressure is 101.3 kPa, water will boil at 100C. 2) The VP of water at 75 C is 38 kPa (see Table H) Boiling occurs when VP=air pressure. So, if air pressure is 38 kPa, water will boil at 75C. 3) The VP of water at 110 C is 147 kPa. Boiling occurs when VP=air pressure. So, if air pressure is 147 kPa, water will boil when its vapor pressure is also 147 kPa which is at 110C. Vapor Pressure v Temperature Graph (Table H) You can find the normal boiling point Answer questions like: what temp will _____ boil when pressure is _______ what pressure will _______boil when temp is ________ H. STP: Standard temperature and pressure 273 K = 0˚C 1 atm = 101.3 kPa = 760 mmHg = 760 torr 4 II. Phase Diagrams -these diagrams show the effects of temperature and pressure on the different phases of a given substance. -the curve from the triple point to the critical point is the vapor pressure curve -The triple point: the temperature and pressure at which all 3 phases of a substance may exist at equilibrium. -The critical point: is the highest condition of temperature and pressure at which it is possible to make the liquid-vapor transition. The substance is a supercritical fluid at higher temperature and pressure than this. -critical pressure/critical temperature ID: solid only, liquid only, gas only, solid and gas, solid and liquid, liquid and gas, all 3 phases, triple point, critical point, critical temperature, critical pressure When the solid-liquid line is to the left of vertical, the solid is less dense than the liquid and will float. When the solid-liquid line is to the right of vertical, the solid is denser than the liquid and will sink. 5 III. Gases Properties and the Kinetic Molecular Theory A) Properties/General Characteristics -weak IMF of attraction -no definite shape and no definite volume -examples include air, N2, O2, CO2, He, Cl2 and many more -as you can see: gases can be elements, compounds, or mixtures -not all gases are colorless. Some gases are green, yellow, brown, purple -All gases behave in similar ways -“Particles” is a general term. You should be able to describe the type of particle that makes up a specific sample of gas: monatomic (single atom)=noble gases; diatomic element = molecule = HOFBrINCl -The number of atoms making up a molecule of a gas does not change the concept that all gases behave similarly -low density, have mass, easily compressed, particles evenly fill containers, diffuse, effuse, exert pressure (force/area) -gas particles collide into the walls of the container. More collisions = higher pressure B) Specific Gases a. Oxygen https://youtu.be/WROdaS82564 -makes up 21% of the atmosphere by volume -preparation of oxygen: 1774 Joseph Priestley discovered oxygen by heating mercuric oxide in a closed container with a magnifying glass. The compound decomposed to produce mercury and oxygen. 2HgO → 2Hg + O2 Today oxygen is usually prepared in the lab by heating an easily decomposed oxygen compound (for example KClO3 potassium chlorate) 2KClO3 + MnO2 → 2KCl + 3O2 + MnO2 2KClO3 → 2KCl + 3O2 KClO3 → KCl + O2 Potassium chlorate → potassium chloride + oxygen You must be able to write the names and formulas of all reactants and products when a chlorate compound is decomposed. *Beware of ion charges* ▪MnO2 is a catalyst in the reaction (not part of the reaction). ▪Catalyst: speeds up a reaction without being consumed by the reaction ▪MnO2 acts as a catalyst by lowering the temperature needed to decompose KClO3. some properties: colorless, odorless, tasteless, glowing splint test (reignites if oxygen is present) ozone = O3 O2 and O3 are allotropes (different forms of the same element) 6 b. Hydrogen https://youtu.be/zQaYLbsl33g -1766 Henry Cavandish was the first person to recognize hydrogen as a separate substance. -preparation of hydrogen: 1. Electrolysis of water: widely used commercial and laboratory method 2. Displace H2 from water molecules using a metal: v. active METAL + H2O → H2 + ____(OH)x Na + H2O → H2 + NaOH You must be able to write the names and formulas of all reactants and products when a metal reacts with water. *Beware of ion charges* 3. Metal + Acid → H2 + salt of acid Zn + 2HCl → H2 + ZnCl2 You must be able to write the names and formulas of all reactants and products when a metal reacts with an acid. *Beware of ion charges* 4. In industry: passing steam over red-hot iron 5. In industry: by decomposing methane with heat (CH4 + H2O → CO + 3H2) -some properties: colorless, odorless, tasteless, density = 0.9g/L at STP. (This is 1/14 the density of air), diffuses more rapidly than any other gas 7  C) Kinetic Molecular Theory (KMT) - A theory of how and why molecules move as they do – based on the idea that particles of matter are always in constant motion. - A model of assumptions that explains why gases behave the way they do (based on the particles that make up a gas) - The KMT answers the question: How would an ideal gas behave? Ideal gases are theoretical. Real gases do not behave as ideal gases would. Assumptions of the KMT (IDEAL GAS) 1. Gases are made up of tiny particles called molecules (or may be called atoms for group 18 only) 2. There is an enormous amount of space between particles. The volume of the individual gas particles is negligible in comparison to the volume of the space between them. Therefore, gas particles have “no volume.” 3. Gas particles move in constant, rapid, random, straight-line (straight-path) motion. (Because of this, gases immediately fill the container and exert pressure) 4. Collisions between particles are “elastic.” This means that even though the individual particles may have different amounts of KE, there is no net change in kinetic energy when particles collide. Individual particles may transfer energy when they collide. At any point, individual particles may have different KEs, but the temperature never changes (temp of the gas depends on the KE of the particles). KE= ½mv2 5. Because gas particles are so far apart, gases have “no forces of attraction” between them. This means they can’t be liquefied. How does a real gas differ from an ideal gas? = How does a real gas deviate from the KMT? Deviations: 1. Real gases DO have volume 2. Real gases DO have forces of attraction between them Ideal gases DO NOT Under what conditions of temperature and pressure will real gases behave most like ideal (particles very far apart)? Low pressure (high volume) and high temperature Gases with low mass behave more like ideal than gases with high mass Which real gases naturally behave most like an ideal gas? Hydrogen (H2) and Helium (He) KMT accounts for physical properties of gases: expansion, fluidity, low density, compressibility, diffusion, and effusion. 8 Variables affecting gas measurement 1. Amount of gas particles in moles (n) 2. Volume (V) 3. Temperature (T) 4. Pressure (P) 1. Amount of gas in moles (n) Mole is like the word dozen. 1 Dozen = 12 1 Mole = 6.02 x 1023 Unit depends on what the number is describing CONVERSION FACTORS FOR DIMENSIONAL ANALYSIS: 1 mole of gas molecules = 6.02 x 1023 gas molecules (not all gas molecules have same # atoms/molecule) (regardless of identity of the gas) 1 mole of gas molecules = 22.4 L (only at STP) (regardless of identity of the gas) 1 mole of gas molecules = gfm (1 mole of gas molecules = molar mass) (different value which depends on the identity of the gas) 9 CONVERSION FACTOR FOR DIMENSIONAL ANALYSIS: 1 mole of gas molecules = 6.02 x 1023 gas molecules (not all gas molecules have same # atoms/molecule) (regardless of identity of the gas) 1 mole of N2 = 6.02 x 1023 nitrogen molecules. Each nitrogen molecule (N2) is made up of two nitrogen atoms. Therefore, 1 mole of nitrogen molecules (N2) contains 2 moles of atoms. 1 mole of Ar = 6.02 x 1023 argon atoms. Argon itself moves around as an individual atom (as do all noble gases). 1 mole of CO2 = 6.02 x 1023 carbon dioxide molecules. Each carbon dioxide molecule (CO2) is made up of 1 carbon atom and 2 oxygen atoms totaling 3 atoms per molecule. Therefore, 1 mole of carbon dioxide molecules (CO2) contains 3 moles of atoms = 3(6.02 x 1023) = 1.806 x 1024 atoms. SOLVE USING DIMENSIONAL ANALYSIS!!!!! a) How many atoms are in 1 CH4 (methane molecule)? b) How many atoms are in 1 mole of CH4 (methane molecules)? c) How many atoms are in CO2? d) How many molecules of fluorine gas are in 3.5 moles of fluorine gas? e) How any atoms of hydrogen are present in an 8.37 mole sample of hydrogen gas? f) How many moles of carbon dioxide are present if you have a sample of the gas that contains 4.12 x 1025 atoms? g) How many moles of ammonia gas are present if your sample contains 9.64 x 1024 molecules? 10 CONVERSION FACTOR FOR DIMENSIONAL ANALYSIS: 1 mole of gas molecules = gfm (1 mole of gas molecules = molar mass) (different value which depends on the identity of the gas) Amount of gas can also be given in mass of the gas. The mass of one mole of a gas is called the molar mass. Each substance has its own molar mass – unique to each substance: gram formula mass, formula mass, molar mass, molecular mass All of the above are solved for in the same way. The only difference is in the units. molar mass (g/mol) gram formula mass (g) formula mass u (amu) molecular mass u (amu) 1 mole = 6.02 x 1023 and there is no specific unit (just like the word dozen). The unit changes based on the amount to which you are referring. H2O could mean 1 water molecule and/or 1 mole of water molecules. subscripts apply to all elements inside parentheses. Example: Ca(OH)2 means 1 mole of calcium ions and 2 moles of hydroxide ions which includes 2 moles of O and 2 moles of H. Ca(OH)2 could also mean 1 calcium ion and 2 hydroxide ions which include 2 O and 2 H. -Each substance has its own unique molar mass. -The molar mass is the mass of one mole of a substance. Solving for molar mass/gfm/fm/mm: -Use the mass on the periodic table for each atom of each element. -Usually, it is okay to round to the tenths. When sig figs are involved, use the entire # provided on the periodic table. 1. Find the molar mass of H2O: element # atoms x mass = total H 2 x 1.0 =2.0 O 1 x 16.0 = 16.0 (2x1)+(1x16)=18 g/mol This means that one mole of H2O molecules has a mass of 18.0 g. The molar mass of H2O is 18.0 g/mol. 2. Solve for the gram formula mass of potassium permanganate. element # atomsx mass = total K 1 x 39.0 = 39.0 Mn 1 x 55.0 = 55.0 O 4 x 16.0 = 64.0 (1x39)+(1x55)+(4x16)=158g 11 3. Determine the formula mass of ammonium phosphate. element # atomsx mass = total Find the sum of all the masses of the atoms in the given formula. This is always the mass (in grams) of one mole of that substance. (molar mass=g/mole) Molar mass of CH4 = Molar mass of CO2 = Molar mass of He = Molar mass of H2 = Molar mass of chlorine gas= Molar mass of nitrogen gas = This is how you convert between mass (of a specific gas-you need to know the identity of the gas) and moles of molecules of that particular substance. SOLVE USING DIMENSIONAL ANALYSIS!!!!! 1. How many moles of nitrogen molecules are in a 205 gram sample? 2. How many grams of chlorine are there in a sample that contains 5.5 moles of gas? 3. How many molecules of fluorine are there in a 98 gram sample of fluorine gas? 4. How many grams of ammonia are present in a sample that has 5.72 x 1026 atoms in the sample? 12 CONVERSION FACTOR FOR DIMENSIONAL ANALYSIS: 1 mole of gas molecules = 22.4 L (only at STP) (regardless of identity of the gas) SOLVE USING DIMENSIONAL ANALYSIS: 1) How many liters will 4.7 moles of helium occupy at STP? 2) How many moles of carbon dioxide molecules are present in a 52.5 L sample at STP? 3) How many molecules of chlorine are present in a 3.5 L sample at STP? 4) What volume will a fluorine gas sample that contains 5.21 x 1032 fluorine atoms occupy at STP? 5) How many moles of gas will there be in 10.0 L at STP? 6) How many molecules of gas will there be in 10.0 L at STP? 7) How many grams of chlorine are present in a 5500 mL sample at STP? 8) What is the mass of a 975 mL volume of oxygen gas at STP? 9) What volume will 520 grams of SO2 (g) occupy at STP? 13 CONVERSION FACTORS FOR DIMENSIONAL ANALYSIS through moles: 1 mole of gas molecules = 6.02 x 1023 gas molecules (not all gas molecules have same # atoms/molecule) (regardless of identity of the gas) 1 mole of gas molecules = 22.4 L (only at STP) (regardless of identity of the gas) 1 mole of gas molecules = gfm (1 mole of gas molecules = molar mass) (different value which depends on the identity of the gas) 2. Volume (V) The volume of a gas is always equal to the volume of its container. Molar volume: 1 mole of any gas at STP occupies 22.4 L. (must be STP conditions) You can still manipulate volume of a gas when conditions are not at STP. This requires the ideal gas law (soon to be discussed). 3. Temperature (T) KELVIN ONLY!!! KELVIN ONLY!!! K = C + 273 and F = 1.8(C) + 32 KELVIN ONLY!!! KELVIN ONLY!!! Standard temperature = 273 K When you are given a temperature (usually in Celsius) convert to Kelvin. If you are asked for a temperature in Celsius that you have solved for in Kelvin, don’t forget to convert back. 4. Pressure (P) ▪gas particles exert pressure by colliding into the walls of the container. More collision and more forceful collisions = higher pressure fewer collisions and less forceful collisions = lower pressure. ▪Standard pressure = 1 atm = 101.3 kPa = 760 torr = 760 mmHg You must be able to convert between these different units of pressure. Use dimensional analysis!! a) Show the correct numerical setup and solve for the pressure of 2.8 atm in kPa. b) Show the correct numerical setup and solve for the pressure of 150. kPa in atm. c) Show the correct numerical setup and solve for 210 kPa in torr. 14 -Atmospheric pressure: the pressure exerted by the air in the atmosphere (exerts pressure on everything it comes in contact with). Q: How is air pressure measured? Barometer: the instrument used to measure air pressure Manometer: the instrument used to measure pressure of an enclosed gas: When Hg is lower on the side exposed to air: When Hg is higher on the side exposed to air: Pair > Pgas Pair < Pgas Pgas = Pair – difference in height P gas = Pair + difference in height 15 The Gas Laws -Gas laws are mathematical relationships between the different variables that affect gases (n, V, T, P) -When studying gases, the samples must be in a closed container (otherwise the sample will escape) -Quite often gases are studied in cylinders with moveable, frictionless pistons. Think of it like a closed syringe: Boyle’s Law (named after Robert Boyle, Irish chemist 1627-1691; studied gases then called airs) -compares P and V -n (amount of gas) and T (temperature) remain unchanged/constant -Boyle’s Law states: the volume of a fixed mass of gas varies inversely with the pressure at constant temperature. -As P________________ V__________________. As P________________ V_____________________. What happens to the volume that the gas occupies when the piston is pushed down (assuming all other conditions are held constant)? Volume ________________________ What happens to the volume that the gas occupies when the piston is raised (assuming all other conditions are held constant)? Volume ________________________ Reminder: Pressure is a result of particles colliding with the container walls (more collision and more forceful collisions = higher P; fewer collisions and less forceful collisions = lower P). When volume is increased, particles will have ________________ collisions with the container walls, and therefore pressure will _____________________. The particles will be moving (faster/slower/at an unchanging speed). When volume is decreased, particles will have ________________ collisions with the container walls, and therefore pressure will _____________________. The particles will be moving (faster/slower/at an unchanging speed). The pressure the piston exerts on the gas is _______________ to pressure the gas exerts on the piston (when the piston is no longer moving). Mathematically, the inverse relationship is represented by PV=k [P=pressure; V=volume; k=constant (not Kelvin)] At any one moment P1V1=k At a different time P2V2=k So, P1V1=P2V2 16 -P1 and P2 must be in the same units (both in atm or both in kPa, etc.) -V1 and V2 must be in the same units (both in mL or both in L, etc.) If P is doubled, V is _____________________ If P is 3x, V is _____________________ If P is 4x, V is __________________ 1. A sample of gas has a volume of 34.2 L when its pressure is 1.49 atm. What volume will the gas occupy at 2.7 atm if temperature remains constant? Your answer must include the correct numerical setup as well as the response with the correct units. 2. If 50.0 mL of hydrogen gas is exerting a pressure of 105.8 kPa has its volume expanded to 75.0 mL, what would the new pressure of the hydrogen gas be? (show all work) 3. 125.0 mL of oxygen gas at 1.85 atm and 273 K would occupy what volume under standard conditions? (show all work) Charles’ Law (named after Jacques-Alexandre-César Charles, French mathematician and physicist, 1746-1823) -compares V and T -n (amount of gas) and P (pressure) remain unchanged (constant) -Charles’ Law states: the volume of a fixed mass of gas varies directly with the Kelvin temperature at constant pressure. -As T _______________, V __________________ As T _______________, V ___________________ Reminders: All temperatures must be in KELVIN!!! (convert if needed: K=C + 273) STP = specific values = 273 K and 1atm=101.3 kPa = 760 mm Hg = 760 torr 𝑉 Mathematically, a direct relationship is represented by 𝑇 = k [V=volume; T=KELVIN Temperature; k=constant (not KELVIN)] If Kelvin temperature is doubled, V is ___________________________. If T (Kelvin) is halved, V is _____________________________. If T is increased particles will move ____________________. Volume will _______________so the number of collisions with the container wall will _________________________________. 17 V1 and V2 must be in the same unit. T1 and T2 must be in Kelvin 1. A sample of gas occupies 500. mL at 40 C and 1 atm. What volume will this gas occupy at STP? 2. Calculate the final volume when a 150.0 mL sample of neon gas at 15 C is cooled to standard temperature and pressure is kept constant. 3. What would the volume be of a sample of nitrogen if the Kelvin temperature of a 200.0 mL sample doubled? Gay-Lussac’s Law (named after Joseph-Louis Gay-Lussac, French chemist and physicist, 1778-1850) -compares P and T -n (amount of gas) and V (volume) remains unchanged (constant) -Gay-Lussac’s Law states: the pressure of a fixed mass of gas varies directly with the Kelvin temperature at constant volume. -As T _________________, P __________________. If Temperature is increased, particles will move ______________. This leads to ________________ number of collisions with the container wall which means the pressure _______________________. 1. A gas exerts 200.0 kPa at 50. C. At what temperature will the pressure be 126.5 kPa? Volume stays constant. 2. If neon gas exerts a pressure of 1.25 atm at 28 C what would the temperature be if the pressure is changed to 725 mmHg? 3. A sample of chlorine gas at STP occupies 1.8 L. If the volume is held constant and the temperature is changed to 60 C, what would the new pressure be (in atm and kPa)? 18 Avogadro’s Law: -There is a direct relationship between volume (V) and moles of gas (n). -Temperature and Pressure are held constant. - Equal volume of any gas at the same temperature and pressure will have equal number of molecules (not necessarily atoms). He N2 CO2 CH4 1) A weather balloon with a volume of 44 L is filled with 2.0 mol of helium. What is the final volume, in liters, if 3.0 mol of helium are added, to give a total of 5.0 mol of helium, if the pressure and temperature do not change? Combined Gas Law -combines Boyle’s, Charles’, and Gay-Lussac’s laws into one. -This expresses the relationship between P, V, and T for a fixed amount of gas. -This can be used for ALL of the above gas law questions. Simply cross out any variable that stays constant and you will be left with the correct individual gas law. -This can also be used if all three variables change. -KELVIN temperatures only!!! 𝑃𝑉 𝑃𝑉 = 𝑛𝑇 𝑛𝑇 1. A sample of gas occupies 5.6L at 25 C and 120.3 kPa. What volume will this gas occupy at STP? 2. A sample of hydrogen has a volume of 1.00L at a pressure of 100. kPa. If the temperature is kept constant and the pressure is raised to 140. kPa, what is the new volume of the gas? 3. When 500. mL of hydrogen gas is heated from 30.0 C to 60.0 C at constant pressure, the volume of the gas at 60.0 C will be______________. 19  4. 200.0 mL of argon gas is at 25 C and exerts a pressure of 795 torr. If the conditions are corrected to STP, what will be the new volume? 5. 155.0 mL of methane gas at standard conditions are heated to 35 C and allowed to expand to 225 mL. Calculate the new pressure in atmospheres. 6. 175 mL of nitrogen gas exerts a pressure of 125.0 kPa. If the temperature is held constant, what would the new pressure be if the volume is changed to 250.0 mL? 𝑃𝑉 𝑃𝑉 = 𝑛𝑇 𝑛𝑇 Pressure Laws Dalton’s Law of Partial Pressures -The total pressure of a mixture of gases is equal to the sum of the partial pressures that each gas would exert if it alone occupied the volume Ptotal = P1 + P2 + P3 +... 1. If the total pressure of a mixture of nitrogen and oxygen gases is 3.5 atm, and the partial pressure of the nitrogen is 2.0 atm, what is the partial pressure of the oxygen gas? 2. 200 mL of hydrogen gas and 100 mL of neon gas exert a total pressure of 150 kPa. Calculate the partial pressure of both the hydrogen and the neon gas. 3. Two moles of hydrogen gas and one mole of neon gas exert a total pressure of 150 kPa. Calculate the partial pressure of both hydrogen and neon gas. 20  4. A mixture of 30.% He and 70.% Ar exerts a pressure of 150. kPa at 25 C. What is the partial pressure of each gas? 5. A sample of NH3 (g) is decomposed into its elements. If the pressure of the nitrogen gas produced equals 40.0 kPa, what would be the pressure of the hydrogen gas (assume no NH3 is left in the container)? Gas Collected Over Water -gas collected by water displacement -gas collected over water Ptotal = Pgas + PH2O -The water vapor above the water in the collection tube (eudiometer, test tube, etc.) exerts a pressure which contributes to the total pressure. -Reminder: vapor pressure depends on the temperature of the liquid. So, you need the temperature of the water in order to determine the vapor pressure of the water. -You would need a graph, table, or to be told what the vapor pressure of water is at the specific temperature in each question. 1. 24.3 mL of hydrogen was collected over water at 16 ˚C and 756.2 mm Hg. Find the partial pressure of the dry gas at these conditions. 2. 723.4 mL of helium gas was collected over water at 80. ˚C and 845.1 mmHg. Find the partial pressure of the dry gas at these conditions. 21 Dalton’s Law along with Combined Gas Law 1. A 475 mL sample of gas is collected over water at 27 ˚C and with a total pressure of 675 mmHg. If the vapor pressure of water at 27 ˚C is 26.7 torr, what is the volume of the gas sample at standard conditions? 2. A 0.55 L sample of hydrogen gas is collected over water at a temperature of 22 ˚C. The total pressure of the collected gas is 735 mm Hg. What would be the volume of the dry hydrogen at 27 ˚C and 1 atm? Graham’s Law of Effusion -relates the rate at which a gas effuses (or diffuses) to the type of molecule in the gas -the rate of effusion of a gas is inversely proportional to the square root of its molecular mass -So, if the molar mass of one gas is 4x that of another, it would diffuse through a porous plug or escape through a small pinhole in a vessel at half the rate of the other. -The lower the mass, the faster the gas will diffuse or effuse. -Hydrogen has the lowest mass and will therefore diffuse faster than any other gas under similar conditions. Rate1 = rate of effusion of the first gas (volume or number of moles per unit time) Rate2 = rate of effusion of the second gas M1 = molar mass of gas 1 M2 = molar mass of gas 2 Example: Compare the rates of effusion of H2 and O2. -molecules of H2 diffuse 4x faster than those of O2. Graham’s Law can also be used to find the approximate mass of a gas when the identity of one gas is known and the ratio between the two gases is known. The equation can be solved for either one of the molar masses when the subscripts are consistent. 1. If equal amounts of helium and argon are placed in a porous container and allowed to escape, which gas will escape faster and how much faster? 2. What is the molecular mass of a gas which diffuse 1/10 as fast as hydrogen? 22 Ideal Gas Law -So far we have kept at least one variable constant while discussing gas laws. -We have not yet manipulated the variable n (amount of gas). -This also takes into account the type of gas Reminders: An ideal gas would have no forces of attraction. Real gases do have weak forces of attraction. -These forces of attraction do vary from gas to gas. This is why the specific gas being studied must be taken into account (not just the amount of the gas). Ideal Gas Law PV = nRT P=pressure (atm) V=volume (L) n=amount of gas, which takes into account the type of gas as well as the amount (moles) R=gas constant = 0.0821 L atm/mol K T=temperature (K) 𝑚𝑎𝑠𝑠 (𝑖𝑛 𝑔𝑟𝑎𝑚𝑠) Molar mass = 𝑚𝑜𝑙𝑒 So: 𝑚𝑎𝑠𝑠 (𝑖𝑛 𝑔𝑟𝑎𝑚𝑠) 𝑚𝑎𝑠𝑠 moles = moles = 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑔𝑓𝑚 𝒎𝒂𝒔𝒔𝑹𝑻 PV = 𝒎𝒐𝒍𝒂𝒓 𝒎𝒂𝒔𝒔 Easy Ideal Gas Law Problems 1. Calculate the volume of 1 mole of hydrogen gas at standard conditions. 2. Calculate the volume of 1 mole of methane gas at standard conditions. 3. Calculate the volume of 28 grams of methane gas (CH4) under standard conditions. 23 Trickier Ideal Gas Law Problems 4. Calculate the mass of neon gas if a sample exerts 725 mm Hg at 27 ˚C and occupies a volume of 350. mL. 5. Calculate the molar mass of a gas when 88.0 grams of the gas exerts a pressure of 825 mm Hg and occupies a volume of 30.0 L at 27 ˚C. Density of a gas using the Ideal Gas Law PV=nRT Density = mass/volume V=Volume Moles = mass/molar mass So, rearrange the ideal gas law to solve for density PV=nRT 𝑚𝑎𝑠𝑠 PV=(𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠)RT PV(molar mass)=(mass)RT PV(molar mass) =mass RT P(molar mass) 𝑚𝑎𝑠𝑠 = 𝑣𝑜𝑙𝑢𝑚𝑒 = density in g/L RT 𝐏(𝐦𝐨𝐥𝐚𝐫 𝐦𝐚𝐬𝐬) d= 𝐑𝐓 24  1. Calculate the density of chlorine gas under standard conditions. 2. If the density of a gas is 5.9 g/L at a pressure of 1.6 atm and 95 K, calculate the molar mass of the gas. 3. If the density of a gas is 0.712 g/mL at a pressure of 450. kPa and -25 ˚C, calculate the molar mass of the gas. Density of a gas at STP: 𝑚𝑜𝑙𝑎𝑟 𝑚𝑎𝑠𝑠 𝑔/𝑚𝑜𝑙 𝑔 = molar mass/22.4 = 𝑚𝑜𝑙𝑎𝑟 𝑣𝑜𝑙𝑢𝑚𝑒 𝐿/𝑚𝑜𝑙 𝐿 1234𝑔 1 𝑚𝑜𝑙𝑒 Or molar mass x molar volume: use dimensional analysis: 𝑥 1 𝑚𝑜𝑙𝑒 22.4 𝐿 1) What is the density of carbon dioxide at STP? 2) What is the density of methane (CH4) at STP? 25  CONVERSION FACTORS FOR DIMENSIONAL ANALYSIS: 1 mole of gas molecules = 6.02 x 1023 gas molecules (not all gas molecules have same # atoms/molecule) (regardless of identity of the gas) 1 mole of gas molecules = 22.4 L (only at STP) (regardless of identity of the gas) 1 mole of gas molecules = gfm (1 mole of gas molecules = molar mass) (different value which depends on the identity of the gas) Simplified: 1 mole = 6.02 x 1023 1 mole = 22.4 L (STP) 1 mole = gfm PV=nRT Reactions involving gases and the ideal gas law (gas stoichiometry) -Always start with a balanced equation!!! **************THE ONLY WAY TO COMPARE DIFFERENT SUBSTANCES IN A CHEMICAL EQUATION IS THROUGH MOLES!!******************* -The coefficients in a chemical reaction represent MOLES!!! Information A → moles A → moles B → info B 1) Info A → moles A a. will need molar mass, molar volume, Avogadro’s number (use dimensional analysis) b. or ideal gas law (no dimensional analysis) 2) Moles A → moles B 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝐵 Will need coefficients: 𝑐𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 𝐴 3) Moles B → info B a. will need molar mass, molar volume, Avogadro’s number (use dimensional analysis) b. or ideal gas law (no dimensional analysis) 26 1. Ammonia (NH3) gas can be synthesized from nitrogen gas + hydrogen gas. What volume of ammonia at 4.4 atm and 80 C can be obtained from the complete reaction of 12.0 g of hydrogen? N2(g) + 3H2(g) → 2NH3(g) 2. Hydrogen gas (and NaOH) is produced when sodium metal is added to water. What mass of Na is needed to produce 20.0 L of H2 at STP? 2Na(s) + 2H2O(l) → H2(g) + 2NaOH(aq) 3. Nitroglycerin explodes according to the following: 4C3H5(NO3)3(l) → 12CO2(g) + 6N2(g) + 10H2O(g) + O2(g) a) Calculate the volume, at STP, of CO2 formed by the reaction of 100.g of C3H5(NO3)3. b) 200.g of C3H5(NO3)3 is ignited (and completely decomposes) in an otherwise empty 50. L gas cylinder. What will the pressure in the cylinder be when the temperature stabilizes at 220 ˚C? 27  4) Mg + 2HCl → MgCl2 + H2 Hydrogen gas can be produced in the lab through the reaction of magnesium with hydrochloric acid. What is the volume, in L, of hydrogen gas produced at 24 C and 835 mm Hg from the reaction of 12.0 g of Mg? https://www.youtube.com/watch?v=13WUqWd_Yk8&list=PL65159266CFC74682&index=7 Mark Rosengarten’s “Rock Me Avogadro” 28