General Chemistry 1: Ideal Gas Law & Dalton's Law Past Paper PDF

GENERAL CHEMISTRY 1: GRADE 12 – DESCARTES (STEM) IDEAL GAS LAW ENGR. MARTYN MIGUEL Q. TADENA IDEAL GAS LAW  IDEAL GAS LAW It is a single equation that sums up and combines the mathematical expression of NOTE: When usin...

GENERAL CHEMISTRY 1: GRADE 12 – DESCARTES (STEM) IDEAL GAS LAW ENGR. MARTYN MIGUEL Q. TADENA IDEAL GAS LAW  IDEAL GAS LAW It is a single equation that sums up and combines the mathematical expression of NOTE: When using the Boyle’s Law, Charles’ Law, and Avogadro’s universal gas constant R: Law. - Volume should be in liters. (L) pV = nRT - Temperature should be in Kelvins. (K) Where; P = Pressure - Pressure should be in atm. n = moles - Number of moles should be in V = Volume mol. T = Temperature (express in Kelvin (K)) R = The universal gas constant (0.0821 atm-L / mol-K) GENERAL CHEMISTRY 1 IDEAL GAS LAW GENERAL CHEMISTRY 1  IDEAL GAS LAW EXAMPLE: A 3.5 L container holds 0.45 moles of O2 gas at 300K. What is the pressure inside the container? ANSWER: 3.17 atm GENERAL CHEMISTRY 1  IDEAL GAS LAW EXAMPLE: If I have 4 moles of a gas at a pressure of 5.6 atm and a volume of 12 liters, what is the temperature? ANSWER: 204.63 K GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE  DALTON’S LAW OF PARTIAL PRESSURE Most of the gases encountered in the surroundings are mixtures. Mixtures are composed of different components. An example of a mixture is air which is a combination of primarily nitrogen and oxygen and other gases. GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE Each individual component in air exerts its own pressure, has its own volume, can have a temperature that is in thermal equilibrium with the other components, and also has its own molar amount. GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE For example, a constant- volume piston shown contains a sample of flue gas, a by- product of combustion, which is composed of nitrogen (1), carbon dioxide (2), and carbon monoxide (3) at a constant temperature of 30°C. GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE Therefore, the number of moles of each component can be interpreted as n1, n2, and n3, and the total number of moles can be shown as: GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE The pressure exerted by the mixture can then be calculated using the ideal gas equation: Therefore, we can also compute for the pressure exerted by each individual component using the ideal gas law equation. GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE Dalton’s Law of Partial Pressure states that: “The pressure exerted by the mixture of gases is the sum of the pressures exerted by each of its component.” Main Proponent: John Dalton Pressures P1, P2, and P3 are called the partial pressures of the gases. GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE EXAMPLE: A sealed vessel holds a mixture of two different gases. The argon inside the vessel exerts a pressure of 20 mmHg. The total pressure inside the vessel is 150 mmHg. What is the pressure of the other gas in the vessel? ANSWER: 130 mmHg GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE EXAMPLE: A gas container has a mixture of several gases. If the total air pressure is 0.99 atm, the partial pressure of carbon dioxide is 0.15 atm, and the partial pressure of hydrogen sulfide is 0.22 atm, what is the partial pressure of the remaining air? ANSWER: 0.62 atm GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE EXAMPLE: In conducting an experiment, I placed 1.5 moles of N2 and 5 moles of O2 in a 45 L container at a temperature of 50 °C, what will be the pressure (in atm) of the resulting mixture of gases? ANSWER: 3.83 atm GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE EXAMPLE: A mixture of hydrogen gas (H2) and oxygen gas (O2) contains 13.3 mol hydrogen gas and 11.24 mol oxygen gas. It was placed in a 200 L container at 273 K. What is the partial pressure of each gas? ANSWER: PH2 = 1.49 atm, PO2 = 1.26 atm GENERAL CHEMISTRY 1  MOLE FRACTION Another way to calculate the partial pressure of gas components is through the mole fraction (X). The mole fraction of a gas is the number of moles of an individual gas divided by the total moles of gas in the mixture. It could be expressed in fraction, decimal or percent. GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE USING MOLE FRACTION EXAMPLE: A mixture contains 1/3 nitrogen and 2/3 neon gas. The total pressure in the container is 2.75 atmospheres. What is the partial pressure of the neon gas? ANSWER: 1.83 atm GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE USING MOLE FRACTION EXAMPLE: A vessel contains 30% argon and the remaining gas is helium. Calculate the partial pressure of helium and argon if the total pressure inside the container is 2.00 atm. ANSWER: PHe = 1.4 atm, PAr = 0.6 atm GENERAL CHEMISTRY 1  DALTON’S LAW OF PARTIAL PRESSURE USING MOLE FRACTION EXAMPLE: A container holds 5 moles of chlorine gas, 2 moles of argon, and 4 mole of helium and has a total pressure of 1.95 atm. Calculate the partial pressure of each gas. ANSWER: PCl = 0.89 atm, PAr = 0.35 atm, PHe = 0.71 atm GENERAL CHEMISTRY 1  REVIEW EXAMPLE: A mixture of 1.25005 mol O2 gas and 9.9935 mol He gas has a total pressure of 0.900 atm. What is the partial pressure of each gas? ANSWER: PO2 = 0.10 atm, PHe = 0.80 atm GENERAL CHEMISTRY 1 GRAHAM’S LAW OF EFFUSION  GRAHAM’S LAW OF EFFUSION Diffusion occurs when gas molecules disperse throughout a container. It is the movement of gas molecules through one or more additional types of gas via random molecular motion. GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION Effusion occurs when a gas passes through an opening or a very small hole that is smaller than the free path of the particle. For example, if you puncture a balloon with the tip of a safety pin, it will deflate in seconds. GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION One of the properties of gases is its ability to diffuse easily. As a result of this property, a gas spreads easily in the air and fills up all available space. The phenomenon of effusion had been known for thousands of years, but it was not until the early 19th century that quantitative experiments related the rate of effusion to molecular properties. GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION Graham’s Law of Effusion states that: “The relationship between the diffusion rate, or the rate at which the gas moves, is inversely proportional to the square root of its molar mass.” Main Proponent: Scottish chemist Thomas Graham (1805–1869) Where: 𝑅1 𝑀2 = R = rate 𝑅2 𝑀1 M = molar mass (g/mol) GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION EXAMPLE: Which of the following gases would effuse more rapidly: helium gas (He) or ethylene oxide (C2H4O)? ANSWER: Helium gas GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION The lighter He atoms (M = 4.00 g/mol) effuse through the small hole more rapidly than the heavier ethylene oxide (C2H4O) molecules (M = 44.0 g/mol), as predicted by Graham’s law. GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION EXAMPLE: Two bottles at the same temperature containing hydrogen sulfide (H2S) and ammonia (NH3) are placed at equal lengths from you and are opened at the same time. Which gas would you smell first? ANSWER: Ammonia (NH3) GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION EXAMPLE: How much faster does hydrogen gas diffuse than sulfur dioxide? ANSWER: 5.65 times GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION EXAMPLE: How will a gas velocity vary if its molecular weight was decreased from 144 g/mol to 64 g/mol? ANSWER: It will be 1.5x faster. GENERAL CHEMISTRY 1  GRAHAM’S LAW OF EFFUSION EXAMPLE: Which of the following gases diffuses the fastest? Oxygen (O2), Hydrogen (H2), Sulfur dioxide (SO2), or Carbon dioxide (CO2)? ANSWER: Hydrogen (H2) GENERAL CHEMISTRY 1  GET READY! Get ready for 25-item Quiz #1 on Wednesday. Good luck! Topics: Ideal Gas Law Equation Dalton’s Law of Partial Pressure Graham’s Law of Effusion GENERAL CHEMISTRY 1 THANK YOU!