CHEM 101 Module 16 111124 PDF

 Announcements TODAY (11:59 pm) is the last day to complete the Real Chem Survey and earn a 5% bonus towards your lowest exam score. Exam 3 is this Friday at 4:00 pm. – Modules 12 – 15 – Lecture hall assignments will be posted by Wednesday. – It is your responsibil...

 Announcements TODAY (11:59 pm) is the last day to complete the Real Chem Survey and earn a 5% bonus towards your lowest exam score. Exam 3 is this Friday at 4:00 pm. – Modules 12 – 15 – Lecture hall assignments will be posted by Wednesday. – It is your responsibility to bring the approved calculator. It would be painful to do this exam without a calculator. Module 16 Gas Laws Gas Pressure Pressure is defined as the Atmospheric force exerted on a given pressure is area. Gas pressure is a measured with a result of the force exerted barometer. by gas molecules colliding with the surface of objects. Unit Description Relationship Pascal (Pa) SI Unit 1 atm = 101,325 Pa atmospheric pressure (atm) 1 atm at sea level 1 atm = 760 mm Hg mmHg Barometer measurement 1 mmHg = 133.322 Pa torr Name for mmHg 1 mmHg = 1 torr Manometer A manometer is used to Pgas < Patm measure the pressure of a Pgas = Patm - h gas trapped in a container. The distance between the liquid levels corresponds to the difference in pressure between the gas in the container and the atmosphere. Pgas > Patm If the gas pressure equals Pgas = Patm + h the atmospheric pressure, the levels will be equal. An open-end manometer contains a sample of gas in the bulb and is open to an external pressure of 790 mm Hg. If the level of Hg in the arm connected to the bulb is 14.5 cm higher than the level of mercury in the arm open to the atmosphere, what is the pressure inside the bulb in mm Hg? Pgas = Patm - h Pgas = Patm + h 14.5 cm or - Pgas < Patm Pgas > Patm Pgas = 790 mm Hg – 145 mm Hg = 645 mm Hg Relating Pressure, Volume, Amount, Temperature There are many different All gases have the same types of gases. dependence on these four properties. ▪ Elements: Volume Ar, He, H2, N2, O2 Amount ▪ Compounds: Temperature CO2, CO, H2O, NH3 Pressure  Pressure and Temperature: Volume and Volume and Volume and Amonton’s Law Temperature: Pressure: Moles: or Gay-Lussac’s Charles’ Law Boyle’s Law Avogadro’s Law Law The volume of a gas The pressure of a The volume of a gas The volume of a gas is directly gas is directly is directly is inversely proportional to its proportional to its proportional to its proportional to its amount (moles of temperature in K. temperature in K. pressure. gas). At constant V At constant P At constant T At constant T k and n, P=kT and n, V=kT and n, V = P and P, V=kn As volume As temperature As temperature As the number of increases, goes up, pressure goes up, volume moles increases, pressure goes up. increases. volume increases. decreases.  The Gas Laws Amonton / Gay-Lussac Charles Boyle Avogadro constant V and n constant P and n constant T and n constant T and P k P=kT V=kT V= V=kn P P1 P2 V1 V2 V1 V2 = = P1V1=P2V2 = T1 T2 T1 T2 n1 n PV PV 1 1 = 2 2 T1 T2 combined gas law  The Ideal Gas Law These four equations can be combined into a single law consisting of all four properties describing an ideal gas. PV = nRT The four constants (k) were combined into a new constant, R, called the ideal gas constant. P is the pressure in atm. T is the temperature in K. V is the volume in L. R is the ideal gas constant. n is the moles of gas. R = 0.08206 atm·L/mol·K  𝑛𝑅𝑇 𝑛𝑅𝑇 𝑃= 𝑉= 𝑉 𝑃 PV = nRT 𝑃𝑉 𝑃𝑉 𝑛= 𝑇= 𝑅𝑇 𝑛𝑅 P is the pressure in atm. T is the temperature in K. V is the volume in L. R is the ideal gas constant. n is the moles of gas. R = 0.08206 atm·L/mol·K  Condition #1 Condition #2 P1V1 = n1RT1 P2V2 = n2RT2 P1V1 P2V2 R= R= n1T1 n2T2 P1 V1 P2 V2 = n1 T1 n2 T2 Amonton / Gay-Lussac Charles Boyle Avogadro constant V and n constant P and n constant T and n constant T and P P1 P2 V1 V2 V1 V2 = = P1V1=P2V2 = T1 T2 T1 T2 n1 n If the volume of a confined gas is quadrupled while its temperature remains constant, what change will be observed? A. The pressure of the gas will decrease by ¼ its original value. B. The pressure of the gas will quadruple. C. The density of the gas will decrease to ½ its original value. Boyle constant T and n P1V1= P2V2 k P1V1 = P2(4V1) V= P P1V1=P2V2 Pressure will decrease by 1/4 A balloon is blown up in the morning (23°C) to a volume of 1.50 liter. If this balloon is left in a hot car with the windows left up and the car warms up to 35°C, what will be the final volume of the balloon? A. 608 L V1 V2 B. 1.44 L = T1 T2 C. 0.112 L D. 1.56 L 1.50 L V2 = 296 K 308 K V2 = 1.56 L A sample of gas at 15°C and 1 atm has a volume of 2.58 L. What will the pressure be at 58°C with no change in volume? A. 1.15 atm P1 P2 = B. 3.87 atm T1 T2 C. 2.20 atm 1 atm P2 D. 0.98 atm = 288 K 331 K P2 = 1.15 atm What is the volume occupied by 0.897 mol of a gas at 27°C and 1.45 atm? A. 39.8 L B. 15.2 L PV = nRT C. 32 L nRT V= D. 4.8 x 103 L P (0.897 mol)(0.08206 atm ∙ LΤmol ∙ K)(27 + 273 K) V= (1.45 atm) V = 15.2 L Solid thorium(IV) fluoride (ThF4, 308 g/mol) has a boiling point of 1680°C. What is the mass of a sample of gaseous thorium(IV) fluoride at its boiling point under a pressure of 2.5 atm in a 1.7 L container? A. 8.16 g B. 5.14 g PV PV = nRT and n= RT C. 10.5 g D. 7.32 g (2.5 atm)(1.7 L) n= = 0.02652 mol (0.08206 atm ∙ LΤmol ∙ K)(1953 K) 308 g 0.02652 mol × = 8.16 g 1 mol At constant temperature, 14.0 L of oxygen at 0.882 atm is compressed to 1.75 L. What is the final pressure of O2? A. 0.111 atm P1 V1 = P2 V2 B. 0.142 atm C. 7.06 atm P1 V1 P2 = D. 21.6 atm V2 E. 27.8 atm (0.882 atm)(14.0 L) P2 = = 7.06 atm 1.75 L If 3.67 g CO2(g) is introduced into an evacuated 2.50 L flask at 65 °C, what is the pressure inside the flask? A. 0.178 atm 1 mol CO2 3.67 g CO2 × = 0.0834 mol B. 0.445 atm 44.01 g C. 0.926 atm PV = nRT D. 40.7 atm nRT E. 496 atm P= V (0.0834 mol)(0.08206 L ∙ atmൗmol ∙ K)(65 + 273.15) P= = 0.926atm 2.50 L Which of the following is correct? A. 1.7 atm = 2.3 x 105 Pa 101,325 Pa 1.7 atm × = 1.7 × 105 Pa 1 atm B. 1292 mmHg = 4.1 atm 1 torr 1 atm 1292 mmHg × × = 1.7 atm 1 mmHg 760 torr C. 187.1 torr = 0.25 atm 1 atm 187.1 torr × = 0.25 atm 760 torr