Chapter 2 Gases COURSE NAME: CHEMISTRY 101 COURSE CODE: 402101-4

Elements that exist as gases at 250C and 1 atmosphere

Physical Characteristics of Gases Gases assume the volume and shape of their containers. Gases are the most compressible state of matter. Gases will mix evenly and completely when confined to the same container. Gases have much lower densities than liquids and solids. NO2 gas 2

(force = mass x acceleration) Area Pressure = (force = mass x acceleration) Units of Pressure 1 pascal (Pa) = 1 N/m2 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa 3

Manometers Used to Measure Gas Pressures closed-tube open-tube 4

5 Boyle’s Law P a 1/V Constant temperature P x V = constant Constant amount of gas P x V = constant P1 x V1 = P2 x V2 5

6 P x V = constant P1 x V1 = P2 x V2 P1 = 726 mmHg P2 = ? V1 = 946 mL A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL? P x V = constant P1 x V1 = P2 x V2 P1 = 726 mmHg P2 = ? V1 = 946 mL V2 = 154 mL P2 = P1 x V1 V2 726 mmHg x 946 mL 154 mL = = 4460 mmHg 6

Variation in Gas Volume with Temperature at Constant Pressure As T increases V increases 7

Variation of Gas Volume with Temperature at Constant Pressure Charles’ Law V a T Temperature must be in Kelvin V = constant x T T (K) = t (0C) + 273.15 V1/T1 = V2 /T2 8

A sample of carbon monoxide gas occupies 3. 20 L at 125 0C A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V1 /T1 = V2 /T2 V1 = 3.20 L V2 = 1.54 L T1 = 398.15 K T2 = ? T1 = 125 (0C) + 273.15 (K) = 398.15 K V2 x T1 V1 1.54 L x 398.15 K 3.20 L = T2 = = 192 K 9

Avogadro’s Law V a number of moles (n) V = constant x n Constant temperature Constant pressure V = constant x n V1 / n1 = V2 / n2 10

Real Gas Equation 1 Boyle’s law: P a (at constant n and T) V Charles’ law: V a T (at constant n and P) Avogadro’s law: V a n (at constant P and T) V a nT P V = constant x = R nT P R is the gas constant PV = nRT 11

PV = nRT PV (1 atm)(22.414L) R = = nT (1 mol)(273.15 K) The conditions 0 0C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. PV = nRT R = PV nT = (1 atm)(22.414L) (1 mol)(273.15 K) R = 0.082057 L • atm / (mol • K) 12

PV = nRT nRT V = P 1.37 mol x 0.0821 x 273.15 K V = 1 atm V = 30.7 L What is the volume (in liters) occupied by 49.8 g of HCl at STP? T = 0 0C = 273.15 K P = 1 atm PV = nRT n = 49.8 g x 1 mol HCl 36.45 g HCl = 1.37 mol V = nRT P V = 1 atm 1.37 mol x 0.0821 x 273.15 K L•atm mol•K V = 30.7 L 13

d is the density of the gas in g/L Density (d) Calculations m is the mass of the gas in g d = m V = PM RT M is the molar mass of the gas Molar Mass (M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L 14

dRT P M = d = m V = = 2.21 1 atm x 0.0821 x 300.15 K M = M = 15 A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0 0C. What is the molar mass of the gas? dRT P M = d = m V 4.65 g 2.10 L = = 2.21 g L 2.21 g L 1 atm x 0.0821 x 300.15 K L•atm mol•K M = M = 54.5 g/mol 15

Dalton’s Law of Partial Pressures V and T are constant P1 P2 Ptotal = P1 + P2 16

PA = nART V PB = nBRT V XA = nA nA + nB XB = nB nA + nB PT = PA + PB Consider a case in which two gases, A and B, are in a container of volume V. PA = nART V nA is the number of moles of A PB = nBRT V nB is the number of moles of B XA = nA nA + nB XB = nB nA + nB PT = PA + PB PA = XA PT PB = XB PT Pi = Xi PT mole fraction (Xi ) = ni nT 17

Pi = Xi PT PT = 1.37 atm 0.116 8.24 + 0.421 + 0.116 Xpropane = A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)? Pi = Xi PT PT = 1.37 atm 0.116 8.24 + 0.421 + 0.116 Xpropane = = 0.0132 Ppropane = 0.0132 x 1.37 atm = 0.0181 atm 18

Kinetic Molecular Theory of Gases A gas is composed of molecules that are separated from each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic. Gas molecules exert neither attractive nor repulsive forces on one another. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energy KE = ½ mu2 19

Kinetic theory of gases and … Compressibility of Gases Boyle’s Law P a collision rate with wall Collision rate a number density Number density a 1/V P a 1/V Gay-Lussac’s Law Collision rate a average kinetic energy of gas molecules Average kinetic energy a T P a T 20

 M2 M1 NH4Cl NH3 17 g/mol HCl 36 g/mol 21 Gas diffusion is the gradual mixing of molecules of one gas with molecules of another by nature of their kinetic properties. r1 r2 M2 M1  = molecular path NH4Cl NH3 17 g/mol HCl 36 g/mol 21

 ( ) M2 M1 22 = r1 r2 t2 t1 M2 = r1 r2 2 x M1 r1 = 3.3 x r2 Gas effusion is the is the process by which gas under pressure escapes from one compartment of a container to another by passing through a small opening. = r1 r2 t2 t1 M2 M1  Nickel forms a gaseous compound of the formula Ni(CO)x What is the value of x given that under the same conditions methane (CH4) effuses 3.3 times faster than the compound? M2 = r1 r2 ( ) 2 x M1 r1 = 3.3 x r2 = (3.3)2 x 16 = 174.2 M1 = 16 g/mol 58.7 + x • 28 = 174.2 x = 4.1 ~ 4 22

( ) } } Van der Waals equation nonideal gas an2 P + (V – nb) = nRT V2 corrected pressure } corrected volume 23

24 Question 1 Question 3 Question 2 Question 4 A sample of gas occupies 2.78 x 103 mL at 25oC and 760 mm Hg. What volume will the gas sample occupy at the same temperature and 475 mm Hg? A) 0.130 L B) 1.04 L C) 1.74 L D) 4.45 L E) None of the above Question 2 A steel tank contains carbon dioxide at a pressure of 13.0 atm when the temperature is 34oC. What will be the internal gas pressure when the tank and its contents are heated to 100oC. A) 38.2 atm B) 9.40 atm C) 10.7 atm D) 15.8 atm Question 3 Calculate the density of nitrogen gas, in grams per liter, at STP. A) 0.625 g/L B) 0.800 g/L C) 1.25 g/L D) 2.50 g/L E) None of the above Question 4 A gas evolved during the fermentation of alcohol had a volume of 19.4 L at 17oC and 746 mm Hg. How many moles of gas were collected? A) 1.25 mol B) 0.800 mol C) 10.5 mol D) 13.6 mol E) 608 mol 24

25 Question 5 Question 6 Question 7 Question 8 How many grams of carbon dioxide are contained in 550 mL of this gas at STP? A) 0.0245 g B) 0.0280 g C) 1080 g D) 0.560 g E) 1.1 g Question 6 A 1.325 g sample of an unknown vapor occupies 368 mL at 114oC and 946 mm Hg. The empirical formula of the compound is NO2. What is the molecular formula of the compound? A) NO2 B) N4O8 C) N3O6 D) N2O4 E) N5O10 Question 7 An organic compound was analyzed and found to contain 55.8% C, 7.03% H, and 37.2% O. A 1.500 g sample of the compound was vaporized and found to occupy 530 cm3 at 100oC and 740 torr. Which of the following is the correct molecular formula of the compound? A) C2H3O B) C6H4O2 C) C3H2O D) C4H6O2 E) C2H3O2 Question 8 What volume of chlorine gas at 646 torr and 32oC would be produced by the reaction of 14.75 g of MnO2 according to the following chemical equation? MnO2(s) + 4 HCl(aq) ----> MnCl2(aq) + Cl2(g) + 2 H2O(l) A) 5.00 L B) 0.170 L C) 2.33 L D) 0.200 L E) None of the above 25

26 Question 9 Question 10 Question 11 Question 12 Question 13 A mixture of neon, argon, and xenon had a total pressure of 1560 mm Hg at 298 K. The mixture was found to contain 1.50 mol Ne, 2.65 mol Ar, and 1.75 mol Xe. What is the partial pressure of Xe? A) 701 mm Hg B) 658 mm Hg C) 396 mm Hg D) 463 mm Hg E) None of the above Question 10 Deviations from the ideal gas law are smaller at: A) low temperatures and high pressures B) low temperatures and low pressures C) high temperatures and high pressures D) high temperatures and low pressures Question 11 Which of the following correctly identifies Boyle's law? A) PV=k1 B) V=k2T Question 12 The magnitude of one Kelvin, one Celsius degree, and one degree on the absolute temperature scale is the same. A) True B) False Question 13 The Kelvin temperature scale is useful when comparing: A) various gas samples at different densities B) volume of a gas sample with temperature at constant pressure C) pressure of gas samples at different volumes and constant temperature D) various liquids at constant pressure 26

Question 14 Which of the following is not an assumption of the kinetic theory of gases? A) Elasticity refers to the molecules random interactions resulting in no net energy change. B) Gas molecules are viewed as points due to large distances between them. C) Gas molecules can attract other gas molecules. D) Temperature in Kelvin and average kinetic energy are proportional. Question 15 A sample of CO2(g) has a volume of 2L at pressure P and temperature T. If the pressure becomes triple the original value, at the same absolute temperature, the volume of CO2 will be L c. L b. 6 L d. 2 L 27