Chemistry: It s a gas Part IV Molar mass of a gas Density of a gas Dalton s Law: high altitudes and scuba diving Kinetic Molecular Theory: fast gases are hot! I have a chemistry test on Friday, there is nothing down there that will make me panic. Warrior Chemistry Club Meeting
Molar Mass of a Gas Warrior Chemistry Club Meeting An experiment shows that a 0.495 g sample of an unknown gas occupies 127 ml at 98 C and 754 torr pressure. Calculate the molar mass of the gas (hint: M = mass/number of moles). V = 127 ml = 0.127 L P = 754 torr = 0.9921 atm T = 98 C = 371 K m = 0.495 g R = 0.0821 (Latm/moleK) M =? PV = nrt PV = n RT 0.9921 atm x 0.127 L = n 0.0821 (Latm/moleK)371K n = 0.00414 moles M = 0.495 g/0.00414 moles M = 120.38 g/mole
Gas Density Density = grams/l Find moles, multiply by molar mass to get grams What is the density of oxygen gas at 25 C and 1 atm? Hint: Pick any volume, 1.0 L is the easiest! n = PV = 1 atm x 1.0L = 0.0409 moles RT 0.0821(Latm/moleK) x 298K 0.0409 moles x 32 g/mole = 1.31 g 1.0 L Warrior Chemistry Club Meeting
Warrior Chemistry Club Meeting What is the density of carbon monoxide gas at 25 C and 1 atm? Assume the volume is 1.0 L. n = 1atm x 1.0 L = 0.0409 moles 0.0821(Latm/moleK)298K 0.0409 moles x 28g/ mole CO = 1.145 g 1.145 g/1.0 L = 1.145 g/l
Dalton s Law and Mole fractions Warrior Chemistry Club Meeting Χ A = mole fraction A = moles of gas A/ total moles of gas Air: χ O2 = 0.2 χ N2 0.8 p O2 = χ O2 P T P T = p O2 + p N2 If a scuba diver is at a depth where the pressure is 5 atm, what should the mole fraction of oxygen be to have a partial pressure of 0.21 atm? 0.21 atm = X 5.0 atm X = 0.042
The partial pressure of a gas is A. the pressure the gas exerts when pure. B. the total pressure of a mixture of gases. C. the pressure due to a gas in a mixture. D. the same as the vapor pressure of the gas. E. the pressure exerted by one molecule of the gas. Warrior Chemistry Club Meeting
p O2 = χ O2 P T What is the partial pressure of oxygen gas if its mole fraction (X) is 0.210 and the atmospheric pressure is 190 mm Hg? p O2 = 0.210(190mmHg/760 mmhg/atm) A. 0.84 atm B. 39.9 atm C. 0.0525 atm D. 19.04 atm
In a mixture of gases, the gas with the largest mole fraction (X) will have the: A. largest number of molecules present. B. highest kinetic energy. C. smallest number of molecules present D. smallest molar mass. E. largest molar mass. Warrior Chemistry Club Meeting
Kinetic Molecular Theory of Gases Assumes that gas molecules: 1. Have tiny volumes compared with the collective volume they occupy 2. Move constantly and randomly 3. Have average kinetic energy that is proportional to absolute temperature (absolute = temp in Kelvin, no motion at OK, outer (empty) space = 2.6K, OK has not been obtained.) 4. Engage in elastic collisions with walls of container and other gas molecules 5. Act independently of other gas molecules
Average Kinetic Energy Average kinetic energy: KE avg = ½m(u rms ) 2 u rms = the root-mean-square speed of the molecules R = 8.314 J/molK T = Kelvin J= kgm 2 /sec 2 M = kg/mole 10
Diffusion and Effusion Graham s Law of Effusion or Diffusion: The effusion/diffusion rate of any gas is inversely proportional to the square root of its molar mass. Effusion The process by which a gas escapes from a container through a tiny hole into a region of lower pressure Diffusion The spread of one substance through another 11 Warrior Chemistry Club Meeting
Diffusion and Effusion (cont. 1) Graham s Law derives a diffusion or effusion rate of two gases: 12
List the following gases, which are at the same temperature, in the order of increasing rates of diffusion: O 2, He, NO, CO 2 A. O 2 < He < NO < CO 2 B. He < O 2 < CO 2 < NO C. He < NO < O 2 < CO 2 D. CO 2 < O 2 < NO< He E. None of these What is the molar mass of each gas? He = 4 g/mole NO = 30 g/mole O 2 = 32 g/mole CO 2 = 44 g/mole What is the relationship between molar mass and root mean speed of a gas?
Calculate the molar mass of a gas if equal volumes of oxygen gas and an unknown gas take 3.25 min and 8.41 min, respectively, to effuse through a small hole at constant pressure and temperature. Oxygen(x): M = 32 g/mole Rate = 1/3.25 min (rate = 1/time) Other gas(y): M = unknown Rate = 1/8.41min 1/3.25 = 8.41 = M 1/8.41 3.25 0.032 kg/mole Square both sides: 2.59 2 = M 0.032 0.032 x 6.69 =.214 kg/mole = 214 g/mole
What is unimportant when using the ideal gas law? A. The chemical identity of the gas sample. B. The temperature of the gas sample. C. The amount of gas. D. The pressure of the gas sample. E. The volume of the container holding the gas sample. Warrior Chemistry Club Meeting
Which of the following reactions will result in an increase in total pressure? A. 2H 2 (g) + O 2 (g) à 2H 2 O(l) B. 2HI(g) à H 2 (g) + I 2 (g) C. CH 4 (g) + 2O 2 (g) àco 2 (g) + 2H 2 O(g) D. 2N 2 O(g) à2n 2 (g) + O 2 (g) E. none of these More gas molecules = more pressure
When is the next Warrior Chemistry Club meeting with tutoring? A. Tuesday at 5 pm in S139 B. Thursday at 5 pm in S139 C. Friday at 9 am in S139 D. Wednesday at 5 pm in S139 E. None of these