Examples and Problems only

**Example #1:** 8.278 x 10¯^{4} mol of an unidentified gaseous substance effuses through a tiny hole in 86.9 s Under identical conditions, 1.740 x 10¯^{4} mol of argon gas takes 81.3 s to effuse.

a) What is the molar mass of the unidentified substance (in g/mol)?

b) What is the molecular formula of the substance?

c) Under identical conditions, how many moles of ethene (C_{2}H_{4}) gas would effuse in 91.0 s?

**Example #2:** It takes 354 seconds for 1.00 mL of Xe to effuse through a small hole. Under the same conditions, how long will it take for 1.00 mL of nitrogen to effuse?

**Example #3:** What is the rate of effusion for a gas that has a molar mass twice that of a gas that effuses at a rate of 4.2 mol/min?

**Example #4:** It takes 110. seconds for a sample of carbon dioxide to effuse through a porous plug and 275 seconds for the same volume of an unknown gas to effuse under the same conditions. What is the molar mass of the unknown gas (in g/mol)?

**Example #5:** What is the molar mass of a compound that takes 2.65 times as long to effuse through a porous plug as it did for the same amount of XeF_{2} at the same temperature and pressure?

**Example #6:** If a gas effuses 4.25 times faster than iodine gas (I_{2}), what is its molar mass?

A. 59.7 g/mol

B. 163 g/mol

C. 123 g/mol

D. 158 g/mol

**Example #7:** Calculate the density of a gas at STP, if a given volume of the gas effuses through an apparatus in 6.60 min and the same volume of nitrogen, at the same temperature and
pressure, effuses through this apparatus in 8.50 minutes.

**Example #8:** If 0.0949 moles of NH_{3} effuses in 881 seconds, how many seconds would it take for the same number of moles of B_{2}H_{6} to effuse?

**Example #9:** The rate of diffusion of an unknown gas was determined to be 2.92 times greater than that of NH_{3}. What is the approximate molar mass of the unknown gas?

**Example #10:** If a molecule of C_{2}H_{6} diffuses a distance of 0.978 m from a point source, calculate the distance (m) that a molecule of CH_{4} would diffuse under the same conditions for the same period of time.

**Example #11:** A sample of oxygen gas (O_{2}) effuses into a vacuum 1 times faster than an unknown gas. O_{2} has a molecular weight of about 32.00 g mol¯^{1}. What is the molecular weight of this unknown gas (in g mol¯^{1})?

**Example #12:** Argon effuses from a container at a rate of 0.0260 L/s. How long will it take for 3.00 L of I_{2} to effuse from the same container under identical conditions?

**Example #13:** Calculate the density of a gas at STP, if a given volume of the gas effuses through an apparatus in 6.60 min and the same volume of oxygen at the same temperature and pressure, effuses through this apparatus in 8.50 minutes.

**Bonus Example #1:** The rate of effusion of an unknown gas at 480 K is 1.6 times the rate of effusion of SO_{2} gas at 300 K. Calculate the molecular weight of the unknown gas.

**Bonus Example #2:** Heavy water, D_{2}O (molar mass = 20.0276 g mol¯^{1}), can be separated from ordinary water, H_{2}O (molar mass = 18.0152 g mol¯^{1}), as a result of the difference in the relative rates of diffusion of the molecules in the gas phase. Calculate the relative rates of diffusion for H_{2}O when compared to D_{2}O.

**Problem #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?

**Problem #2:** What is the molecular weight of a gas which diffuses 1/50 as fast as hydrogen?

**Problem #3:** Two porous containers are filled with hydrogen and neon respectively. Under identical conditions, 2/3 of the hydrogen escapes in 6 hours. How long will it take for half the neon to escape?

**Problem #4:** If the density of hydrogen is 0.090 g/L and its rate of effusion is 5.93 times that of chlorine, what is the density of chlorine?

**Problem #5:** How much faster does hydrogen escape through a porous container than sulfur dioxide?

**Problem #6:** Compare the rate of diffusion of carbon dioxide (CO_{2}) & ozone (O_{3}) at the same temperature.

**Problem #7:** 2.278 x 10¯^{4} mol of an unidentified gaseous substance effuses through a tiny hole in 95.70 s. Under identical conditions, 1.738 x 10¯^{4} mol of argon gas takes 81.60 s to effuse. What is the molar mass of the unidentified substance?

**Problem #8:** A compound composed of carbon, hydrogen, and chlorine diffuses through a pinhole 0.411 times as fast as neon. Select the correct molecular formula for the compound:

(a) CHCl_{3}

(b) CH_{2}Cl_{2}

(c) C_{2}H_{2}Cl_{2}

(d) C_{2}H_{3}Cl

**Problem #9:** Which pair of gases contains one which effuses at twice the rate of the other in the pair?

(a) He and Ne

(b) Ne and CO_{2}

(c) He and CH_{4}

(d) CO_{2}and HCl

(e) CH_{4}and HCl

**Problem #10:** If a molecule of CH_{4} diffuses a distance of 0.530 m from a point source, calculate the distance (in meters) that a molecule of N_{2} would diffuse under the same conditions for the same period of time.

**Bonus Problem #1:** Calculate the density of a gas at STP, if a given volume of the gas effuses through an apparatus in 6.60 min and the same volume of nitrogen at the same temperature and pressure, effuses through this apparatus in 8.50 minutes.

**Bonus Problem #2:** At 25.0 °C and 380.0 mmHg, the density of sulfur dioxide is 1.31 g/L. The rate of effusion of sulfur dioxide through an orifice is 4.48 mL/s. (a) What is the density of a sample of gas that effuses through an identical orifice at the rate of 6.78 mL/s under the same conditions? (b) What is the molar mass of the gas?

**Problem #11:** What is the rate of effusion for a gas that has a molar mass twice that of a gas that effuses at a rate of 3.62 mol/min?

**Problem #12:** Calculate the rate of effusion of NO_{2} compared to SO_{2} at the same temperature and pressure.

**Problem #13:** Assume you have a sample of hydrogen gas containing H_{2}, HD, and D_{2} that you want to separate into pure components. What are the various ratios of relative rates of effusion?

**Problem #14:** A 3.00 L sample of helium was placed in container fitted with a porous membrane. Half of the helium effused through the membrane in 25 hours. A 3.00 L sample of oxygen was placed in an identical container. How many hours will it take for half of the oxygen to effuse though the membrane?

**Problem #15:** At a certain temperature, hydrogen molecules move at an average velocity of 1.84 x 10^{3} m/s. Estimate the molar mass of a gas whose molecules have an average velocity of 311 m/s.

**Problem #16:** An unknown gas effuses 1.66 times more rapidly than CO_{2}. What is the molar mass of the unknown gas.

**Problem #17:** A sample of hydrogen gas effuse through a porous container 8.91 times faster than an unknown gas. Estimate the molar mass of the unknown gas.

**Problem #18:** N_{2} is contaminated with a noble gas.The contaminant effuses at 1.87x N_{2}. What is the noble gas?

**Problem #19:** In an effusion experiment, it was determined that nitrogen gas, N_{2}, effused at a rate 1.812 times faster than an unknown gas. What is the molar mass of the unknown gas?

**Problem #20:** Why are the rates of diffusion of nitrogen gas and carbon monoxide almost identical at the same temperature?

**Problem #21:** In running a diffusion experiment, ammonia is found to diffuse 30.0 cm during the same amount of time hydrogen chloride moves 20.0 cm. Calculate the percentage deviation from Graham's Law.

**Problem #22:** A sample of Br_{2}(g) take 10.0 min to effuse through a membrane. How long would it take the same number of moles of Ar(g) to effuse through the same membrane?

**Problem #23:** At a particular pressure and temperature, it takes just 8.256 min for a 4.893 L sample of Ne to effuse through a porous membrane. How long would it take for the same volume of I_{2} to effuse under the same conditions?

**Problem #24a:** How much faster does U^{235}F_{6} effuse than U^{238}F_{6}?

**Problem #24b:** Calculate the ratio of effusion rates for U^{238}F_{6} and U^{235}F_{6}. Express your answer using five significant figures and as the following ratio:

rate U^{238}F_{6}/ rate U^{235}F_{6}

**Problem #25:** O_{3} effuses 0.8165 times as fast as O_{2}. What % of the molecules effusing first would be O_{2}?

**Bonus Problem #1:** HCl and NH_{3} diffuse through a tube and a white disc of NH_{4}Cl is formed. Where in the tube?

**Bonus Problem #2:** One way of separating oxygen isotopes is by gaseous diffusion of carbon monoxide. The gaseous diffusion process behaves like an effusion process. Calculate the relative rates of effusion of:

^{12}C^{16}O^{12}C^{17}O^{12}C^{18}O