**Graham's Law** states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass.

**Effusion** involves a gas escaping a container through an opening.

Concept #1: Understanding Graham's Law of Effusion.

When comparing the **rate or speed of two gases** then we must use **Graham’s Law of Effusion**.

Example #1: Calculate the ratio of the effusion rates of helium and methane (CH_{4}).

The gas named first will represent gas 1 and the second gas will represent gas 2. Once that is established we simply use Graham’s Law of Effusion.

Example #2: Rank the following in order of increasing rate of effusion:

O_{2} AlF_{5} CO_{2} Xe

Calculate the ratio of effusion rates for Ar and Kr.

A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the gas.

A sample of N2O effuses from a container in 42 seconds. How long would it take the same amount of gaseous I2 to effuse from the same container under identical conditions?

The graph shows the distribution of molecular velocities for two different molecules (A and B) at the same temperature. Which molecule has the higher molar mass? Which molecule would have the higher rate of effusion?

At a given temperature and pressure, a sample of Gas A is observed to diffuse twice as fast as a sample of a different gas, B. Based on this:
A. The molar mass of A is one fourth that of B
B. The molar mass of A is one half that of B
C. The molar mass of A is 0.707 times that of B
D. The molar mass of A is 1.414 times that of B
E. The molar mass of A is four times that of B

How many times faster will He gas pass through a pin hole than SO2 gas?
a) 4
b) 1/4
c) 16
d) 1/16
e) none of the given answers

Using Graham's Law of effusion, calculate the ratio of the effusion rates of H 2 to CO through a pinhole.

An unknown gas Q diffuses at a RATE 1.65 times faster than that of propane, C 3H8. Which of these are most likely to be Q?
a. He
b. Ne
c. H2O
d. CH4
e. O2

The mass particle is 10% larger than that of particle B. If particle B travels 100 m during effusion, how far would particle A travel during effusion?
a) 90 m
b) 95 m
c) 100 m
d) 105 m
e) 110 m

Exactly 10 mL, of gas A (MM = 15.0 g/mol) effuse through an opening in 2.0 sec. Exactly 10 mL of gas B effuse through the same opening in 8.0 sec. What is the molar mass of gas B?
a) 60 g/mol
b) 480 g/mol
c) 240 g/mol
d) 120 g/mol

A sample of N2 gas is contaminated with a gas (A) of unknown molar mass. The partial pressure of each gas is known to be 200 Torr at 25°C. The gases are allowed to effuse through a pinhole, and it is found that gas A escapes at three times the rate of N2. The molar mass of gas A is:
a) 3.11
b) 252
c) 84.0
d) 9.33
e) none of these

Second-hand smoke consist of many molecules including nicotine. How much faster or slower does the nicotine diffuse, compared to carbon dioxide? (MW nicotine = 160g/mol)
1. About half as fast
2. As gases, the two molecules diffuse at the same rate
3. About 4 times faster
4. About a fourth as fast
5. About twice as fast

The gas for which instance will effuse faster?

Oxygen gas effuses at a rate that is 1.49 times that of an unknown gas (at the same temperature). What is the identity of the unknown gas?
A) Ar
B) HBr
C) SO2
D) Cl2
E) He

The mass of particle A is 10% larger than that of particle B. If particle B travels 100m during effusion, how far would particle A travel during effusion?
a. 90 m
b. 95 m
c. 100 m
d. 105 m
e. 110 m

At a particular temperature and pressure, it takes 4.55 min for a 1.5 L sample of He to effuse through a porous membrane. How long would it take for a 1.5 L of F2 to effuse under the same conditions?
a. 18 min
b. 14 min
c. 10 min
d. 5 min
e. 1.5 min

A sample of helium effuses through a porous container 7.70 times faster than does unknown gas X. What is the molar mass of the unknown gas?
1. 129.96
2. 153.76
3. 169.0
4. 112.36
5. 190.44
6. 237.16
7. 275.56
8. 392.04
9. 201.64
10. 368.64

At any given temperature, how much more quickly will He effuse than Xe?
1. 5.7 times more quickly
2. .03 times more quickly
3. 8.1 times more quickly
4. They will diffuse at the same rate
5. 0.12 times more quickly
6. 32.8 times more quickly

Carbon dioxide effuses through a pinhole at a rate of 0.232 ml/min at 25.0 °C. Another gas effuses at a rate of 0.363 ml/min. What is the molar mass of the gas?

NO2 gas effuses ________times faster than Cl 2 gas.
a. 1.54
b. 0.649
c. 1.24
d. 0.770
e. 2.37

Consider the chemical reaction: 2 SO2 (g) → SO(g) + SO3 (g)
Determine if the sentence below is true or false
Between the two products, SO3 would have the highest rate of effusion.

The rate of effusion of oxygen to an unknown gas is 0.935. What is the other gas?
A) Ar
B) F2
C) Ne
D) N2

Consider a 1.0-L sample of helium gas and a 1.0-L sample of argon gas, both at room temperature and atmospheric pressure.
d. Which gas sample would have the faster rate of effusion?

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon.
d. If a small hole were opened in the flask, which gas would effuse more quickly?

A sample of N2 O effuses from a container in 47 seconds.How long would it take the same amount of gaseous I2 to effuse from the same container under identical conditions?

An illustration of Grahams law of effusion.Because pressure and temperature are constant in this figure but volume changes, which other quantity in the ideal-gas equation must also change?

Explain the difference between diffusion and effusion.

How is the effusion rate of a gas related to its molar mass?

Consider a 1.0-L sample of helium gas and a 1.0-L sample of argon gas, both at room temperature and atmospheric pressure.Which gas sample would have the fastest rate of effusion?

Rank from the highest to lowest effusion rate. To rank items as equivalent, overlap them.
H2, Ar, Ne, C4H8, CO

Given the gases Ne, He, H2, Kr, put them in order of their INCREASING rate of effusion.
1. Kr < Ne < He < H 2
2. H2 < He < Ne < Kr
3. He < H2 < Kr < Ne
4. Ne < Kr < H 2 < He

Which gas is the predominant nitrogen-containing pollutant in the atmosphere?a) N2b) NH3c) NO2d) N2O5

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 12C16O, 12C17O, and 12C18O. Name some advantages and disadvantages of separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide.

The rate of effusion of two different gases is known asA) Avogadro's Law B) Graham's Law C) Charles's Law D) Boyle's LawE) Dalton's Law

Calculate the ratio of effusion rates of Cl2 to F2.

Calculate the ratio of effusion rates for Ar and Kr.

A mixture of gaseous disulfur difluoride, dinitrogen tetrafluoride, and sulfur tetrafluoride is placed in an effusion apparatus.(c) If gas X is added, and it effuses at 0.935 times the rate of sulfur tetrafluoride, find the molar mass of X.

A compound contains only C, H, and N. It is 58.51% C and 7.37% H by mass. Helium effuses through a porous frit 3.20 times as fast as the compound does. Determine the empirical and molecular formulas of this compound.

Naturally found uranium consists of 99.274%, 238U, 0.720% 235U, and 0.006% 233U (by mass). As we have seen, 235U is the isotope that can undergo a nuclear chain reaction. Most of the 235U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF6(g).(a) What is the mass of UF6 in a 30.0-L vessel of UF6 at a pressure of 695 torr at 350 K?(b) What is the mass of 235U in the sample described in part a? The atomic mass of uranium-235 is 235.044 u.(c) Now suppose that the UF6 is diffused through a porous barrier and that the change in the ratio of 238U and 235U in the diffused gas can be described by the equation large{frac{{{{ r}_{1}}}}{{{{ r}_{2}}}}=frac{{{{ u}_{{
m{{
m rms1}}}}}}}{{{{ u}_{{
m{{
m rms2}}}}}}}=sqrt {frac{{{ 3RT}/{{M}_{,1}}}}{{{3RT}/{{ M}_{,2}}}}}=sqrt {frac{{{{ M}_{,2}}}}{{{{ M}_{,1}}}}}}. What is the mass of 235U in a sample of the diffused gas analogous to that in part a?

Freon-12 is used as a refrigerant in central home air conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass = 137.4 g/mol) is 1.07:1. The formula of Freon-12 is one of the following: CF4, CF3Cl, CF2Cl2, CFCl3, or CCl4. Which formula is correct for Freon-12?

The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane (CH4) gas is 47.8 mL/min. What is the molar mass of the unknown gas?

In a certain experiment, magnesium boride (Mg 3B2) reacted with acid to form a mixture of four boron hydrides (BxHy), three as liquids (labeled I, II, and III) and one as a gas (IV).(c) Sample IV was found to be 78.14% boron. The rate of effusion for this gas was compared to that of sulfur dioxide; under identical conditions, 350.0 mL of sample IV effused in 12.00 min and 250.0 mL of sulfur dioxide effused in 13.04 min. What is the molecular formula of sample IV?

From the relative rates of effusion of 235UF6 and 238UF6, find the number of steps needed to produce a sample of the enriched fuel used in many nuclear reactors, which is 3.0 mole% 235U. The natural abundance of 235U is 0.72%.

A sample of Xe takes 75 seconds to effuse out of a container. An unknown gas takes 37 seconds to effuse out of the identical container under identical conditions.What is the most likely identity of the unknown gas?

A mixture of gaseous disulfur difluoride, dinitrogen tetrafluoride, and sulfur tetrafluoride is placed in an effusion apparatus.(b) Find the ratio of effusion rates of disulfur difluoride and dinitrogen tetrafluoride.

A balloon filled with helium gas is found to take 6 hours to deflate to 50% of its original volume. How long will it take for an identical balloon filled with the same volume of hydrogen gas (instead of helium) to decrease its volume by 50%?

Calculate the relative rate of diffusion of 1H2 (molar mass 2.0 g/mol) compared to that of 2H2 (molar mass 4.0 g/mol) and the relative rate of diffusion of O2 (molar mass 32 g/mol) compared to that of O3 (molar mass 48 g/mol).

Naturally found uranium consists of 99.274%, 238U, 0.720% 235U, and 0.006% 233U (by mass). As we have seen, 235U is the isotope that can undergo a nuclear chain reaction. Most of the 235U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF6(g).Naturally found uranium consists of 99.274%, 238U, 0.720% 235U, and 0.006% 233U (by mass). As we have seen, 235U is the isotope that can undergo a nuclear chain reaction. Most of the 235U used in the first atomic bomb was obtained by gaseous diffusion of uranium hexafluoride, UF6(g).(a) What is the mass of UF6 in a 30.0-L vessel of UF6 at a pressure of 695 torr at 350 K?(b) What is the mass of 235U in the sample described in part a? The atomic mass of uranium-235 is 235.044 u.(c) Now suppose that the UF6 is diffused through a porous barrier and that the change in the ratio of 238U and 235U in the diffused gas can be described by the equation . What is the mass of 235U in a sample of the diffused gas analogous to that in part a?(d) After one more cycle of gaseous diffusion, what is the percentage of 235UF6 in the sample? (In your calculations unrounded values from previous parts should be used.)

It took 4.5 minutes for 1.0 L helium to effuse through a porous barrier. How long will it take for 1.0 L Cl2 gas to effuse under identical conditions?

Calculate the ratio of effusion rates for Ar and Kr.

The following graph shows the distribution of molecular velocities for two different molecules (A and B) at the same temperature. Which molecule would have the higher rate of effusion?

We separate U-235 from U-238 by fluorinating a sample of uranium to form UF6 (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes.Calculate the ratio of effusion rates for 238 UF6 and 235 UF6. The atomic mass of U-235 is 235.054 amu and that of U-238 is 238.051 amu.

When two cotton plugs, one moistened with ammonia and the other with hydrochloric acid, are simultaneously inserted into opposite ends of a glass tube that is 87.0 cm long, a white ring of NH4Cl forms where gaseous NH3 and gaseous HCl first come into contact. NH3 (g) + HCl(g) ⟶ NH4Cl(s) At approximately what distance from the ammonia moistened plug does this occur? (Hint: Calculate the rates of diffusion for both NH3 and HCl, and find out how much faster NH3 diffuses than HCl.)

What is the ratio of effusion rates for the lightest gas, H 2, and the heaviest known gas, UF6?

What is the ratio of effusion rates for O 2 and Kr?

As discussed in the “Chemistry Put to Work” box in Section 10.8 in the textbook, enriched uranium can be produced by effusion of gaseous UF6 across a porous membrane. Suppose a process were developed to allow effusion of gaseous uranium atoms, U(g).Compare the ratio of diffusion rates for 235U and 238U to the ratio for UF6 given in the essay in the textbook.

Phosphorus trichloride is important in the manufacture of insecticides, fuel additives, and flame retardants. Phosphorus has only one naturally occurring isotope, 31P, whereas chlorine has two, 35Cl (75%) and 37Cl (25%). (c) What is the ratio of the effusion rates of the heaviest and the lightest PCl 3 molecules?

At a given pressure and temperature, it takes 4.85 min for a 1.5-L sample of He to effuse through a membrane. How long does it take for 1.5 L of F2 to effuse under the same conditions?

Explain why the numbers of molecules are not identical in the left- and right-hand bulbs shown in the center illustration of Figure 9.27.

Starting with the definition of rate of effusion and Graham’s finding relating rate and molar mass, show how to derive the Graham’s law equation, relating the relative rates of effusion for two gases to their molecular masses.

Which of the following gases diffuse more slowly than oxygen? F2, Ne, N2O, C2H2, NO, Cl2, H2S

Rank the three halogens (F2, Cl2, and Br2) with respect to their rate of effusion.

Show that the ratio of the rate of diffusion of Gas 1 to the rate of diffusion of Gas 2, is the same at 0 °C and 100 °C.

You may want to reference (Pages 416 - 419) Section 10.8 while completing this problem.Which of the following statements are true?(a) O2 will effuse faster than Cl2.(b) Effusion and diffusion are different names for the same process.(c) Perfume molecules travel to your nose by the process of effusion.(d) The higher the density of a gas, the shorter the mean free path.

Containers A, B, and C are attached by closed stopcocks of negligible volume.If each particle shown in the picture represents 106 particles, (a) How many blue particles and black particles are in B after the stopcocks are opened and the system reaches equilibrium?

Calculate the root-mean-square velocity and kinetic energy of CO, CO2, and SO3 at 286 K .Which gas has the greatest effusion rate?

A mixture of gaseous disulfur difluoride, dinitrogen tetrafluoride, and sulfur tetrafluoride is placed in an effusion apparatus.(a) Rank the gases in order of increasing effusion rate.

Find the ratio of effusion rates of hydrogen gas and krypton gas.

If 250 mL of methane, CH4, effuses through a small hole in 28 s, the time required for the same volume of helium to pass through the hole under the same conditions will be

The rate of effusion of oxygen to an unknown gas is 0.935. What is the other gas?

A thin glass tube 1 m long is filled with Ar gas at 1 atm, and the ends are stoppered with cotton plugs: HCl gas is introduced at one end of the tube, and simultaneously NH3 gas is introduced at the other end. When the two gases diffuse through the cotton plugs down the tube and meet, a white ring appears due to the formation of NH4Cl(s).At which location - a, b, or c - do you expect the ring to form?

The rate of effusion of SO2 gas through a porous barrier is observed to be 7.01 x 10-4 mol/h. Under the same conditions, the rate of effusion of CH4 gas would be __________ mol/h.

The rate of effusion of Xe gas through a porous barrier is to be 7.31 x 10-4 mol/h. Under the same conditions, the rate of effusion of O2 gas would be __________ mol/h.

Arsenic(III) sulfide sublimes readily, even below its melting point of 320 oC. The molecules of the vapor phase are found to effuse through a tiny hole at 0.28 times the rate of effusion of Ar atoms under the same conditions of temperature and pressure.What is the molecular formula of arsenic(III) sulfide in the gas phase?

White phosphorus melts and then vaporizes at high temperatures. The gas effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. How many atoms are in a molecule of gaseous white phosphorus?

A sample of neon effuses from a container in 77 seconds. The same amount of an unknown noble gas requires 157 seconds.Identify the second gas.

In a given diffusion apparatus, 15.0 mL of HBr gas diffuses in 1.0 min. In the same apparatus and under the same conditions, 20.3 mL of an unknown gas diffuses in 1.0 min. The unknown gas is a hydrocarbon.Find its molecular formula.

A gas of unknown identity diffuses at a rate of 83.3 mL/s in a diffusion apparatus in which carbon dioxide diffuses at the rate of 102 mL/s. Calculate the molecular mass of the unknown gas.

Aluminum chloride is easily vaporized above 180°C. The gas escapes through a pinhole 0.122 times as fast as helium at the same conditions of temperature and pressure in the same apparatus. What is the molecular formula of aluminum chloride gas?

Heavy water, D2O (molar mass = 20.03 g mol–1), can be separated from ordinary water, H2O (molar mass = 18.01), 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 of H2O and D2O.

A sample of an unknown gas effuses in 11.1 min. An equal volume of H 2 in the same apparatus under the same conditions effuses in 2.42 min. What is the molar mass of the unknown gas?

Two identical balloons are filled to the same volume, one with air and one with helium. The next day, the volume of the air-filled balloon has decreased by 5.1 % .By what percent has the volume of the helium-filled balloon decreased? (Assume that the air is four-fifths nitrogen and one-fifth oxygen, and that the temperature did not change.)

The rate of effusion of CH4 gas through a porous barrier is observed to be 5.48 x 10-4 mol/h. Under the same condition, the rate of effusion of Xe gas would be ____ mol/h.

The average molecular speed in a sample of O3 gas at a certain temperature is 386 m/s. The average molecular speed in a sample of Ar gas is temperature.

A sample of CH4 gas is observed to effuse through a porous barrier in 5.53 minutes. Under the same conditions, the same number of moles of an unknown gas requires 7.07 minutes to effuse through the same barrier. The molar mass of the unknown gas is g/mol.

How much faster do ammonia (NH 3) molecules effuse than carbon monoxide (CO) molecules?Enter the ratio of the rates of effusion. Express your answer numerically using three significant figures.

An organic compound containing only C, H, and N yields the following data.i. Complete combustion of 35.0 mg of the compound produced 33.5 mg CO2 and 41.1 mg H2O.ii. A 65.2-mg sample of the compound was analyzed for nitrogen by the Dumas method (see Exercise 129), giving 35.6 mL of dry N2 at 740. torr and 25°C.iii. The effusion rate of the compound as a gas was measured and found to be 24.6 mL/min. The effusion rate of argon gas, under identical conditions, is 26.4 mL/min. What is the molecular formula of the compound?

During the discussion of gaseous diffusion for enriching uranium, it was claimed that 235UF6 diffuses 0.4% faster than 238UF6. Show the calculation that supports this value. The molar mass of 235UF6 = 235.043930 + 6 × 18.998403 = 349.034348 g/mol, and the molar mass of 238UF6 = 238.050788 + 6 × 18.998403 = 352.041206 g/ mol.

Hydrogen has two naturally occurring isotopes, 1H and 2H. Chlorine also has two naturally occurring isotopes, 35Cl and 37Cl. Thus, hydrogen chloride gas consists of four distinct types of molecules: 1H35Cl, 1H37Cl, 2H35Cl, and 2H37Cl. Place these four molecules in order of decreasing rate of effusion.

A gas of unknown molecular mass was allowed to effuse through a small opening under constant-pressure conditions. It required 115 s for 1.0 L of the gas to effuse. Under identical experimental conditions it required 31 s for 1.0 L of O2 gas to effuse.Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; that is, rate and time are inversely proportional.)

As discussed in the “Chemistry Put to Work” box in Section 10.8 in the textbook, enriched uranium can be produced by effusion of gaseous UF6 across a porous membrane. Suppose a process were developed to allow effusion of gaseous uranium atoms, U(g).Calculate the ratio of effusion rates for 235U and 238U.

Consider two 1-L samples of gas, one H2 and one O2, both at 1 atm and 25°C. Compare the samples in terms of the characteristics listed. time for a given fraction of O2 molecules to effuse____time for a given fraction of H2 molecules to effuse a. is greater thanb. is less than c. is equal to d. is unrelated to e. None of these

The rate of effusion of SO2 gas through a porous barrier is observed to be 5.29 x 10-4 mol/h. Under the same conditions, the rate of effusion of NO2 gas would be mol/h.

1.560 x 10-4 mol of an unidentified gaseous substance effuses through a tiny hole in 98.8 s.Under identical conditions, 1.749 x 10-4 mol of argon gas takes 84.9 s to effuse. What is the molar mass of the unidentified substance (in g/mol)? The percentage C by mass in the above unidentified substance is 53.0%. It may also contain H and/or O, but no other element. What is the molecular formula of the substance? In typing this formula use the convention of C first, H second and O last. For example, C6H8O2 would be C6H802.) Under identical conditions, how many moles of acetylene (C2H2) gas would effuse in 86.5 s?

A sample of O3 gas is observed to effuse through a pourous barrier in 1.07 minutes. Under the same conditions, the same number of moles of an unknown gas requires 1.44 minutes to effuse through the same barrier. The molar mass of the unknown gas is ___________ g/mol.

A sample of Br2(g) takes 34.0 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?

The effusion rate of A gas molecules will be twice higher than one of B gas molecules when B molar mass is ____ higher than A molar mass. (a) None of the above (b) 4 times (c) 3 times (d) 2 times

Calculate the ratio of effusion rates for Ar and Kr.