### Chemistry End of Chapter Exercises

A balloon filled with helium gas takes 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%?

## Solution

4.2 hours

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

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.

## Solution

Effusion can be defined as the process by which a gas escapes through a pinhole into a vacuum. Graham’s law states that with a mixture of two gases A and B: $$(\frac{rate\;A}{rate\;B})=(\frac{molar\;mass\;of\;B}{molar\;mass\;of\;A})^{\frac{1}{2}}$$. Both A and B are in the same container at the same temperature, and therefore will have the same kinetic energy: $$KE_A=KE_B\qquad KE=\frac{1}{2}mv^2$$ Therefore, $$\frac{1}{2}m_Av_A^2=\frac{1}{2}m_Bv_B^2$$ $$\frac{v_A^2}{v_B^2}=\frac{m_B}{m_A}$$ $$(\frac{v_A^2}{v_B^2})^{\frac{1}{2}}=(\frac{m_B}{m_A})^{\frac{1}{2}}$$ $$\frac{v_A}{v_B}=(\frac{m_B}{m_A})^{\frac{1}{2}}$$

Heavy water, D_{2}O (molar mass = 20.03 g mol^{–1}), can be separated from ordinary water, H_{2}O (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 H_{2}O and D_{2}O.

Which of the following gases diffuse more slowly than oxygen? F_{2}, Ne, N_{2}O, C_{2}H_{2}, NO, Cl_{2}, H_{2}S

## Solution

F_{2}, N_{2}O, Cl_{2}, H_{2}S

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

Calculate the relative rate of diffusion of ^{1}H_{2} (molar mass 2.0 g/mol) compared with ^{2}H_{2} (molar mass 4.0 g/mol) and the relative rate of diffusion of O_{2} (molar mass 32 g/mol) compared with O_{3} (molar mass 48 g/mol).

## Solution

1.4; 1.2

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.

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 NH_{4}Cl forms where gaseous NH_{3} and gaseous HCl first come into contact.
$$NH_3\;(g)+HCl\;(g)⟶NH_4Cl\;(g)$$ At approximately what distance from the ammonia moistened plug does this occur? (Hint: Calculate the rates of diffusion for both NH_{3} and HCl, and find out how much faster NH_{3} diffuses than HCl.)

## Solution

51.7 cm