Chapter 13, Problem 4STP

Interpretation Introduction

Interpretation:

The gas that exerts the greater partial pressure has to be identified.

Concept Introduction:

The ideal gas law can be expressed as-

  $\mathrm{P}\mathrm{V}=\mathrm{n}\mathrm{R}\mathrm{T}$

Where, R is Universal gas constant.

The pressure of a gas is directly proportional to the number of moles when volume ( V ) and temperature ( T ) remain constant.

  $\mathrm{P}\propto \mathrm{n}$

Answer to Problem 4STP

The partial pressure of a gas depends on the number of moles of gas and directly proportional to the number of moles. Number of moles of hydrogen is greater than number of moles of helium. Thus, the hydrogen gas exerts the greater partial pressure by factor of 2 than the helium gas.

C. The hydrogen gas exerts about twice as much pressure as the helium gas.

Explanation of Solution

Considering both helium and hydrogen have M gm.

Number of moles of helium:

  ${\mathrm{n}}_{\mathrm{H}\mathrm{e}}=\frac{\mathrm{M}\mathrm{g}}{4\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}}=\frac{\mathrm{M}}{4}\mathrm{m}\mathrm{o}\mathrm{l}$

Number of moles of hydrogen:

  ${\mathrm{n}}_{{\mathrm{H}}_2}=\frac{\mathrm{M}\mathrm{g}}{2\mathrm{g}/\mathrm{m}\mathrm{o}\mathrm{l}}=\frac{\mathrm{M}}{2}\mathrm{m}\mathrm{o}\mathrm{l}$

The partial pressure of helium:

  ${\mathrm{P}}_{\mathrm{H}\mathrm{e}}=\frac{{\mathrm{n}}_{\mathrm{H}\mathrm{e}}\mathrm{R}\mathrm{T}}{\mathrm{V}}$

The partial pressure of hydrogen:

  ${\mathrm{P}}_{{\mathrm{H}}_2}=\frac{{\mathrm{n}}_{{}_{{\mathrm{H}}_2}}\mathrm{R}\mathrm{T}}{\mathrm{V}}$

Now,

  $\begin{array}{c}\frac{{\mathrm{P}}_{{\mathrm{H}}_2}}{{\mathrm{P}}_{\mathrm{H}\mathrm{e}}}=\frac{{\mathrm{n}}_{{}_{{\mathrm{H}}_2}}}{{\mathrm{n}}_{\mathrm{H}\mathrm{e}}}\\ \frac{{\mathrm{P}}_{{\mathrm{H}}_2}}{{\mathrm{P}}_{\mathrm{H}\mathrm{e}}}=\frac{\left(\raisebox{1ex}{$\mathrm{M}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right)}{\left(\raisebox{1ex}{$\mathrm{M}$}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right)}\\ =\frac{\mathrm{M}\times 4}{\mathrm{M}\times 2}\\ =2\\ {\mathrm{P}}_{{\mathrm{H}}_2}=2\times {\mathrm{P}}_{\mathrm{H}\mathrm{e}}\end{array}$

Conclusion

Reasons for incorrect options:

From the calculation, it can be concluded that hydrogen gas exerts the greater partial pressure by factor of 2 than the helium gas.

So, the answer is option C.

Therefore, options A, B and D are incorrect.