Chapter 13, Problem 34A

Interpretation Introduction

Interpretation: -Partial pressure is the pressure which each gas would exert if present alone in a vessel.

Concept Introduction: - The total pressure of a mixture of gases which do not react chemically is the sum of the partial pressure of the component gases.

  $\mathrm{P}=P_1+P_2+P_3$

Where,

  $\mathrm{P}$ = total pressure.

  ${\mathrm{P}}_1$ = Partial pressure of gas A

  ${\mathrm{P}}_2$ = Partial pressure of gas B

  ${\mathrm{P}}_3$ = Partial pressure of gas C

Answer to Problem 34A

Partial pressure of gases is as follows.

  $\begin{array}{l}\text{He = 0}\text{.5atm}\\ \text{Ne = 0}\text{.3atm}\\ \text{Ar = 0}\text{.2atm}\end{array}$

Explanation of Solution

For calculating partial pressure of component gases and the total pressure Dalton’s law pf partial pressure is applied.

  $\mathrm{P}=P_1+P_2+P_3$

  ${\mathrm{P}}_T=P_{He}+P_{Ne}+P_{Ar}$

From Ideal gas equation

  $\begin{array}{l}PV=nRT\\ P_T=\frac{n_{T}RT}{V}\end{array}$

  $P_T=P_1+P_2+P_3$

  ${\mathrm{n}}_T=n_1+n_2+n_3$

  $\therefore {\mathrm{P}}_T=\frac{(n_1+n_2+n_3)RT}{V}$

For calculating partial pressure of individual gases formula is

Partial pressure of Helium (He)

  $\begin{array}{l}\frac{P_{He}}{P_T}=\frac{n_{He}}{n_T}\\ P_{He}=\frac{n_{He}}{n_T}\times P_T\end{array}$

  ${\mathrm{n}}_{He}$ = no. of moles of helium = 5moles.

  $\begin{array}{l}Totalmolesofgases\\ =3+2+5\\ =10moles.\end{array}$

  ${\mathrm{P}}_{He}$ = Partial Pressure of Helium.

  ${\mathrm{P}}_T$ = Total Pressure

  $\begin{array}{l}{P}_{He}=\frac{n_{He}}{n_T}\times P_T\\ P_{He}=\frac{5}{10}\times 1=0.5atm\end{array}$

Partial Pressure of Neon (Ne)

  $\frac{P_{Ne}}{P_T}=\frac{n_{Ne}}{n_T}$

  $\begin{array}{l}{P}_{Ne}=\frac{n_{Ne}}{n_T}\times P_T\\ P_{Ne}=\frac{3}{10}\times 1=0.3atm\end{array}$

Partial Pressure of Argon (Ar)

  $\frac{P_{Ar}}{P_T}=\frac{n_{Ar}}{n_T}$

  $\begin{array}{l}{P}_{Ar}=\frac{n_A}{n_T}\times P_T\\ P_{Ar}=\frac{2}{10}\times 1=0.2atm\end{array}$

Conclusion

  $\begin{array}{l}Helium=P_{He}=0.5atm\\ Neon=P_{Ne}=0.3atm\\ Argon=P_{Ar}=0.2atm\end{array}$