Chapter 13, Problem 33A

Interpretation Introduction

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

Concept Introduction: The total pressure of a mixture of gases that do not react chemically is the sum of the partial pressure of the component gases. This is known as Dalton’s law of partial pressure.

  $P=P_1+P_2+P_3$

Answer to Problem 33A

Partial pressure of ${\mathrm{O}}_2=0.66atm$

Partial pressure of $\mathrm{He}=5.54atm$

Total pressure of gases $=6.20\mathrm{atm}$

Explanation of Solution

For calculating partial pressure of component gas and the total pressure, the Dalton’s law partial pressure is used.

According to this law

  $P=P_1+P_2+P_3$

  $P$ = total pressure.

  $P_1$ = Partial pressure of gas - a

  $P_2$ = Partial pressure of gas - b

  $P_3$ = Partial pressure of gas − c

For calculating partial pressure of ${\mathrm{O}}_2$ and He, putting the values.

From Ideal gas equation,

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

  $\begin{array}{l}P=?\\ R=0.0821\text{ L atm/K mol}\\ T=65°C=65+273K=338K\\ V=5.0L\\ n=?\end{array}$

  $\begin{array}{l}\text{n = no}\text{. of moles =}\frac{\text{mass(m)}}{\text{molecular mass}}\\ \text{no}{\text{. of moles of O}}_2=\frac{4.0}{32}=0.12\end{array}$

No. of moles of He = $\frac{4}{4}=1$

  $\begin{array}{l}{P}_T=\frac{n_{T}RT}{V}\\ P_T=\frac{(n_1+n_2)RT}{V}\\ P_T=\frac{(1.12+1)0.0821\times 338}{5}\\ P_T=\frac{1.12\times 0.0821\times 338}{5}=\frac{31.07}{5}\end{array}$

Or,

  $\begin{array}{l}{P}_T=\frac{31.07}{5}=6.21atm\\ P_T=(P_1+P_2)\end{array}$

For calculating partial pressure of ${\mathrm{O}}_2$

  $\begin{array}{l}\frac{P_1}{P_T}=\frac{n_1}{n_T}\\ P_1=\frac{n_1}{n_T}\times P_T\end{array}$

Putting the values.

  $\begin{array}{l}{P}_1=\frac{0.12}{1.12}\times 6.21=\frac{0.74}{1.12}=0.66atm\\ P_1=0.66atm\end{array}$

For calculating Partial pressure of He,

  $\frac{P_2}{P_T}=\frac{n_2}{n_T}$

  $\begin{array}{l}{P}_2=\frac{n_2}{n_T}\times P_T\\ P_2=\frac{1}{1.12}\times 6.21=\frac{6.21}{1.12}=5.54atm\\ P_2=5.54atm\end{array}$

Conclusion

Partial pressure of ${\mathrm{O}}_2=0.66atm$

Partial pressure of $\mathrm{He}=5.54atm$

Total pressure of gases $=6.20\mathrm{atm}$