Chapter 5, Problem 5.85QP

Interpretation Introduction

Interpretation:

The partial pressure of each of the gases from a certain volcano whose total pressure of volcanic gas were 760 mmHg has to be calculated.

Concept Introduction:

Partial Pressure:

Dalton’s law of partial pressure states that “the total pressure (P) of the mixture is equal to the sum of the partial pressures ${\text{(P}}_{\text{A}}{\text{, P}}_{\text{B}}{\text{, P}}_{\text{C}}\mathrm{.....}\text{)}$ of all the component gases $\text{(A, B, C}\mathrm{......}\text{)}$  present in the mixture” and is given as,

${\text{P = P}}_{\text{A}}{\text{ + P}}_{\text{B}}{\text{ + P}}_{\text{C}}\text{ + }\mathrm{.......}$

The ideal gas law for the individual gas component A is given as,

${\text{P}}_{\text{A}}{\text{V = n}}_{\text{A}}\text{RT}$

Mole fraction:

Mole fraction of a component gas is defined as “the fraction of moles of that component in the total moles of gas mixture” and is given as,

$\text{Mole fraction of A = }\frac{n_{\text{A}}}{n}\text{ = }\frac{{\text{P}}_{\text{A}}}{\text{P}}$

Answer to Problem 5.85QP

The partial pressure of each of the gases from a certain volcano is:

• The partial pressure of ${\text{H}}_{\text{2}}$ is 190.0 mmHg
• The partial pressure of ${\text{CO}}_{\text{2}}$ is 494 mmHg
• The partial pressure of $\text{HCl}$ is 41 mmHg
• The partial pressure of $\text{HF}$ is 21 mmHg
• The partial pressure of ${\text{SO}}_{\text{2}}$ is 13 mmHg
• The partial pressure of ${\text{H}}_{\text{2}}\text{S}$ is 0.8 mmHg

Explanation of Solution

To Calculate: The partial pressure of each of the gases from a certain volcano whose total pressure of volcanic gas were 760 mmHg

Given data:

The gas from a certain volcano had the following composition in mole percent $\text{(mole fraction}\times \text{100)}$: 65.0 % ${\text{CO}}_{\text{2}}$ , 25.0 % ${\text{H}}_{\text{2}}$, 5.4 % $\text{HCl}$, 2.8 % $\text{HF}$, 1.7 % ${\text{SO}}_{\text{2}}$ and 0.1 % ${\text{H}}_{\text{2}}\text{S}$.

The total pressure of volcanic gas were 760 mmHg    

Calculation of Partial Pressure:

On rearranging the mole fraction equation, we get

${\text{P}}_{\text{(gas)}}\text{ = P}\times \text{(mole fraction of gas)}$

The parital pressure of the given volcanic gases are calculated as follows,

Partial pressure of ${\text{H}}_{\text{2}}$:

$\begin{array}{l}{\text{P}}_{{\text{(H}}_{\text{2}}\text{)}}\text{= 760 mmHg}\times \text{0}\text{.250}\\ \text{=190}\text{.0 mmHg}\end{array}$

Therefore, the partial pressure of ${\text{H}}_{\text{2}}$ is 190.0 mmHg

Partial pressure of ${\text{CO}}_{\text{2}}$:

$\begin{array}{l}{\text{P}}_{{\text{(CO}}_{\text{2}}\text{)}}\text{= 760 mmHg}\times \text{0}\text{.650}\\ \text{=494}\text{.0 mmHg}\end{array}$

Therefore, the partial pressure of ${\text{CO}}_{\text{2}}$ is 494 mmHg

Partial pressure of $\text{HCl}$:

$\begin{array}{l}{\text{P}}_{\text{(HCl)}}\text{= 760 mmHg}\times \text{0}\text{.054}\\ \text{=41}\text{.04 mmHg}\end{array}$

Therefore, the partial pressure of $\text{HCl}$ is 41 mmHg

Partial pressure of $\text{HF}$:

$\begin{array}{l}{\text{P}}_{\text{(HF)}}\text{= 760 mmHg}\times \text{0}\text{.028}\\ \text{=21}\text{.28 mmHg}\end{array}$

Therefore, the partial pressure of $\text{HF}$ is 21 mmHg

Partial pressure of ${\text{SO}}_{\text{2}}$:

$\begin{array}{l}{\text{P}}_{{\text{(SO}}_{\text{2}}\text{)}}\text{= 760 mmHg}\times \text{0}\text{.017}\\ \text{=12}\text{.92 mmHg}\end{array}$

Therefore, the partial pressure of ${\text{SO}}_{\text{2}}$ is 13 mmHg

Partial pressure of ${\text{H}}_{\text{2}}\text{S}$:

$\begin{array}{l}{\text{P}}_{{\text{(H}}_{\text{2}}\text{S)}}\text{= 760 mmHg}\times \text{0}\text{.001}\\ \text{=0}\text{.76 mmHg}\end{array}$

Therefore, the partial pressure of ${\text{H}}_{\text{2}}\text{S}$ is 0.8 mmHg

Conclusion

The partial pressure of each of the gases from a certain volcano was found as:

• The partial pressure of ${\text{H}}_{\text{2}}$ is calculated as 190.0 mmHg
• The partial pressure of ${\text{CO}}_{\text{2}}$ is calculated as 494 mmHg
• The partial pressure of $\text{HCl}$ is calculated as 41 mmHg
• The partial pressure of $\text{HF}$ is calculated as 21 mmHg
• The partial pressure of ${\text{SO}}_{\text{2}}$ is calculated as 13 mmHg
• The partial pressure of ${\text{H}}_{\text{2}}\text{S}$ is calculated as 0.8 mmHg