Chapter 11, Problem 11.1KSP

Determine the mole fraction of helium in a gaseous mixture consisting of 0.524 g He, 0.275 g Ar, and 2.05 g CH₄.

(a) 0.0069

(b) 0.0259

(c) 0.481

(d) 0.493

(e) 0.131

Interpretation Introduction

Interpretation:

The mole fraction of Helium in a gaseous mixture has to be calculated.

Concept introduction:

The mole fraction is calculated using below the formula

$\text{Mole fraction =}\frac{\text{mole}\text{of}\text{helium}}{\text{total}\text{mole}\text{of}\text{the}\text{mixture}}$

Answer to Problem 11.1KSP

The mole fraction of Helium in a gaseous mixture is $\text{0}\text{.4932}$ . Option (d)

Explanation of Solution

To determine: The mole fraction of Helium in a gaseous mixture

Reasons for correct options:

The mole fraction of Helium in a gaseous mixture is calculated below

Given,

$\begin{array}{l}\text{weight}\text{of}\text{helium}\text{=}\text{0}\text{.524}\text{g}\\ \\ \text{weight}\text{of}\text{Ar}\text{=}\text{0}\text{.524}\text{g}\\ \\ \text{weight}\text{of}{\text{CH}}_{\text{4}}\text{=}\text{0}\text{.524}\text{g}\end{array}$

Where

$\begin{array}{l}\text{mole}\text{of}\text{the}\text{He}\text{=}\frac{\text{0}\text{.524}\text{g}}{\text{4}}\\ \text{=0}\text{.131}\end{array}$

$\begin{array}{l}\text{mole}\text{of}\text{the}\text{Ar}\text{=}\frac{\text{0}\text{.275}\text{g}}{\text{39}\text{.94}\text{g/mole}}\\ \text{=0}\text{.0068}\text{mole}\end{array}$

$\begin{array}{l}\text{mole}\text{of}\text{the}{\text{CH}}_{\text{4}}\text{=}\frac{\text{2}\text{.05}\text{g}}{\text{16}\text{.04}\text{g/mole}}\\ \text{=0}\text{.1278}\text{mole}\end{array}$

$\text{Mole fraction =}\frac{\text{mole}\text{of}\text{helium}}{\text{total}\text{mole}\text{of}\text{the}\text{mixture}}$

$\begin{array}{l}\text{Mole fraction of}\text{He}\text{=}\frac{\text{0}\text{.131}\text{mole}}{\text{0}\text{.2656}\text{mole}}\\ \text{=}\text{0}\text{.4932}\end{array}$

The mole fraction of Helium in a gaseous mixture is $\text{0}\text{.4932}$

So the correct answer is option (d) $\text{0}\text{.4932}$.

Reasons for incorrect options:

The calculated result shows that the mole fraction of Helium in a gaseous mixture is $\text{0}\text{.4932}$. So the correct answer is (d) $\text{0}\text{.4932}$.  Hence, the options (a), (b), (c) and (e) are incorrect.

Conclusion

The mole fraction of Helium in a gaseous mixture was calculated.