Chapter 13.6, Problem 13.10SC

Interpretation Introduction

Interpretation:

The partial pressure of H₂ and the number of moles of H₂ present in the sample should be determined.

Concept Introduction:

The problem can be solved using ideal gas law and Dalton’s gas law. The total number of moles (moles of hydrogen gas plus moles of water vapor) can be calculated using ideal gas law as follows

$\begin{array}{l}\text{P}\text{V}=\text{n}\text{R}\text{T}\\ \text{n}=\frac{\text{P}\text{V}}{\text{R}\text{T}}\end{array}$

Where, P is the total pressure of the mixture

V is the volume of the mixture

R is the gas constant

T is the absolute temperature and,

n is the total number of moles of hydrogen gas and water vapor.

Now,

${\text{n = n}}_{{\text{H}}_{\text{2}}}{\text{+ n}}_{{\text{H}}_{\text{2}}\text{O}}$

${\text{n}}_{{\text{H}}_{\text{2}}}={\text{n - n}}_{{\text{H}}_2\text{O}}$

${\text{n}}_{{\text{H}}_2\text{O}}$ can be determined using the Daltons law as follows:

${\text{P}}_{{\text{H}}_{\text{2}}\text{O}}{\text{= x}}_{{\text{H}}_{\text{2}}\text{O}}{\text{.P}}_{\text{total}}\text{ = }\left(\frac{{\text{n}}_{{\text{H}}_{\text{2}}\text{O}}}{{\text{n}}_{\text{total}}}\right){\text{. P}}_{\text{total}}$

Once ${\text{n}}_{{\text{H}}_{\text{2}}}$ is calculated, one can use Dalton’s law to find out the partial pressure of hydrogen gas in the mixture as follows:

${\text{P}}_{{\text{H}}_2}$ = ${\mathrm{x<mrow><msub><mtext>H</mtext><mn>2</mn></msub></mrow>}}_{}$ ?P_{t o t a l}

Where ${\text{P}}_{{\text{H}}_2}$ is the partial pressure of hydrogen gas in the mixture

${\text{x}}_{{\text{H}}_2}$ is the mole fraction of hydrogen gas and,

P_{t o t a l} is the total pressure of the mixture.