Chapter 13, Problem 95A

Oxygen Consumption If 5.00 L of hydrogen gas,measured at a temperature of 20.0°C and a pressure of80.1 kPa, is burned in excess oxygen to form water, whatmass of oxygen will be consumed? Assume temperatureand pressure remain constant.

Interpretation Introduction

Interpretation:

The mass of oxygen gas used by $5L$ hydrogen gas to produce water is to be calculated.

Concept introduction:

It involves stoichiometry concepts and Avogadro’s law.

Answer to Problem 95A

$\text{2}\text{.63}\text{g}$ oxygen gas is consumed.

Explanation of Solution

The given equation is:

$2H_2+O_2\to 2H_{2}O$

Equation shows $2L$ of hydrogen gas consumes $1L{O}_2$

Therefore $5L{H}_2$ will consume:

$\begin{array}{c}5L{H}_2=5L{H}_2\times \frac{1L{O}_2}{2L{H}_2}\\ =2.5L{O}_2\end{array}$

Now mass of oxygen can be calculated by number of moles which is calculated by using ideal gas equation.

According to this law,

$\mathrm{PV}=nRT$

Or

$\mathrm{n}=\frac{PV}{RT}$

Given data is:

$\text{P=80}\text{.1}\text{kPa}$

$\text{V=2}\text{.5}\text{L}$

$\text{R=8}\text{.314}\text{LkPa}{K}^{-1}mo{l}^{-1}$

$\begin{array}{c}\text{T=20}\text{°C}\\ \text{=20+273}\\ \text{=}293\text{K}\end{array}$

Now substituting the values into formula,

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{80.1\times 2.50}{8.314\times 293}\\ =0.0822mol\end{array}$

Molar mass of oxygen is 32 g/mol

Mass of oxygen gas is given by:

$\begin{array}{c}\text{m=M×n}\\ \text{=32×0}\text{.0822}\\ \text{=2}\text{.63}\text{g}\end{array}$

Conclusion

$\text{2}\text{.63}\text{g}$ oxygen gas is consumed.