Chapter 13, Problem 90A

Interpretation Introduction

Interpretation:

The number of moles of carbon dioxide produced by $10L$ acetylene gas is to be calculated.

Concept introduction:

It involves stochiometry concepts and Avogadro’s law.

Answer to Problem 90A

The moles of carbon dioxide produced are $\text{0}\text{.817}\text{mol}$

Explanation of Solution

The given equation is:

$2C_2{H}_2+5O_2\to 2H_{2}O+4C{O}_2$

Equation shows $2L$ of acetylene gas forms 4L of carbon dioxide.

Therefore $10Lacetylene$ will be form carbon dioxide.

$\begin{array}{c}10Lacetylene=10Lacetylene\times \frac{4LC{O}_2}{2Lacetylene}\\ =20LC{O}_2\end{array}$

Now, the number of moles is calculated by using ideal gas equation.

According to this law,

$\mathrm{PV}=nRT$

Or

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

Given data is:

$\mathrm{V}=20L$

$\mathrm{P}=1atm$

$\text{R=}0.0821Latm{K}^{-1}mo{l}^{-1}$

$\text{T=25}\text{°C}$

To convert temperature into Kelvin,

$\begin{array}{c}\mathrm{T}\left(K\right)=T\left(°C\right)+273\\ =25+273\\ =298K\end{array}$

Now substituting the values into formula,

$\begin{array}{c}n=\frac{PV}{RT}\\ =\frac{1\times 20}{0.0821\times 298}\\ =0.817mol\end{array}$

Conclusion

$0.817mol$ carbon dioxide is produced.