Chapter 13, Problem 39A

Interpretation Introduction

Interpretation: -Volume of the ${\mathrm{CO}}_2$ measured using the given variable values needs to be determined.

Concept Introduction: - For calculating the volume of ${\mathrm{CO}}_2$ , Ideal gas equation is used.

According to this equation

  $\begin{array}{l}PV=nRT\\ V=\frac{nRT}{P}\end{array}$

Answer to Problem 39A

Volume of ${\mathrm{CO}}_2$ used is $3.384L$ .

Explanation of Solution

There is a relation between volume of a gas and number of molecules of a gas participate in a reaction which is expressed by Avogadro Law.

Balanced equation is

  ${\mathrm{CaCO}}_3(s)\to CaO(s)+C{O}_2(g)$

Number of moles of ${\mathrm{CaCO}}_3$

No. of moles = $\frac{\text{mass}}{\text{molar mass}}$

  $\begin{array}{l}n=\frac{15.2g}{100.08g/mol}\\ n=0.150mol\end{array}$

According to Ideal gas equation

  $\begin{array}{l}PV=nRT\\ V=\frac{nRT}{P}\end{array}$

Here, at standard temperature and pressure value of

  $\begin{array}{l}P=1atm\\ V=?\\ T=273K\\ R=0.0821\frac{atmL}{kmol}\end{array}$

Putting the values in Ideal gas equation

  $\mathrm{V}=\frac{nRT}{P}$

  $\begin{array}{l}V=\frac{0.150mol\times 0.0821atmL\times 273K}{1atm\times kmol}\\ V=0.150\times 0.0821L\times 273\\ V=3.384L\end{array}$

Volume of ${\mathrm{CO}}_2$ used is $3.384L$ .

Conclusion

Volume of ${\mathrm{CO}}_2$ used is $3.384L$ .