Chapter 13, Problem 58A

(a)

To determine

Number of moles of carbon dioxide in $2L$ bottle of soda.

Answer to Problem 58A

There are $0.32mol$ of carbon dioxide in $2L$ of bottle of soda.

Explanation of Solution

Given: $8.0L$ of carbon dioxide gas at atmospheric pressure.

Temperature $=300.0K$

Volume of $Bottleofsoda:2L$

  $1L=0.001m^3$

Formula used: From the ideal gas law:

  $n=\frac{PV}{RT}$

Here, n is the number of moles, P is the pressure, R is the gas constant, V is the volume and T is the temperature.

Calculation: Number of moles of carbon dioxide in 2 L soda:

  $n=\frac{(1.01\times {10}^{5}Pa)(0.0080m^3)}{(8.31Pa\cdot m^3/mol\cdot K)(300.0K)}$

  $n=0.32mol$

Conclusion: The number of moles of carbon dioxide is $0.32mol$ .

(b)

To determine

The mass of carbon dioxide in $2L$ bottle of soda.

Answer to Problem 58A

The mass of carbon dioxide is $14g$ in $2L$ soda.

Explanation of Solution

Given: $8.0L$ of carbon dioxide gas at atmospheric pressure.

Temperature $T=300.0K$

Volume of $Bottleofsoda:2L$

  $1L=0.001m^3$

Formula used: $m=nM$

Where, m is mass, n is number of moles and M is the molecular weight.

Calculation: The molecular weight of carbon dioxide is:

  $M=12+2(16)=44g/mol$

The mass is:

  $m=nM$

  $\begin{array}{l}m=(0.32mol)(44g/mol)\\ m=14g\end{array}$

Conclusion: The mass of carbon dioxide in $2L$ of soda is $14g$ .