Chapter 13, Problem 94A

Solution

(a)

Interpretation:

The volume of given amount of carbon dioxide is to be calculated.

Concept introduction:

Avogadro’s Law is used to find out the result.

The volume of carbon dioxide is $4.48L$

According to Avogadro’s Law, equal numbers of molecules of all gases occupy 22.4 liters volume at STP.

$\begin{array}{l}44gC{O}_{2}occupiesvolume=22.4L\\ 8.80gwilloccupy=8.80\times \frac{22.4}{44}\\ =4.48L\end{array}$

(b)

Interpretation:

The volume of the gas is to be calculated when pressure, temperature and amount of the gas are given.

Concept introduction:

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Where

$\mathrm{P}$ is pressure of the gas

$\mathrm{V}$ is volume of the gas

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

The volume of the gas is $2.37L$

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\mathrm{V}=\frac{nRT}{P}$

Given data is:

$\begin{array}{l}\mathrm{m}=8.80g\end{array}$

$\mathrm{P}=3atm$

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

$\begin{array}{l}\mathrm{T}=160°C\\ =160+273\\ =433K\end{array}$

$\begin{array}{l}n=\frac{m}{M}\\ n=\frac{8.80}{44}\\ =0.2mol\end{array}$

Now substituting the values into formula,

$\begin{array}{c}V=\frac{nRT}{P}\\ =\frac{0.2\times 0.0821\times 433}{3}\\ =2.37L\end{array}$

Therefore volume of the gas is $2.37L$

(c)

Interpretation:

The volume of the gas is to be calculated when pressure, temperature and amount of the gas are given.

Concept introduction:

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Where

$\mathrm{P}$ is pressure of the gas

$\mathrm{V}$ is volume of the gas

$\mathrm{n}$ is the number of moles of the gas

$\mathrm{R}$ is the ideal gas constant

$\mathrm{T}$ is the temperature of the gas

The volume of the gas is $4.06L$

Ideal gas equation helps to calculate volume of a gas at given temperature and pressure. According to this law,

$\mathrm{PV}=nRT$

Or

$\mathrm{V}=\frac{nRT}{P}$

Given data is:

$\begin{array}{l}\mathrm{m}=8.80g\end{array}$

$\mathrm{P}=118kPa$

$\mathrm{R}=8.314LkPa{K}^{-1}mo{l}^{-1}$

$\mathrm{T}=288K$

$\begin{array}{l}n=\frac{m}{M}\\ n=\frac{8.80}{44}\\ =0.2mol\end{array}$

Now substituting the values into formula,

$\begin{array}{c}V=\frac{nRT}{P}\\ =\frac{0.2\times 8.314\times 288}{118}\\ =4.06L\end{array}$

Therefore volume of the gas is $4.06L$