Chapter 6, Problem 6.24E

Interpretation Introduction

Interpretation:

The unknown quantity for the given gas samples are to be calculated.

Concept introduction:

The ideal gas equation is used to represent the relation between the volume, pressure, temperature and number of moles of an ideal gas. The ideal gas equation is given as,

$PV=nRT$

Where,

• $V$ represents the volume occupied by the ideal gas.

• $P$ represents the pressure of the ideal gas.

• $n$ represents the number of moles of the ideal gas.

• $T$ represents the temperature of the ideal gas.

• $R$ represents the ideal gas constant with value $0.0821\text{L}\cdot \text{atm}\cdot {\text{K}}^{-1}\cdot {\text{mol}}^{-1}$.

Answer to Problem 6.24E

The final pressure of given sample A is $1.50\text{atm}$.

The final volume of given sample B is $4.49\text{L}$.

The final temperature of given sample C is $220.55\text{K}$.

Explanation of Solution

The combined gas law is,

$\frac{P_i{V}_i}{T_i}=\frac{P_f{V}_f}{T_f}$

Where,

• $P_i$ and $P_f$ is the initial and final pressure.

• $V_i$ and $V_f$ is the initial and final volume.

• $T_i$ and $T_f$ is the initial and final temperature.

For sample A,

The initial pressure is $1.50\text{atm}$.

The initial volume is $2.00\text{L}$.

The initial temperature is $300\text{K}$.

The final volume is $3.00\text{L}$.

The final temperature is $450\text{K}$.

To calculate the final pressure the formula used is,

$P_f=\frac{P_i{V}_i{T}_f}{T_i{V}_f}$

Substitute the values of initial and final volume, initial and final temperature and initial pressure to calculate the value of final pressure.

$\begin{array}{rll}{P}_f& =& \frac{1.50\text{atm}\times 2.00\text{L}\times 450\text{K}}{300\text{K}\times 3.00\text{L}}\\ & =& 1.50\text{atm}\end{array}$

Thus, the final pressure of given sample A is $1.50\text{atm}$.

For sample B,

The initial pressure is $2.35\text{atm}$.

The initial volume is $1.97\text{L}$.

The initial temperature is $293\text{K}$.

The final pressure is $1.09\text{atm}$.

The final temperature is $310\text{K}$.

To calculate the final volume the formula used is,

$V_f=\frac{P_i{V}_i{T}_f}{T_i{P}_f}$

Substitute the values of initial volume, initial and final temperature and initial and final pressure to calculate the value of final volume.

$\begin{array}{rll}{V}_f& =& \frac{2.35\text{atm}\times 1.97\text{L}\times 310\text{K}}{293\text{K}\times 1.09\text{atm}}\\ & =& 4.49\text{L}\end{array}$

Thus, the final volume of given sample B is $4.49\text{L}$.

For sample C,

The initial pressure is $9.86\text{atm}$.

The initial volume is $11.7\text{L}$.

The initial temperature is $500\text{K}$.

The final pressure is $5.14\text{atm}$.

The final volume is $9.90\text{L}$.

To calculate the final temperature the formula used is,

$T_f=\frac{P_f{V}_f{T}_i}{P_i{V}_i}$

Substitute the values of initial and final volume, initial temperature and initial and final pressure to calculate the value of final temperature.

$\begin{array}{rll}{T}_f& =& \frac{5.14\text{atm}\times 9.90\text{L}\times 500\text{K}}{9.86\text{atm}\times 11.7\text{L}}\\ & =& 220.55\text{K}\end{array}$

Thus, the final temperature of given sample C is $220.55\text{K}$.

Conclusion

The final pressure of given sample A is $1.50\text{atm}$.

The final volume of given sample B is $4.49\text{L}$.

The final temperature of given sample C is $220.55\text{K}$.