Chapter 16, Problem 19STP

Interpretation Introduction

Interpretation:

The new volume of the gas when a sample of argon gas is compressed into a volume of $0.712\text{L}$ by a piston exerting $3.92\text{atm}$ of the pressure needs to be determined.

Concept introduction:

Boyle’s law states the relationship between volume of a gas and its pressure at constant temperature. It is represented as follows:

$P_1{V}_1=P_2{V}_2$

Here, $P_1$ and $V_1$ initial pressure and volume and $P_2$, $V_2$ represents final pressure and volume respectively.

Answer to Problem 19STP

Option E is correct.

Explanation of Solution

According to Boyle’s law

$P_1{V}_1=P_2{V}_2$ …… (1)

Given data,

$\begin{array}{l}{V}_1=0.712\text{L}\\ V_2=?\\ P_1=3.92\text{atm}\\ P_2=1.50\text{atm}\end{array}$

Substitute the above values in equation (1)

$\begin{array}{c}{P}_1{V}_1=P_2{V}_2\\ 0.712\text{L}\times \text{3}\text{.92}\text{atm=1}\text{.50}\text{atm}\times V_2\\ V_2=\frac{2.791}{1.50}\text{L}\\ \text{=1}\text{.86}\text{L}\end{array}$

Therefore, new volume is $\text{1}\text{.86}\text{L}$.

Conclusion

The calculation shows that the correct option is E. Therefore, option A, B, C and D are not correct.