Chapter 7, Problem 31P

Interpretation Introduction

(a)

Interpretation:

The following table is to be completed by assuming the gas at a constant temperature.

$P_1$	$V_1$	$P_2$	$V_2$
2.0atm	3.0L	8.0atm	?

Concept Introduction:

The concept of Boyle's law will be used. This is represented as-

  $P_1{V}_1=P_2{V}_2$

Or,

  $V_2=\frac{P_1{V}_1}{P_2}$

Here, P is pressure and V is the volume of the gas.

Answer to Problem 31P

$P_1$	$V_1$	$P_2$	$V_2$
2.0atm	3.0L	8.0atm	0.75L

Explanation of Solution

According to Boyle's law, the pressure of the ideal gas is inversely proportional to the volume of the ideal gas at constant temperature. This is represented as

  $P\propto V$

Or,

  $P_1{V}_1=P_2{V}_2$ ..................... (1)

Or,

  $V_2=\frac{P_1{V}_1}{P_2}$

Given that −

P₁, initial pressure = 2.0atm

V₁, initial volume = 3.0L

P₂, final pressure = 8.0atm

Put the above values in equation (1),

  $V_2=\frac{\text{2}\text{.0 atm×3}\text{.0 L}}{\text{8}\text{.0 atm}}=0.\text{75 L}$

Final volume = 0.75 L

Interpretation Introduction

(b)

Interpretation:

The following table is to be completed by assuming the gas at a constant temperature.

$P_1$	$V_1$	$P_2$	$V_2$
55 mmHg	0.35 L	18 mmHg	?

Concept Introduction:

The concept of Boyle's law will be used. This is represented as-

  $P_1{V}_1=P_2{V}_2$

Or,

  $V_2=\frac{P_1{V}_1}{P_2}$

Here, P is pressure and V is the volume of the gas.

Answer to Problem 31P

$P_1$	$V_1$	$P_2$	$V_2$
55mmHg	0.35L	18mmHg	1.07L

Explanation of Solution

According to Boyle's law, the pressure of the ideal gas is inversely proportional to the volume of the ideal gas at a constant temperature. This is represented as

  $P\propto V$

Or,

  $P_1{V}_1=P_2{V}_2$ ..................... (1)

Or,

  $V_2=\frac{P_1{V}_1}{P_2}$ .............. (2)

Given that −

P₁, initial pressure = 55mmHg

V₁, initial volume = 0.35mL

P₂, final pressure = 18mmHg

Put the above values in equation (2)

  $V_2=\frac{\text{55mmHg×0}\text{.35L}}{\text{18mmHg}}\text{=1}\text{.07L}$

Final volume = 1.07L

Interpretation Introduction

(c)

Interpretation:

The following table is to be completed by assuming the gas at a constant temperature.

$P_1$	$V_1$	$P_2$	$V_2$
705mmHg	215mL	?	1.52L

Concept Introduction:

The concept of Boyle's law will be used. This is represented as-

  $P_1{V}_1=P_2{V}_2$

Or,

  $V_2=\frac{P_1{V}_1}{P_2}$

Here, P is pressure and V is the volume of the gas.

Answer to Problem 31P

$P_1$	$V_1$	$P_2$	$V_2$
705mmHg	215mL	100mmHg	1.52L

Explanation of Solution

According to Boyle's law, the pressure of the ideal gas is inversely proportional to the volume of the ideal gas at a constant temperature. This is represented as

  $P\propto V$

Or,

  $P_1{V}_1=P_2{V}_2$ ..................... (1)

Or,

  $V_2=\frac{P_1{V}_1}{P_2}$ .............. (2)

Given that −

P₁, initial pressure = 705mmHg

V₁, initial volume = 215mL

Or,

  $=\text{215mL×}\frac{\text{1L}}{\text{1000mL}}\text{=0}\text{.215L}$

V₂, final pressure = 1.52 L

  $P_2=\frac{P_1{V}_1}{V_2}$

Put the values in the above equation,

  $P_2=\frac{\text{705 mmHg×0}\text{.215 L}}{\text{1}\text{.52 L}}=\text{99}\text{.7 mmHg}\approx \text{100 mmHg}$

Final pressure = 100mmHg

The final table is −

$P_1$	$V_1$	$P_2$	$V_2$
705mmHg	215mL	100mmHg	1.52L