Q. 8.17 - An Introduction to General, Organic, and Biological Chemistry

Question

A sample of nitrogen (N₂) has a volume of 50.0 L at a pressure of 760 mm Hg. What is the final volume, in liters, of the gas at each of the following pressures, if there is no change in temperature and amount of gas?

a. 725 mmHg 

b. 2.0 atm

c. 0.500 atm 

d. 850 Torr

Step-by-Step Solution

Answer

a. The final volume, in liters, of the gas at Pressure of $725 mmHg$is $52.41 L$

b. The final volume, in liters, of the gas at Pressure of  $2.0 atm$is $25.0 L$

c. The final volume, in liters, of the gas at Pressure of $.500 atm$is $100.0 L$

d. The final volume, in liters, of the gas at Pressure of  $850 Torr$ is $44.70 L$

Part(a) Step 1: Given information

We need to find the final volume of gas for given data.

Part(a) Step 2: Explanation

Using Boyle's law

$P1V1=P2V2$

Now,

$$\begin{gathered} P1=760 mmHg \\ V1=50.0 L \\ P2=750 mmHg \end{gathered}$$

Substituting the given values we get,

$V2=\frac{760 mmHg \times 50 L}{750 mmHg}=52.41 L$

Part(b) Step 1: Given information

We need to find the final volume of gas for given data.

Part(b) Step 2: Explanation

Using Boyle's law

$P1V1=P2V2$

Now,

$$\begin{gathered} P1=760 mmHg \\ V1=50.0 L \\ P2=2.0 atm \end{gathered}$$

Substituting the given values we get,

$V2= \frac{760 mmHg\times 50 L}{2 atm}=25.0 L$

Part(c) Step 1: Given information

We need to find the final volume of gas for given data.

Part(c) Step 2: Explanation

Using Boyle's law 

$P1V1=P2V2$

Now,

$P1=760 mmHg$

$$\begin{gathered} P2=0.50 atm \\ V1=50.0 L \end{gathered}$$

Substituting the given values we get,

$V2= \frac{760 mmHg \times 50 L}{0.50 atm}=100.0 L$

Part(d) Step 1: Given information

We need to find the final volume of gas for given data.

Part(d) Step 2: Explanation

Using Boyle's law

$P1V1=P2V2$

Now,

$$\begin{gathered} P1=760 mmHg \\ P2=850 Torr \\ V1=50.0 L \end{gathered}$$

Substituting the given values we get,

$V2=\frac{760 mmHg\times 50 L}{850 torr}=44.70 L$