Q. 8.66 - An Introduction to General, Organic, and Biological Chemistry

Question

Indicate which diagram $(1,2 or 3)$ represents the volume of the gas sample in a flexible container when each of the following changes $(a to b)$ takes place:$\left(8.2 , 8.3\right)$

a. Temperature increases if the pressure does not change.

b. Temperature decreases if the pressure does not change.

c. Atmospheric pressure decreases if the temperature does not change.

d. Doubling the atmospheric pressure and doubling the Kelvin temperature. 

Step-by-Step Solution

Answer

a. The volume of the gas increase with the increase in temperature.

b. The volume of the gas decrease with a decrease in temperature. 

c. The volume of the gas increase when atmospheric pressure decreases.

d. The volume of the gas will remain the same. 

Part (a) step 1: Given Information

We need to explain how the volume will be effected the temperature increases if the pressure does not change. 

Part (a) step 2: Explanation

There is no change in the amount of gas and pressure is constant too.

Therefore from the combined gas law:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

Volume is directly related to temperature with increasing temperature will increase too.

Part (b) step 1: Given Information

We need to explain how the volume will be effected  the temperature decreases if the pressure does not change. 

Part (b) step 2: Explanation

There is no change in the amount of gas and pressure is constant too.

Therefore from the combined gas law:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

Volume is directly related to temperature with decreasing temperature will decrease too.

Part (c) step 1: Given Information

We need to explain how the volume will be effected  the atmospheric pressure decreases if the temperature does not change. 

Part (c) step 2: Explanation

Here, are the principles of Boyle's law, since there is no change in the temperature.

Recall that Boyle's law states that pressure and volume are inversely proportional:

$P_1\times V_1=P_2\times V_2$

This means an increase in pressure is followed by a decrease in volume and vice versa.

Therefore, in this a decrease in the atmospheric pressure, which according to Boyle's law, is followed by an increase in the volume of the gas sample.

Expending of the flexible container is represented in the diagram $3$.

Part (d) step 1: Given Information

We need to explain how the volume will be effected doubling the atmospheric pressure and doubling the Kelvin temperature. 

Part (d) step 2:Explanation

Here, are the principles of Boyle's law, since there is no change in the temperature.

Recall that Boyle's law states that pressure and volume are inversely proportional:

$P_1\times V_1=P_2\times V_2$

This means an increase in pressure is followed by a decrease in volume and vice versa.

Charles's law:

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

This means an increase in temperature is followed by an increase in volume and vice versa.

Combined gas law:

$\frac{P_1\times V_1}{T_1}=\frac{P_2\times V_2}{T_2}$

If a double increase in the pressure, according to Boyle's law, will cause a double decrease in the volume of the gas.

and a double increase in the pressure, according to Charles's law, will cause a double increase in the volume of the gas. 

The combined gas law equation:

$\frac{P_1\times V_1}{T_1}=\frac{2\times P_2\times V_2}{2T_2}$

Then, $V_1=V_2$

The volume of the gas will stay the same after a double increase in the pressure and the temperature.