Q. 8.67 - An Introduction to General, Organic, and Biological Chemistry

Question

A balloon is filled with helium gas at a partial pressure of $1.00 atm$ and neon gas with a partial pressure of $0.50 atm$. For each of the following changes (a to e) of the initial balloon, select the diagram (A, B, or C) that shows the final volume of the balloon:$\left(8.2, 8.3 , 8.6\right)$

a. The balloon is put in a cold storage unit ($P and n$do not change).

b. The balloon floats to a higher altitude where the pressure is less ($n and T$ do not change).

c. All of the neon gas is removed ($T and P$ do not change).

d. The Kelvin temperature doubles and half of the gas atoms leak out ($P$ does not change).

e. $2.0 moles of O_2$ gas is added ($T and P$ do not change).

Step-by-Step Solution

Answer

a. The volume will decrease and is shown in diagram A 

b. The volume will decrease and is shown in diagram C.

c. The volume will decrease and is shown in diagram A.

d.  The volume will be constant and is shown in diagram B. 

e. The volume will increase and is shown in diagram C.

Part (a) step 1: Given Information

We need to find the final volume of the balloon if the balloon is put in a cold storage unit.

Part (a) step 2: Explanation

If $P and N$ are constant, by decreasing temperature, volume will be smaller then initial ballon.

Part (b) step 1: Given Information

We need to find the final volume of the balloon if the balloon floats to a higher altitude where the pressure is less. 

Part (b) step 2: Explanation

There is no change in the amount of gas and the temperature 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 the inverse of pressure with decreasing pressure volume will increase. 

Part (c) step 1: Given Information

We need to find the final volume of the balloon if all of the neon gas is removed.

Part (c) step 2: Explanation

There is no change in the temperature 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 the number of moles with decreasing moles volume will decrease too. 

Part (d) step 1: Given Information

We need to find the final volume of the balloon if the Kelvin temperature doubles and half of the gas atoms leak out.  

Part (d) step 2: Explanation

Pressure is constant.

Therefore from the combined gas law:

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

Volume is  related to the number of moles of gas and temperature. If the temperature is doubled and moles are halved then the will neutral effect of each other on the volume of gas is constant. 

Part (e) step 1: Given Information

We need to find the final volume of the balloon if $2.0 moles of O_2$ gas is added.

Part (e) step 2: Explanation

There is the temperature 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 the number of moles of gas with increasing moles volume will increase too.