Q. 8.26 - An Introduction to General, Organic, and Biological Chemistry

Question

Indicate whether the final volume of gas in each of the following is the same, larger, or smaller than the initial volume, if pressure and amount of gas do not change:
a. A volume of $505 mL$of air on a cold winter day at $15°C$ is breathed into the lungs, where body temperature is $37°C$
b. The heater used to heat the air in a hot-air balloon is turned off.
c. A balloon filled with helium at the amusement park is left in a car on a hot day.

Step-by-Step Solution

Answer

Part(a)  Final volume will be more than initial volume 

Part(b)  Final volume will be same as initial volume 

Part(c)  Final volume will be more than initial volume

Part(a) Step 1 : Given information

We need to compare an initial and final volume on the different condition of temperature.  

Part(a) Step 2 : Simplify

Using Charle's Law : $\frac{V_1}{T_1}=\frac{V_2}{T_2}$,

$$\begin{gathered} V_1=505 mL \\ {T}_1= 15°C \\ {T}_2= 37°C \end{gathered}$$

Now, we can clearly see that final temperature is greater than initial temperature so according to Charle's law final volume will be greater than initial volume.

Part(b) Step 1 : Given information

We need to compare an initial and final volume on the different condition of temperature.  

Part(b) Step 2 : Simplify

The heater that heats the air in a hot-air balloon is switched off, according to the query.
As a result, there will be no temperature change.
As a result of Charle's law, there will be no change in volume.

Part(c) Step 1 : Given information

We need to compare an initial and final volume on the different condition of temperature.  

Part(c) Step 2 : Simplify

We all know what happens when a helium-filled balloon is left in a hot car at an amusement park.
As a result, the ultimate temperature will be higher than the initial temperature.

According to Charles's law $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

so final volume will be more than initial volume.