Chapter U3, Problem 4RE

Interpretation Introduction

Interpretation: The new volume of the balloon needs to be determined.

Concept Introduction:

The ideal gas equation is represented as follows:

  $PV=nRT$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature of the gas.

Answer to Problem 4RE

588 mL.

Explanation of Solution

Given Information:

The initial volume and temperature of the air in balloon is 600 mL and 27 ^oC respectively. The final temperature is 21 ^oC .

Calculation:

First convert the given temperature to K as follows:

  $0{}^{\text{o}}\text{C}=\text{273}\text{.15 K}$

Thus,

  $27{}^{\text{o}}\text{C}=27+\text{273}\text{.15 K}=\text{300}\text{.15 K}$

Thus,

  $T_1=300.15\text{ K}$

Also,

  $21{}^{\text{o}}\text{C}=21+\text{273}\text{.15 K}=\text{294}\text{.15 K}$

Thus,

  $T_2=294.15\text{ K}$

The ideal gas equation is as follows:

  $PV=nRT$

For constant pressure and number of moles:

  $\frac{V_1}{T_1}=\frac{V_2}{T_2}$

On rearranging,

  $V_2=\frac{V_1}{T_1}\times T_2$

Putting the values,

  $V_2=\frac{600\text{ mL}}{300.15\text{ K}}\times 294.15\text{ K=588 mL}$

Conclusion

Thus, the new volume of the air in balloon is 588 mL.