Chapter U3.6, Problem 5E

Interpretation Introduction

Interpretation: The temperature required to change the initial volume of the gas to 220 mL needs to be determined.

Concept Introduction:

The Charles’s law states that at constant pressure, the volume of the gas is directly proportional to its temperature. It is mathematically represented as follows:

  $\frac{T_1}{V_1}=\frac{T_2}{V_2}$

Here, T₁ is initial temperature, V₁ is initial volume, T₂ is final temperature and V₂ is final volume.

Answer to Problem 5E

186.67 K.

Explanation of Solution

Given Information:

The initial volume and temperature of the gas is 330 mL and 280 K respectively.

Calculation:

The initial volume and temperature of the gas is 330 mL and 280 K respectively.

Thus,

  $T_1=280\text{ K}$ and $V_1=330\text{ mL}$

Now, the final volume is given 220 mL.

Thus, final temperature can be calculated from Charles’s law as follows:

  $\frac{T_1}{V_1}=\frac{T_2}{V_2}$

Putting the values,

  $\frac{280\text{ K}}{330\text{ mL}}=\frac{T_2}{220\text{ mL}}$

On rearranging,

  $T_2=\frac{280\text{ K}}{330\text{ mL}}\times 220\text{ mL=186}\text{.67 K}$

Conclusion

Thus, the final temperature of the gas must be 186.67 K.