Chapter U3.54, Problem 4E

Interpretation Introduction

Interpretation: The volume of the gas at 130 ^oC needs to be determined if it is initially 980 mL at 27 ^oC temperature.

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 4E

1316.3 mL

Explanation of Solution

The initial volume and temperature of the gas is 980 mL and 27 ^oC respectively. First convert the temperature from ^oC to K as follows:

  $T=\left(27+273.15\right)\text{ K}=300.15\text{ K}$

Thus,

  $T_1=300.15\text{ K}$ and $V_1=980\text{ mL}$

Now, the final temperature is given 130 ^oC which can be converted into K as follows:

  $T_2=\left(130+273.15\right)\text{ K}=403.15\text{ K}$

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

  $\frac{T_1}{V_1}=\frac{T_2}{V_2}$

Putting the values,

  $\frac{300.15\text{ K}}{980\text{ mL}}=\frac{403.15\text{ K}}{V_2}$

On rearranging,

  $V_2=\frac{403.15\text{ K}}{300.15\text{ K}}\times 980\text{ mL=1316}\text{.3 mL}$

Conclusion

Thus, the volume of the gas becomes 1316.3 mL at 130 ^oC.