Chapter 14, Problem 83A

Interpretation Introduction

Interpretation: The final temperature of a gas in degrees Celsius should be determined if $3.50L$ of the gas sample at $20°C$ and $86.7kPa$ is expanded to the volume of $8.00L$ which makes the final pressure of the gas as $56.7kPa$ .

Concept introduction:

The ideal gas law is used to determine the variables like pressure, temperature, volume, and moles of gases. The mathematical relation of these variables can be calculated with the help of the given gas law.

  $\text{P}\times \text{V = n}\times \text{R}\times \text{T}$

The ideal gas law is the combination of all the gas laws like Boyle’s law, Charles’s law, etc.

Answer to Problem 83A

Final temperature of the gas must be ${\text{T}}_{\text{2}}\text{= 438}\text{.2 K}$ .

Explanation of Solution

The combined gas equation is used to calculate the variables of gas under different conditions. It can be written as:

  $\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{ =}\frac{{\text{ P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$

Given:

• Initial volume = $3.50L$
• Initial temperature = $20°C=20+273=293K$
• Initial pressure = $86.7kPa=\text{0}\text{.855}atm$
• Final pressure = $56.7kPa=\text{0}\text{.5595}atm$
• Final volume = $8.00L$
• Final temperature = need to calculate

Substitute the values:

  $\begin{array}{l}\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{ =}\frac{{\text{ P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}\\ \frac{\text{0}\text{.855 atm × 3}\text{.50 L}}{\text{293 K}}\text{ =}\frac{\text{ 0}\text{.5595 atm ×8}\text{.00 L}}{{\text{T}}_{\text{2}}}\\ {\text{T}}_{\text{2}}\text{=}\frac{\text{0}\text{.5595 atm ×8}\text{.00 L×293 K}}{\text{0}\text{.855 atm × 3}\text{.50 L}}\\ {\text{T}}_{\text{2}}\text{= 438}\text{.2 K}\end{array}$

Conclusion

The combined gas equation is:

  $\frac{{\text{P}}_{\text{1}}{\text{V}}_{\text{1}}}{{\text{T}}_{\text{1}}}\text{ =}\frac{{\text{ P}}_{\text{2}}{\text{V}}_{\text{2}}}{{\text{T}}_{\text{2}}}$