Chapter U3, Problem 12STP

Interpretation Introduction

Interpretation:

The new volume of the balloon as it transitions from an initial volume of 0.75 L and pressure of 1.0 atm to a final pressure of 0.50 atm needs to be calculated.

Concept introduction:

The relation between volume (V) and pressure (P) of a gas under temperature is represented through Boyles Law.

As per Boyles law, pressure is inversely related to volume:

$\begin{array}{l}\text{P α }\frac{\text{1}}{\text{V}}\text{ i}\text{.e}\text{. P = k}\times \frac{\text{1}}{\text{T}}\\ \text{where k is a proportionality constant}\\ {\text{(or) P}}_{\text{1}}{\text{V}}_{\text{1}}{\text{ = P}}_{\text{2}}{\text{V}}_{\text{2}}\text{ -----(1)}\end{array}$

Answer to Problem 12STP

(D) 1.5 L

Explanation of Solution

Given Information:

Initial volume of balloon, V₁ = 0.75 L

Initial pressure, P₁ = 1 atm

Final pressure, P₂ = 0.5 atm

Calculation:

Let V₂ represent the final volume of the balloon

Based on equation (1):

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

$\begin{array}{l}{\text{V}}_2=\frac{{\text{P}}_{\text{1}}{\text{×V}}_{\text{1}}}{{\text{P}}_{\text{2}}}\\ \text{=}\frac{\text{1}\text{.0 atm ×0}\text{.75 L}}{\text{0}\text{.5 atm}}=1.5\text{ L}\end{array}$

Conclusion

The volume of balloon at a final pressureof 0.5 atm is 1.5 L.