Chapter 13, Problem 63A

Interpretation Introduction

Interpretation:

The volume of the balloon on the bases of the given information is to be calculated.

Concept introduction:

The ideal gas equation for one mole gas is written as

  $PV=nRT$

P = pressure of the gas

V = volume of the gas

R= gas constant

T = temperature of the gas

And,

n is the number of moles.

Answer to Problem 63A

The volume of the balloon is $\text{3}\text{L}$ .

Explanation of Solution

Given information:

Initial temperature, ( T₁ ) = $\text{23°C}$

The initial temperature in K= $\text{23+273}\text{=}\text{296K}$

Final temperature ( T₂ ) = $\text{-31°C}$

Or, in Kelvin = $\text{-31+273 =}\text{242K}$

Initial volume ( V₁ ) = $\text{1L}$

Initial pressure ( P₁ ) = $\text{1atm}$

Final pressure ( P₂ ) = $\text{220}\text{torr}$

Final pressure in atmospheric pressure = $\frac{\text{220}}{\text{760}}\text{=}\text{0}\text{.289}\text{=}\text{0}\text{.23}\text{atm}$

Calculation:

According to ideal gas law,

  $\begin{array}{c}\frac{P_1{V}_1}{T_1}=\frac{P_2{V}_2}{T_2}\\ V_2=\frac{P_1{V}_1{T}_2}{P_2{T}_1}\\ \text{=}\frac{\text{1×1×242}}{\text{0}\text{.29×296}}\\ V_2\text{=}\text{2}\text{.82}\\ V_2\text{=3L}\end{array}$

Conclusion

Balloon consists $\text{3}\text{L}$ .