Question

3) A child has a toy balloon with a volume of 1.8 liters. The temperature of the balloon when it was filled was 22° C and the pressure was 1.0 atm. If the child were to let go of the balloon and it rose into the sky where the pressure is 0.86 atm and the temperature is 8° C, what would the new volume of the balloon be?​

Answer 1

This is a combined gas law problem, according to which

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

where P is the pressure of the gas, V is the volume of the gas, and T is the temperature of the gas, and the subscripts 1 and 2 correspond to the initial and final conditions of the gas. In this problem, we are given the initial pressure, volume, and temperature of the gas in the balloon:

P₁ = 1.0 atm

V₁ = 1.8 L

T₁ = 295.15 K (K = °C + 273.15).

Moreover, we are given the final pressure and temperature of the gas in the balloon.

P₂ = 0.86 atm

T₂ = 281.15 K.

What we want to find is the final volume, V₂, which we can obtain by rearranging the combined gas equation to solve for V₂:

$V_2=\frac{P_1V_1T_2}{T_1P_2} = \frac{(1.0 \text{ atm})(1.8 \text{ L})(281.15 \text{ K})}{(295.15 \text{ K})(0.86 \text{ atm})} \\ V_2 = 1.99 \text{ L}$

This answer has three significant figures. However, the question as written would warrant an answer that comprises one significant figure (as 8 °C has only one sig fig). In that case, the answer would be 2 L. If the answer is to be given to two significant figures, the volume would then be 2.0 L.