# Problem: A balloon is filled to a volume of 7.00 x 102 mL at a temperature of 20.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 x 102 K. What is the final volume of the balloon?

###### FREE Expert Solution

For this problem, we have to determine the final volume of the balloon at 1.00 x 102 K

Recall that the ideal gas law is:

$\overline{){\mathbf{PV}}{\mathbf{=}}{\mathbf{nRT}}}$

The pressure and volume of a gas are related to the number of moles, gas constant and temperatureThe value nRT is constant

Therefore, the initial and final pressure and volume of the gas are related by Charles' Law:

$\overline{)\frac{{\mathbf{T}}_{\mathbf{1}}}{{\mathbf{V}}_{\mathbf{1}}}{\mathbf{=}}\frac{{\mathbf{T}}_{\mathbf{2}}}{{\mathbf{V}}_{\mathbf{2}}}}$

The given values are:

T1 = 20°C + 273.15 = 293.15 K              T2 = 1.00 x 102 K

V1 = 7.00 x 102 mL                                             V2 = ??

We can rearrange the combined gas law to solve for V2:

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###### Problem Details

A balloon is filled to a volume of 7.00 x 102 mL at a temperature of 20.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 x 102 K. What is the final volume of the balloon?