How to Calculate Temperature Using Charles' Law Equation

What was the initial temperature of the carbon dioxide sample?

A 684.6 mL sample of carbon dioxide was heated to 387 K. If the volume of the carbon dioxide sample at 387 K is 933.9 mL, what was its temperature at 684.6 mL?

Answer:

The initial temperature of the carbon dioxide sample at 684.6 mL volume was 283.60 K.

Charles' Law states that the volume of a gas container with a certain amount of gas within is precisely proportional to the temperature when the pressure is constant. In this case, we can use Charles' Law equation to calculate the initial temperature of the carbon dioxide sample.

Calculation:

Given:

[tex]V_{1}[/tex] = 684.6 mL

[tex]V_{2}[/tex] = 933.9 mL

[tex]T_{2}[/tex] = 387 K

Using Charles' Law equation:

[tex]\\frac{684.6}{T_{1}} = \\frac{933.9}{387}[/tex]

[tex]T_{1} = \\frac{684.6 \times 387}{933.9}[/tex]

[tex]T_{1} = 283.60 K[/tex]

Therefore, based on the calculations using Charles' Law equation, the initial temperature of the carbon dioxide sample at 684.6 mL volume was 283.60 K.