Question 10.2.2: A sample of gas has a volume of 2.48 L at a temperature of 5......
A sample of gas has a volume of 2.48 L at a temperature of 58.0 ºC. The gas sample is cooled to a temperature of -5.00 ºC (assume pressure and amount of gas are held constant). Predict whether the new volume is greater or less than the original volume, and calculate the new volume.
You are asked to calculate the volume of a gas sample when only the temperature is changed.
You are given the original volume and temperature and the new temperature of the gas sample.
According to Charles’s law, temperature and volume are directly related when the pressure and amount of gas are held constant. In this case, the temperature decreases from 58.00 ºC to -5.00 ºC, so the volume should also decrease. It will be less than the original volume.
To calculate the new volume, first make a table of the known and unknown volume and temperature data. In this case, the initial volume and temperature and the new temperature are known and the new volume must be calculated. Note that all temperature data must be in kelvin temperature units.
V_{1} = 2.48 L V_{2} = ?
T_{1} = 58.00 ºC + 273.15 = 331.15 K T_{2} = – 5.00 ºC + 273.15 = 268.15 K
Rearrange Charles’s law to solve for V_{2}, and calculate the new volume of the gas sample.
\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}
V_{2} = \frac{V_{1}T_{2}}{T_{1}}=\frac{\left(2.48\text{ L}\right) \left(268.15\text{ K}\right) }{331.15\text{ K}} = 2.01 L
The temperature units (K) cancel, leaving volume in units of liters.
Is your answer reasonable? The final volume is less than the initial volume, as we predicted