Question

A gas has a volume of 2.50L. When the sample is cooled in ice water at T = 0.00 Celcius, the volume decreases to 2.45 L. What was the initial temperature of the gas?

Answer 1

Answer on Question#40043-Chemistry-Other

Question

A gas has a volume of 2.50 L. When the sample is cooled in ice water at T = 0.00 Celcius, the volume decreases to 2.45 L. What was the initial temperature of the gas?

Solution

According to the combined gas law or general gas equation:

$$\frac {p _ {1} V _ {1}}{T _ {1}} = \frac {p _ {2} V _ {2}}{T _ {2}}$$

It is given that $V_{1} = 2.50 \, \text{L}$, $V_{2} = 2.45 \, \text{L}$, $T_{2} = 0.00{}^{\circ} \text{C} = 273.15 \, \text{K}$.

Since the other is not specified, we can assume $p_1 = p_2$ and thus:

$$\frac {V _ {1}}{T _ {1}} = \frac {V _ {2}}{T _ {2}}$$

Hence

$$T _ {1} = \frac {T _ {2} V _ {1}}{V _ {2}} = \frac {273.15 \cdot 2.50}{2.45} = 278.72 \, \text{K}$$

Answer: 278.72 K