Question

A gas sample has a volume of 500 mL at 20C. At what Celsius temperature would the gas have a volume half as large?

a. 10C

b. 147C

c. -147C

d. -127C

Answer 1

By applying Charles's Law and converting temperatures to Kelvin, we find that halving the volume of gas at constant pressure from an initial temperature of 20°C results in a new temperature of -127°C.

Step-by-step explanation:

To solve this problem, we will use Charles's Law, which states that for a given mass and constant pressure, the volume of a gas is directly proportional to its temperature in kelvins. The formula is V1/T1 = V2/T2, where V is volume and T is temperature in kelvins.

First, we convert the initial temperature from Celsius to Kelvin by adding 273.15: 20°C + 273.15 = 293.15 K. Half the volume would be 500 mL / 2 = 250 mL.

Now we apply Charles's Law: (500 mL / 293.15 K) = (250 mL / T2). Solving for T2 gives us:
T2 = (250 mL * 293.15 K) / 500 mL = 146.575 K, which is approximately 147 K. Converting this back to Celsius by subtracting 273.15 gives us -127°C.