Question

Hydrogen gas is at a temperature of -45.°C when it occupies a volume of 2.7 liters. To what temperature Celsius should it be raised to occupy a volume of 42.0 liters, and the pressure remains the same?

Answer 1

To occupy a volume of 42.0 liters with the pressure remaining the same, the hydrogen gas should be raised to a temperature of -233.33 °C.

Step-by-step explanation:

The relationship between the temperature, volume, and pressure of a gas is described by the combined gas law. The formula for the combined gas law is:

p1V1 / T1 = p2V2 / T2

In this case, the initial temperature is -45.°C and the initial volume is 2.7 liters. The final volume is given as 42.0 liters and the pressure remains the same. To find the final temperature, we need to solve for T2:

p1V1 / T1 = p2V2 / T2

Using the given values, we have:

T2 = (p2V2 * T1) / (p1V1)

Substituting the values into the formula:

T2 = (1 * 42.0 * (-45.)) / (1 * 2.7)

T2 = -630.0 / 2.7 = -233.33 °C

Therefore, the hydrogen gas should be raised to a temperature of -233.33 °C to occupy a volume of 42.0 liters, assuming the pressure remains the same.