A Sample of Gas at STP: Calculating Temperature in °C

A sample of gas occupies 30.0 liters at STP. What will be its temperature in °C if the volume is reduced to 22.5 liters under 3.50 atmospheres pressure?

Final answer:

To calculate the temperature in °C of a gas when its volume is reduced from 30.0 liters at STP to 22.5 liters under a pressure of 3.50 atmospheres, the combined gas law is used, followed by converting the temperature from kelvins to °C.

Explanation:

The student asks how to find the temperature in °C of a gas sample when the volume is reduced from 30.0 liters at STP to 22.5 liters under a pressure of 3.50 atmospheres. Standard temperature and pressure (STP) are defined as 0°C (273 K) and 1 atmosphere. To solve this, one could use the combined gas law:

P₁ * V₁ / T₁ = P₂ * V₂ / T₂

However, since we need to find the final temperature in degree Celsius, it's easier to first find the temperature in kelvins and then convert it to °C:

The combined gas law rearranged to solve for T₂ (the final temperature in kelvins) is:

T₂ = (P₂ * V₂ * T₁) / (P₁ * V₁)

Plugging in the values:

T₂ = (3.50 atm * 22.5 L * 273 K) / (1.00 atm * 30.0 L) = (857.25 atm·L·K) / (30.0 atm·L) = 28.575 K

Finally, to convert from kelvins to degrees Celsius, subtract 273:

T₂ in °C = 28.575 K - 273 = -244.425°C

This is the final temperature of the gas in degrees Celsius when its volume is 22.5 liters under a pressure of 3.50 atmospheres.