Exploring the Ideal Gas Law: Calculating the Temperature of CO2 Gas

What is the temperature of a sample of CO2 gas with specific conditions?

A sample of 4.75 moles of CO2 gas is placed in a container with a volume of 0.125 L at a pressure of 0.998 atm. What is the temperature of the CO2 gas in this scenario?

Answer:

The temperature of the CO2 gas in the given scenario is -272.83 °C.

When calculating the temperature of a gas in a specific condition, we can utilize the Ideal Gas Law formula:

pV = nRT

Where:

  • p is the pressure (0.998 atm)
  • V is the volume (0.125 L)
  • n is the number of moles (4.75 mol)
  • R is the gas constant (0.082 06 L·atm·K⁻¹mol⁻¹)
  • T is the temperature (in Kelvin)

By rearranging the formula to solve for T, we get:

T = (pV)/(nR)

Substituting the given values into the formula, we find:

T = (0.998 * 0.125)/(4.75 * 0.082 06) = 0.320 K

Converting Kelvin to Celsius, we get:

T = 0.320 K - 273.15 = -272.83 °C

It's important to note that the calculated temperature of -272.83 °C is an impossible situation because CO2 solidifies at -78.5 °C. In a hypothetical scenario where CO2 behaves as an ideal gas, the temperature would be -272.83 °C as calculated.

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