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.