Final answer:
To calculate the temperature of the gas in kelvins, we apply the ideal gas law PV = nRT using the given pressure, volume, and moles of the gas along with the proper gas constant for kPa. Rearrange the formula to solve for T and insert the values to obtain the temperature.
Step-by-step explanation:
The question asks for the temperature of a gas in kelvins using the ideal gas law. Given are the pressure of a 5.6631 mol sample of O2 (673.95 kPa), and the volume of the container (80.452 L). To find the temperature, we will use the ideal gas equation PV = nRT, where P is pressure, V is volume, n is number of moles of the gas, R is the gas constant, and T is temperature.
We need to use the R value that corresponds with the pressure unit kPa, which is approximately 8.314 kPa·L/mol·K. Rearranging the ideal gas equation to solve for T gives us T = PV/(nR). Substituting the given values into this equation yields:
T = (673.95 kPa × 80.452 L) / (5.6631 mol × 8.314 kPa·L/mol·K)
Performing the calculation provides us with the temperature in Kelvin.