Final answer:
Using the ideal gas law, the temperature of the ideal gas sample was calculated to be 392.45 °C. However, this temperature does not match any of the given options, indicating a possible error in the provided choices.
The correct answer is none of above.
Step-by-step explanation:
To calculate the temperature of the sample in degrees Celsius, we will use the ideal gas law which is PV = nRT, where P is pressure, V is volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin. First, we solve for T by rearranging the equation: T = PV / (nR). Here we know that P = 2.70 atm, V = 74.51 L, and n = 3.67 mol. The value of R to use is 0.0821 L·atm/(mol·K) when pressure is in atm and volume is in liters.
T = (2.70 atm * 74.51 L) / (3.67 mol * 0.0821 L·atm/(mol·K))
T = 200.577 atm·L / (0.301387 mol·K)
T = 665.6 K
To convert Kelvin to Celsius, we subtract 273.15 from the Kelvin temperature.
T in Celsius = 665.6 K - 273.15 = 392.45 °C
However, it appears there might be an error with the given options, as none of them match the calculated temperature. The correct temperature of the sample is 392.45 °C.