Final answer:
Using the ideal gas law, PV=nRT, and the given values of pressure, volume, and moles, the temperature of the gas sample is calculated to be 281.08 K. After converting Kelvin to degrees Celsius, the temperature is found to be 7.93°C.
Step-by-step explanation:
To find the temperature of a sample of ideal gas given the pressure, volume, and amount in moles, we can use the ideal gas law equation: PV = nRT. Here, P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the amount of substance in moles (mol), R is the ideal gas constant (0.0821 Latm/molK), and T is the temperature in Kelvin (K).
First, we rearrange the equation to solve for T, which gives us T = PV/nR. Substituting the given values:
- P (pressure) = 2.15 atm
- V (volume) = 64.37 L
- n (moles) = 3.71 mol
And using the ideal gas constant R = 0.0821 Latm/molK:
T = (2.15 atm * 64.37 L) / (3.71 mol * 0.0821 Latm/molK) = 281.08 K
To convert from Kelvin to degrees Celsius, we use the formula °C = K - 273.15, which means:
T = 281.08 K - 273.15 = 7.93 °C
The temperature of the gas sample in degrees Celsius is 7.93°C.