Answer:
T = 362.2°C.
Step-by-step explanation:
We can use the Ideal Gas Law to solve this problem, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
First, we need to convert the given pressure of 2000 mmHg to atm. We have:
P = 2000 mmHg = 2000/760 atm = 2.63 atm (rounded to two decimal places)
Next, we can plug in the values of the given pressure, volume, gas constant, and number of moles into the Ideal Gas Law and solve for T:
PV = nRT
T = PV / nR
T = (2.63 atm) x (50 L) / [(5 mol) x (0.08206 L•atm/mol•K)]
T = 635.2 K
Finally, we need to convert the temperature from Kelvin to Celsius:
T = 635.2 K - 273 = 362.2°C
Therefore, the temperature is 362.2°C.