Final answer:
Using the ideal gas law and converting the pressure from torr to atmospheres, 0.746 moles of gas are required to fill a 10L container at 450K with a pressure of 2100 torr.
Step-by-step explanation:
To calculate the number of moles of gas required to fill a 10L container at 450K with a pressure of 2100 torr, we can use the ideal gas law equation PV = nRT. First, we need to convert the pressure from torr to atmospheres because the gas constant (R) value typically used is in liters·atm/(mol·K). There are 760 torr in one atmosphere, so 2100 torr is equal to 2100 torr / 760 torr/atm = 2.76316 atm.
Next, we can solve for 'n' (number of moles) using the rearranged ideal gas law formula: n = PV / RT. We need the gas constant R, which is 0.0821 L·atm/(mol·K).
Using these values:
n = (2.76316 atm × 10 L) / (0.0821 L·atm/(mol·K) × 450 K) = 0.746 moles of gas
Therefore, 0.746 moles of gas would be required to fill a 10L container at 450K with a pressure of 2100 torr.