Final answer:
Using the Ideal Gas Law, PV = nRT, and converting the pressure from torr to atm, the volume of the container that holds 17.79 moles of gas at a pressure of 69.12 torr and temperature of 329.1 K is found to be approximately 52404.7 liters.
Step-by-step explanation:
To find the volume of the container that the gas is in, we can use the Ideal Gas Law, which is PV = nRT. Here, P represents the pressure of the gas, V is the volume we need to find, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvins. The pressure needs to be converted from torr to atmospheres (atm) since the ideal gas constant is usually given in L atm/(mol K). Then we can solve for V by rearranging the equation to V = nRT/P.
First, let's convert the pressure from torr to atm by using the conversion factor 1 atm = 760 torr. So, 69.12 torr is equivalent to 69.12 torr × (1 atm / 760 torr) = 0.0910 atm. Now that we have all the necessary values in proper units, we can plug them into the Ideal Gas Law equation:
V = (17.79 moles × 0.0821 L atm/(mol K) × 329.1 K) / 0.0910 atm
After calculating the values, we find that the volume of the container is approximately 52404.7 Liters.