Final answer:
To find the volume that 5.21 mol of a gas would occupy under the same conditions of 44 °C and 793 torr, one can use the proportionality of moles to volume. When calculated, 5.21 mol of the gas would occupy approximately 90.6 liters.
Step-by-step explanation:
The question provided is related to the Ideal Gas Law, which is an important concept in chemistry. Using the conditions provided of 44 °C and 793 torr for 3.21 mol occupying 56.2 L, we can calculate the volume of 5.21 mol under the same conditions. To solve this, we can use the direct proportionality of moles and volume at constant temperature and pressure, as stated by Avogadro's hypothesis.
First, we need to convert the pressure to atmospheres since the volume of 1 mol of an ideal gas at STP (0 °C and 1 atm) is 22.4 L. With 793 torr, we have 793 torr / 760 torr/atm = 1.0434 atm. Since the initial conditions are not at STP, we cannot directly use the 22.4 L molar volume.
Using the proportionality, we can say that if 3.21 mol occupies 56.2 L, then 5.21 mol will occupy X L. Setting up the proportion, (3.21 mol / 56.2 L) = (5.21 mol / X L), solving this for X gives us the volume that 5.21 mol would occupy under the given conditions. Let's not forget to include our example calculation of, 2.44 atm x 4.01 L / 1.93 atm is equal to 5.07 L, to underline the direct relationship between pressure, volume, and the amount in moles.
Upon solving, X is found to be approximately 90.6 L. Therefore, 5.21 mol of this gas under the given conditions of 44 °C and 793 torr would occupy a volume of about 90.6 liters.