### Video Transcript

At standard temperature and pressure, STP, a sample of SO2 occupies a volume of 2.5 liters. How many moles of SO2 are present in this sample? Take the molar gas volume to be 22.4 liters per mole and give your answer to two decimal places.

To answer this question, we need to relate the volume of SO2, a gas, to the number of moles of gas. We are given the molar gas volume. Molar gas volume, given the symbol ๐ subscript ๐, is a proportionality constant that relates the volume and number of moles of a gas. It indicates the volume occupied by one mole of a gas at a specific temperature and pressure.

In the question, the gas is at standard temperature and pressure, which are zero degrees Celsius and one atmosphere. Under these conditions, the molar gas volume is 22.4 liters per mole. This means that at zero degrees Celsius and one atmosphere, one mole of SO2 gas will occupy a volume of 22.4 liters. But we want to know how many moles of SO2 gas will occupy a volume of 2.5 liters.

Avogadroโs law tells us that the volume and number of moles of a gas are directly proportional at a constant temperature and pressure. So one way to solve this problem is to set up a proportion. We can set one mole of gas per 22.4 liters equal to ๐ฅ moles per 2.5 liters. We can then multiply both sides of the equation by 2.5 liters. The unit liters will cancel, leaving us with the unit moles. Performing the calculation gives us an answer of 0.1116 moles.

Another way to arrive at this answer is to use the equation ๐ equals ๐๐ ๐, where ๐ is the volume in liters, ๐ is the amount of gas in moles, and ๐ ๐ is the molar gas volume in liters per mole. Using this equation, we can substitute the volume and molar gas volume given in the question. We then divide both sides of the equation by 22.4 liters per mole. The liter units cancel, leaving us with the unit moles. Performing the calculation gives us the same answer, 0.1116 moles. The question tells us to round our answer to two decimal places. So the number of moles of SO2 present in a sample that occupies a volume of 2.5 liters at STP is 0.11 moles.