Question Video: Calculating the Volume of Ammonia Gas at STP Given the Mass Chemistry

What volume would 8.5 g of NH₃ gas occupy at standard temperature and pressure (STP) taking the molar gas volume to be 22.4 L/mol? Give your answer in units of liters. [N = 14 g/mol. H = 1 g/mol].

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Video Transcript

What volume would 8.5 grams of NH3 gas occupy at standard temperature and pressure, STP, taking the molar gas volume to be 22.4 liters per mole? Give your answer in units of liters. N equals 14 grams per mole. H equals one gram per mole.

Molar gas volume is a proportionality constant that relates the volume and number of moles of a gas via the equation 𝑉 equals 𝑛𝑉 subscript π‘š, where 𝑉 is the volume in liters, 𝑛 is the number of moles, and 𝑉 subscript π‘š is the molar gas volume. The molar gas volume indicates the volume occupied by one mole of gas at a specific temperature and pressure. In this question, the NH3 gas is at standard temperature and pressure, abbreviated as STP. Standard temperature and pressure are zero degrees Celsius and one atmosphere, respectively. We are told that the molar gas volume at STP is 22.4 liters per mole. This means that one mole of gas at standard temperature and pressure will occupy a volume of 22.4 liters.

The question asked us to determine a volume of gas given a mass and the molar gas volume. As the problem did not provide the number of moles of gas, we will need to convert the mass of NH3 into moles of NH3. This can be accomplished by using the equation 𝑛 equals lowercase π‘š divided by capital 𝑀, where 𝑛 is the number of moles, lowercase π‘š is the mass in grams, and capital 𝑀 is the molar mass in grams per mole. The mass was provided in the question, but we will need to determine the molar mass of ammonia, NH3.

The molar mass of ammonia can be calculated by summing the average molar masses of the constituent atoms, which were provided in the question. We need to multiply the average molar mass of hydrogen by three as there are three atoms of hydrogen in each molecule of ammonia. We perform the calculation and determine the molar mass of ammonia to be 17 grams per mole. We can then substitute the mass given in the question and the molar mass into the equation to determine the number of moles of ammonia to be 0.5 moles.

Now that we know the number of moles and the molar gas volume, we are ready to solve for the volume. We substitute the value we determined for the number of moles and the molar gas volume given in the question into the equation. We perform the calculation and determine the volume to be 11.2 liters.

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