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 𝑚, where 𝑉 is the volume in liters, 𝑛 is
the number of moles, and 𝑉 subscript 𝑚 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 𝑚 divided by capital 𝑀, where 𝑛 is the number of
moles, lowercase 𝑚 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.