Video Transcript
Under standard temperature and
pressure, STP, a gas occupies a volume of two liters. How many moles of gas molecules are
there? Give your answer to two decimal
places.
Avogadro’s law states that at
constant temperature and pressure, the volume and number of moles of a gas are
directly proportional. This proportion can be expressed by
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, a proportionality
constant that indicates the volume occupied by one mole of gas at a specific
temperature and pressure. Molar gas volume has the unit of
liters per mole. In this question, the gas is under
standard temperature and pressure, abbreviated STP. Standard temperature and pressure
are zero degrees Celsius and one atmosphere, respectively. At STP, one mole of any gas will
occupy a volume of 22.4 liters and have a molar gas volume of 22.4 liters per
mol.
Looking at the question, we see
that the gas occupies a volume of two liters, and we want to determine how many
moles of gas molecules there are. We also know that as the gas is
under standard temperature and pressure, we can use 22.4 liters per mol as the molar
gas volume. We can then substitute the volume
and molar gas volume into the equation and rearrange to solve for the number of
moles. We perform the calculation and
determine that the number of moles is equal to 0.08928 moles. But the question asked us to give
our answer to two decimal places. Rounding appropriately, we have
determined that there are 0.09 moles of gas molecules in two liters of gas under
standard temperature and pressure.
