What is the molar volume of a gas
at standard temperature and pressure, to two significant figures?
This value is commonly listed as a
reference value. In this problem, we’re simply
deriving that value so we know where it comes from. If you have the molar volume of a
gas at standard temperature and pressure memorized, you can use that reference value
without doing the math shown here. But for this problem, we will carry
out the calculations. As a reminder, molar volume is the
number of liters taken up by a mole of the gas. Standard temperature and pressure
refers to a temperature of zero degrees C and a pressure of one bar. Since we want our temperature to be
in kelvin instead of degrees C, we simply add 273 to our value in degrees C to find
that temperature in kelvin.
The formula for molar volume is 𝑉
m equals 𝑉 divided by 𝑛, where 𝑉 m equals the molar volume, 𝑉 equals the volume,
and 𝑛 equals the amount in moles. However, we don’t know the volume
or the amount in moles, so we can’t carry out the calculation directly. However, we do know the pressure,
the temperature, and the value of the gas constant. If we look at the ideal gas law, we
can put 𝑉 over 𝑛 in terms of numbers that we already know to find a value for 𝑉
over 𝑛. If we use algebra and divide both
sides of the equation by 𝑃 times 𝑛, we end up with the equation 𝑉 over 𝑛 equals
𝑅𝑇 over 𝑃. We’ve grouped all of the variables
that we don’t know the value of on the left side of the equation and all the
variables that we do know the value of on the right side of the equation.
We know that the molar volume
equals 𝑉 over 𝑛. We don’t know directly the value of
𝑉 over 𝑛, but we do know that it equals 𝑅𝑇 over 𝑃, a value that we can
calculate. We wanna use the value of 𝑅 that
matches the units that we’re using, namely, liters and bars. So we wanna use the value 𝑅 equals
0.8315 liter bars per mole kelvin. If we plug our known values back
into the equation, we get 0.8315 liter bar per mole kelvin times 273 kelvin divided
by one bar. If we carry out the arithmetic, we
arrive at our final answer.
Note that if we had used the
alternate value of one atmosphere instead of one bar for the pressure at STP, we
would use a value of 𝑅 with different units, which would change our final
answer. In this case, we’ve used a value of
one bar for the pressure and calculated the molar volume of a gas at standard
temperature and pressure to be 22.7 liters per mole.