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Molar Gas Volume

Key Concepts

1 mole of a gas occupies a specific volume at a particular temperature and pressure.
This is known as the molar volume and given the symbol V_m
The units most commonly used for molar volume, V_m, are litres per mole, L mol^-1

Examples of molar gas volume (V_m) for ideal gases:

Temperature Pressure Molar Volume

^oC (K) kPa (atm) (V_m) / L mol^-1

0^oC (273.15K) 100kPa (0.987 atm) 22.71

25^oC (298.15 K) 100 kPa (0.987 atm) 24.79

0^oC (273.15K) and 100kPa (0.987 atm) is known as Standard Temperature and Pressure and is often abbreviated to STP ^*
25^oC (298.15 K) and 100 kPa (0.987 atm) is sometimes referred to as Standard Ambient Temperature and Pressure, SATP, or even as Standard Laboratory Conditions, SLC.^**

Calculations involving molar gas volumes:
n(gas) = moles of gas
V(gas) = volume of gas
V_m = molar gas volume (at some specified temperature and pressure)
n(gas) = V(gas) / V_m
or
V(gas) = n(gas) x V_m

Example : Calculating Moles of Gas

1. A sample of pure helium gas occupies a volume of 6.8 L at 0^oC and 100 kPa.
How many moles of helium gas are persent in the sample?

Extract the data from the question:
V(He) = 6.8 L
V_m = 22.71 L mol^-1 (at STP 1 mole of gas occupies 22.71 L)
n(He) = ? mol
Check for consistency in units, are all the volumes in the same units?
V(He) is given in L
V_m is given in L (mol^-1)
Both volumes are in the same units, L, so no conversion is necessary.
Write the equation:
n(He) = V(He) / V_m
Substitute the values into the equation and solve:
n(He) = 6.8 / 22.71 = 0.3 L

2 A sample of nitrogen gas, N_2(g), has a volume of 956 mL at 273.15K and 100kPa.
How many moles of nitrogen gas are present in the sample?

Extract the data from the question:
V(N₂) = 956 mL
V_m = 22.71 L mol^-1 (at STP 1 mole of gas occupies 22.71 L)
n(N₂) = ? mol
Check for consistency in units, are all the volumes in the same units?
V(N₂) is given in mL
V_m is given in L (mol^-1)
Convert the gas volume, V(N₂), from a volume in millilitres, mL, to a volume in litres, L.
V(N₂) = 956 mL = 956 x 10^-3 L
Write the equation:
n(N₂) = V(N₂) / V_m
Substitute the values into the equation and solve:
n(N₂) = 956 x 10^-3 / 22.71 = 0.04 L

Example : Calculating Volume of Gas

1. A balloon contains 0.5 moles of pure helium gas at standard temperature and pressure.
What is the volume of the balloon?

Extract the data from the question:
n(He) = 0.5 mol
V_m = 22.71 L mol^-1 (at STP 1 mole of gas occupies 22.71 L)
V(He) = ? L
Write the equation:
V(He) = n(He) x V_m
Substitute in the values and solve:
V(He) = 0.5 x 22.71 = 11.4 L

2. What is the volume occupied by 3.7 moles of N_2(g) at STP?

Extract the data from the question:
n(N₂) = 3.7 mol
V_m = 22.71 L mol^-1 (at STP 1 mole of gas occupies 22.71 L)
V(N₂) = ? L
Write the equation:
V(N₂) = n(N₂) x V_m
Substitute in the values and solve:
V(N₂) = 3.7 x 22.71 = 84.0 L

Practice Questions

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^* Prior to 1982, standard temperature and pressure were defined as 0^oC (273.15 K) and 1 atm (101.3 kPa), so 1 mole of gas would occupy 22.41 L
^**At 25^oC (298.15 K) and 1 atm (101.3 kPa), 1 mole of gas occupies 24.47 L.

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