Skip to content

ChemistryEdu Logo Mole Concept | Calculation of Number of Moles for an Ideal Gas#

Ideal Gas Equation#

Number of moles of an ideal gas can be calculated by ideal gas equation:

\(PV = nRT\)

Here, P = Pressure
V = Volume
R = Universal Gas Constant
T = Temperature in Kelvin
n = Number of moles

Units of Pressure#

  • It should be remembered that the S.I. unit of pressure is Pascal (Pa).

Remember

  • \(1\ atm = 10^5\ Pa\)
  • \(1\ atm = 10^5\ N/m^2\)
  • \(1\ atm = 76\ cm\ of\ Hg_{(l)}\)
  • \(1\ atm = 760\ mm\ of\ Hg_{(l)}\)
  • \(1\ atm = 760\ torr\)
  • \(1\ atm ≈ 1\ bar\)

Values of R in different units#

Remember

  • \(R = 0.0821\ L\ atm\ mol^{-1}K^{-1}\)
  • \(R = 8.314\ J\ mol^{-1}K^{-1}\)
  • \(R = 2\ calorie\ mol^{-1}K^{-1}\)

Note

  • \(1\ calorie = 4.186\ Joules\)

Units of Volume#

  • It should be remembered that the S.I unit of volume is m3.

Remember

  • \(1\ cm^3 = 1\ mL\)
  • \(1\ L = 10^3\ cm^3\)
  • \(1\ L = 10^{-3}\ m^3\)

Volume Occupied by one mole of an Ideal Gas at STP#

  • STP stands for Standard Temperature and Pressure.
  • At STP, temperature is 273 K and pressure is 1 atm.
  • Using ideal gas equation, let us calculate the volume of one mole ideal gas at STP:
\[PV = nRT\]
\[V = {nRT \over P}\]
\[V = {{1 \times 0.0821 \times 273} \over {1}}\]
\[V = 22.4 L\]
  • Hence, one mole of any ideal gas(NH3, N2, O2, CO2) will occupy 22.4 L at STP.

Questions#

An ideal nitrogen gas is kept in a container of 10 litres under 1.5 atm pressure at 300 K. Calculate (a) number of moles of nitrogen gas (b) mass of nitrogen gas. Molecular mass of nitrogen = 28 u.

(a) The number of moles of ideal nitrogen gas can be calculated by ideal gas equation:

\[PV = nRT\]
\[1.5 \times 10 = n \times 0.0821 \times 300\]
\[n = {{1.5 \times 10} \over {0.0821 \times 300}}\]
\[n = {500 \over 821}\]

(b) The mass of nitrogen can be calculated by:

\[Mass = Number\ of\ moles \times molecular\ mass\]
\[Mass\ of\ N_2\ gas = {500 \over 821} \times 28\ grams\]
\[Mass\ of\ N_2\ gas = {1400 \over 821}\ grams\]

Calculate in 5.6 L ideal N2 gas at STP, (a) number of moles (b) mass.

(a) The number of moles of ideal nitrogen gas can be calculated by:

\[Moles = {5.6 \over 22.4}\]
\[Moles = 0.25\ L\]

(b) The mass of nitrogen can be calculated by:

\[Mass = Number\ of\ moles \times molecular\ mass\]
\[Mass\ of\ N_2\ gas = 0.25 \times 28\ grams\]
\[Mass\ of\ N_2\ gas = 7\ grams\]