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How to Calculate Molar Mass of a Gas Given Density, Temperature, and Pressure?

Published in Chemistry Calculations 2 mins read

You can calculate the molar mass of a gas using the ideal gas law and a modified formula incorporating density. Here's how:

Deriving the Formula

We start with the Ideal Gas Law:

PV = nRT

Where:

  • P = Pressure
  • V = Volume
  • n = Number of moles
  • R = Ideal gas constant
  • T = Temperature

We also know that:

n = m / M

Where:

  • m = mass
  • M = Molar mass

And density (ρ) is:

ρ = m / V

Substituting n = m/M into the Ideal Gas Law gives:

PV = (m/M)RT

Rearranging to solve for M (Molar mass):

M = (mRT) / PV

Now, substitute ρ = m/V into the equation. This gives us m = ρV

M = (ρVRT) / PV

The Volumes cancel out, resulting in the formula for molar mass:

M = (ρRT) / P

Where:

  • M = Molar mass
  • ρ = Density
  • R = Ideal gas constant (0.0821 L·atm/mol·K or 8.314 J/mol·K, depending on the units of P, V, and ρ)
  • T = Temperature (in Kelvin)
  • P = Pressure (in atm or Pa, depending on the value of R)

Steps for Calculation:

  1. Identify the given values: Density (ρ), Temperature (T), and Pressure (P). Ensure the units are consistent with the value of R you intend to use.
  2. Choose the appropriate value for the Ideal Gas Constant (R):
    • If Pressure is in atmospheres (atm), Volume is in liters (L), and Density is in g/L, use R = 0.0821 L·atm/mol·K.
    • If Pressure is in Pascals (Pa), Volume is in cubic meters (m3), and Density is in kg/m3, use R = 8.314 J/mol·K.
  3. Convert Temperature to Kelvin: K = °C + 273.15
  4. Plug the values into the formula: M = (ρRT) / P
  5. Calculate the Molar Mass (M). The units will be g/mol.

Example:

Let's say we have a gas with:

  • Density (ρ) = 2.1 g/L
  • Temperature (T) = 273 K
  • Pressure (P) = 1 atm

Using R = 0.0821 L·atm/mol·K:

M = (2.1 g/L 0.0821 L·atm/mol·K 273 K) / 1 atm
M ≈ 47.0 g/mol

Therefore, the molar mass of the gas is approximately 47.0 g/mol.

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