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How do you find the density of a gas at temperature and pressure?

Published in Gas Density 3 mins read

You can determine the density of a gas at a given temperature and pressure using the ideal gas law, rearranged specifically for density. The following explains how.

Using the Ideal Gas Law for Density

The ideal gas law is typically represented as PV = nRT, where:

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

However, a form of the ideal gas law that's more useful for determining gas density is:

PV = gRT/M

where:

  • g = weight of the gas
  • M = molecular mass of the gas

From this form of the ideal gas law, we can derive the density (r) of the gas:

Density (r) is defined as mass (g) divided by volume (V) therefore r = g/V. Rearranging the ideal gas equation to isolate g/V we get:

r = g/V = PM/RT

Therefore, to find the density, you need the following information:

  • P: Pressure of the gas.
  • M: Molar mass of the gas.
  • R: Ideal gas constant (which has several values depending on the units used).
  • T: Temperature of the gas in Kelvin.

Step-by-Step Calculation

Here's how to calculate the density of a gas:

  1. Identify the given values: Determine the pressure (P), the molar mass (M) of the gas, the ideal gas constant (R), and the temperature (T) of the gas. Remember to express temperature in Kelvin (K). Convert Celsius to Kelvin by adding 273.15.
  2. Choose the correct value for R: The value of R will depend on the units used for pressure and volume:
    • If P is in Pascals and V is in cubic meters, R is 8.314 J/mol·K
    • If P is in atmospheres and V is in liters, R is 0.0821 L·atm/mol·K
  3. Apply the formula: Substitute the values into the formula: r = PM/RT.
  4. Calculate and report the density: Solve the equation to get the density of the gas. Pay close attention to the units when reporting your answer.

Example

Let's calculate the density of nitrogen gas (N2) at 27°C and 1 atmosphere.

  • P = 1 atm
  • M = 28 g/mol (molecular mass of N2)
  • R = 0.0821 L·atm/mol·K
  • T = 27°C + 273.15 = 300.15 K

r = (1 atm 28 g/mol) / (0.0821 L·atm/mol·K 300.15 K)

r = 1.14 g/L

The density of nitrogen gas under these conditions is approximately 1.14 g/L.

Key Points

  • Ideal Gas Assumption: This method assumes that the gas behaves ideally, which is a good approximation at moderate pressures and high temperatures.
  • Unit Consistency: Ensure all units are consistent when using the formula.
  • Molar Mass Importance: The molar mass of the gas is a critical factor for accurately calculating density.

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