Gas Density Calculator, Formula, Gas Density Calculation

Gas Density Calculator:

Enter the values of pressure, P_(Pa), molar mass, M_(kg/mol), universal gas constant, R_(J/mol.K) and temperature, T_(K) to determine the value of Density of a gas, d_(kg/m3).

Gas Density Formula:

Gas density is the measure of the mass of gas per unit volume, typically expressed in kilograms per cubic metre. It reflects how much mass is contained in a given volume of gas. Factors such as pressure, temperature, and molecular mass of the gas influence its density.

Higher pressure increases density, while higher temperature decreases density. The density of a gas can be determined using the Ideal Gas Law, which relates pressure, volume, temperature, and the number of moles of gas.

Pressure – the force exerted by the gas molecules on the container walls. Higher pressure signifies more molecules crammed into the space, increasing density.

Molar mass – the mass of one mole of the gas. Different gases have different molar masses.

Gas constant – a universal constant relating pressure, volume, and temperature for ideal gases.

Temperature – the average kinetic energy of the gas molecules. Higher temperature often leads to lower density as the gas molecules move faster and spread out more.

Density of a gas, d_(kg/m3) in kilograms per cubic metres is calculated by multiplying the pressure, P_(Pa) in Pascals by the molar mass, M_(kg/mol) in kilograms per mole and then dividing by the product of the universal gas constant, R_(J/mol.K) in joules per mole Kelvin and the temperature, T_(K) in Kelvin.

Density of a gas, d_(kg/m3) = P_(Pa) * M_(kg/mol) / R_(J/mol.K) * T_(K)

d_(kg/m3) = density of gas in kilograms per cubic metres, kg/m³.

P_(Pa) = pressure in Pascals, Pa.

M_(kg/mol) = molar mass in kilograms per mole, kg/mol.

R_(J/mol.K) = universal gas constant in joules per mole Kelvin, J/mol.K.

T_(K) = temperature in Kelvin, K.

Gas Density Calculation:

1. A gas is kept at a pressure of 101325 Pa (1 atm) and a temperature of 298 K . The molar mass of the gas is 0.02896 kg/mol (air). Calculate the density of the gas.

Given: P_(Pa) = 101325Pa, M_(kg/mol) = 0.02896kg/mol,  R_(J/mol.K) = 8.314J/mol.K, T_(K) = 298K.

Density of a gas, d_(kg/m3) = P_(Pa) * M_(kg/mol) / R_(J/mol.K) * T_(K)

d_(kg/m3) = 101325 * 0.02896 / 8.314 * 298

d_(kg/m3) = 2934.86 / 2476.972

d_(kg/m3) = 1.184kg/m³.

2. A gas with a molar mass of 0.044 kg/mol (CO₂) is at a temperature of 350 K. Its density is measured to be 1.98 kg/m³. Calculate the pressure of the gas.

Given: d_(kg/m3) = 1.98kg/m³, M_(kg/mol) = 0.044kg/mol,  R_(J/mol.K) = 8.314J/mol.K,

T_(K) = 350K.

Density of a gas, d_(kg/m3) = P_(Pa) * M_(kg/mol) / R_(J/mol.K) * T_(K)

P_(Pa) = d_(kg/m3) * R_(J/mol.K) * T_(K) / M_(kg/mol)

P_(Pa) = 1.98 * 8.314 * 350 / 0.044

P_(Pa) = 5782.452 / 0.044

P_(Pa) =  131420.27Pa.

Gas Density and Molar Mass Formula, Examples, and Practice Problems