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Density Of An Ideal Gas

Ideal Gas Law Example Problem

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Most of the time, the Ideal Gas Law can be used to make calculations for real gases.

Most of the time, the Ideal Gas Law can be used to make calculations for real gases.

Ben Edwards, Getty Images

The ideal gas law can be manipulated to find the density of a gas if the molecular mass is known.

Problem:

What is the density of a gas with molar mass 100 g/mol at 0.5 atm and 27 °C?

Solution:

First, start with the ideal gas law:

PV = nRT

where
P = pressure
V = volume
n = number of moles of gas
R = gas constant = 0.0821 L·atm/mol·K
T = absolute temperature

To find the density, we need to find the mass of the gas and the volume. First, find the volume. Solve the equation for V.

V = nRT/P

Second, find the mass. The number of moles is the place to start. The number of moles is the mass (m) of the gas divided by its molecular mass (MM).

n = m/MM

Substitute this into the volume equation for n.

V = mRT/MM·P

Density (ρ) is mass per volume. Divide both sides by m.

V/m = RT/MM·P

Invert the equation.

m/V = MM·P/RT

ρ = MM·P/RT

Plug in the given information:

Remember to use absolute temperature for T: 27 °C + 273 = 300 K

ρ = (100 g/mol)(0.5 atm)/(0.0821 L·atm/mol·K)(300 K) ρ = 2.03 g/L

Answer:

The density of the gas is 2.03 g/L at 0.5 atm and 27 °C.

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