 # Density of Gas Formula

## Density of gas

We can define it as the mass per unit volume of a substance under specific conditions of temperature and pressure. In addition, the density of a gas is equal to its mass divided by its volume. Moreover, you can calculate the molar mass of a substance once you know the density of a gas. Besides, the density gas varies with pressure and temperature. Learn the Density of Gas Formula here. ### Density of gas formula

The formula of the density of the gas is the same as the formula that we use to calculate the density of liquids and solids. That is:

$$\rho = \frac{m}{V}$$

Here, ‘$$\rho$$’ is the density of gas, letter ‘m’ is the mass of the object, and ‘V’ is the volume of the gas. Besides, in some cases, we can define the density as the weight per unit volume. But, this is scientifically inaccurate as this quantity is more specifically known as the specific weight of the unit.

However, we can express density in moles per liter, and the density of gas formula  they will be:

$$d = \frac {n}{V} = \frac {P}{RT} = P \left ( \frac{MW}{RT} \right )$$

### Derivation of the formula

P = refers to the pressure of the gas

V = refers to the volume of the gas

n = refers to the number of gaseous substances in moles

R = refers to the universal gas constant

T = refers to the temperature of the gas

Furthermore, the density for pure substances has the same numerical value as its mass concentration. On the other hand, different elements usually have different densities and it can be appropriate to buoyancy, packing, and purity.

### Changes in the Density

Generally, we can change the density of an element or compound by changing either the temperature or the pressure. Furthermore, increasing the pressure always increase the density of a substance. On the other hand, increasing the temperature generally decreases the density but there are certain exceptions to it.

For example, in the case of water, its density increases between its melting point at $$0^{o}C$$ and $$4^{o}C$$, also scientists have observed similar behavior in Silicon at low temperature.

### Common unit to measure densities

Generally, the SI (International System of Units) of density is kilogram per meter cube or kilogram per cubic meter ($$kg / m^{3}$$). However, the liter and metric tons are not part of the SI units, but sometimes are acceptable for use with it. This lead to units such as:

• Kilogram per liter (kg/L).
• Metric ton per cubic meter ($$t / m^{3}$$)
• Gram per millimeter (g/mL)

Besides, there are some imperial units which we use rarely in practice. But they were used earlier and we can find them in records.

## Solved Example for You

Question-1: The volume of chlorine at $$27^{o} C$$ is 564.3 mL. It has a mass of 1.607 g and torr is 740. Now calculate the density of chlorine.

Solution: Firstly, reduce the volume to the standard conditions.

$$V2 = \frac {564.3 × 273 K}{300 K} × \frac {740 torr}{760 torr}$$ = 500 mL

So, the mass of the chlorine remains unchanged

$$\frac {x}{1 mL} = \frac {1.607} {500 mL}$$

x = 0.003214 g/mL

So, the density of chlorine gas is 0.003214.

Question-2: Calculate the density of $$SO_{2}$$ gas at $$40^{o}C$$ and at 730 mmHg.

Solution: In this, the molecular weight of $$SO_{2}$$ is 64 g/mol. By putting it in the equation discussed above we can get the answer.

$$d = \frac {P(MW)}{RT}$$

$$d = \frac {730 × 64}{62.4 × 313 K}$$

d = 2.39 g/L

So the density of $$SO_{2}$$ gas is 2.39 g/L.

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