Density Of Gas Formula: Definition, Equation, Solved Examples

Density Of Gas Formula : Gas density refers to the mass per unit volume of a substance, and it is influenced by specific conditions of temperature and pressure. To calculate the density of a gas, you simply divide its mass by its volume. Once you know the density of the gas, you can further determine the molar mass of the substance. It’s important to note that gas density can vary with changes in temperature and pressure.

Density Of Gas Formula

Mathematically, the formula for gas density is expressed as:

Where:

Density of Gas is the density in kilograms per liter (Kg/l)

Molar Mass (M) is in grams per mole (g/mol)

Pressure (P) is in atmospheres (atm)

Universal Gas Constant (R) is approximately 8.32 Joules per mole-kelvin (Joule)

Temperature (T) is in Kelvin (K)

Also Check – Gibbs Free Energy Formula

Density Of Gas Formula Solved Examples

Example 1: Calculate the density of a gas at 40°C, with a pressure of 5 atm, and a molar mass of 80.15 g/mol.

Solution:

Given:

Molar Mass (M) = 80.15 g/mol

Pressure (P) = 5 atm

Temperature (T) = 40°C = 313.15 K (convert to Kelvin)

Universal Gas Constant (R) ≈ 8.32 Joule

Using the Density of Gas formula:

Density of Gas = (80.15 g/mol * 5 atm) / (8.32 Joule * 313.15 K)

Density of Gas ≈ (400.75 g*atm) / (2612.48 J)

Density of Gas ≈ 0.1532 Kg/l

So, the density of the gas at these conditions is approximately 0.1532 kilograms per liter (Kg/l).

Also Check – Percentage Yield Formula

Example 2: How can you determine the density of a gas sample, considering factors like its molar mass, pressure, and temperature?

Suppose you have a gas with a molar mass (M) of 32.00 g/mol, it’s subjected to a pressure (P) of 3.5 atmospheres (atm), and its temperature (T) is 298.15 Kelvin (K). How would you use the ideal gas density formula to calculate the gas density in kilograms per liter (Kg/l)?

Ideal Gas Density Formula:

Given Values:

Molar Mass (M) = 32.00 g/mol

Pressure (P) = 3.5 atm

Temperature (T) = 298.15 K

Universal Gas Constant (R) ≈ 8.32 Joule

Now, let’s Put these values into the formula to calculate the gas density:

Density of Gas = (32.00 g/mol * 3.5 atm) / (8.32 Joule * 298.15 K)

Density of Gas ≈ (112.00 g*atm) / (2477.04 J)

Density of Gas ≈ 0.0452 Kg/l

So, the density of this gas sample at the specified conditions is approximately 0.0452 kilograms per liter (Kg/l).

Also Check – Percent by Weight Formula

Example 3: Calculating Gas Density at Standard Temperature and Pressure (STP)

Suppose you have a gas sample at standard temperature and pressure (STP), where the temperature (T) is 273.15 Kelvin (0°C) and the pressure (P) is 1 atmosphere (atm). Let’s say the gas has a molar mass (M) of 28.97 g/mol. Calculate the density of this gas.

Given Values:

Molar Mass (M) = 28.97 g/mol

Pressure (P) = 1 atm

Temperature (T) = 273.15 K

Universal Gas Constant (R) ≈ 8.32 Joule

Using the ideal gas density formula:

Density of Gas = (28.97 g/mol * 1 atm) / (8.32 Joule * 273.15 K)

Density of Gas ≈ (28.97 g*atm) / (2269.57 J)

Density of Gas ≈ 0.0128 Kg/l

So, at standard temperature and pressure (STP), the density of the gas is approximately 0.0128 kilograms per liter (Kg/l).

Also Check – Partial Pressure Formula

Example 4: Calculating Gas Density at Elevated Temperature and Pressure

Consider a gas with a molar mass (M) of 44.01 g/mol, experiencing a pressure (P) of 10 atmospheres (atm), and a temperature (T) of 400 Kelvin (127°C). Determine the gas density under these conditions.

Given Values:

Molar Mass (M) = 44.01 g/mol

Pressure (P) = 10 atm

Temperature (T) = 400 K

Universal Gas Constant (R) ≈ 8.32 Joule

Using the ideal gas density formula:

Density of Gas = (44.01 g/mol * 10 atm) / (8.32 Joule * 400 K)

Density of Gas ≈ (440.1 g*atm) / (3328 J)

Density of Gas ≈ 0.1321 Kg/l

So, at the given elevated temperature and pressure, the density of the gas is approximately 0.1321 kilograms per liter (Kg/l).

These examples demonstrate how to calculate gas density under different conditions using the ideal gas density formula, taking into account molar mass, pressure, and temperature. Gas density calculations are essential in various scientific and industrial applications, such as chemistry, engineering, and environmental studies.