Calculating Ideal Gas Law

The Ideal Gas Law Calculator finds the unknown variable in the equation PV = nRT when three of the variables are known.

Ideal Gas Law Formula

The ideal gas law formula states that pressure multiplied by volume is equal to moles times the universal gas constant times temperature.

P V = n R T

where:

P = pressure
V = volume
n = number of moles
T = temperature
R = gas constant

Example

Calculating Ideal Gas Law

The ideal gas law describes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is a fundamental equation used to model the behavior of gases under various conditions.

The general approach to calculating the properties of gases using the ideal gas law includes:

Identifying the given variables: pressure, volume, temperature, and moles of the gas.
Using the ideal gas law formula to calculate the unknown variable.

Ideal Gas Law Formula

The general formula for the ideal gas law is:

\[ PV = nRT \]

Where:

P is the pressure of the gas (in atmospheres, atm, or pascals, Pa).
V is the volume of the gas (in liters, L, or cubic meters, m³).
n is the number of moles of gas (in mol).
R is the ideal gas constant, \( R = 0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K} \) or \( 8.314 \, \text{J} / \text{mol} \cdot \text{K} \).
T is the temperature of the gas (in kelvins, K).

Example:

If a gas is in a container with a volume of \( 10 \, \text{L} \), a pressure of \( 2 \, \text{atm} \), and a temperature of \( 300 \, \text{K} \), and we want to find the number of moles of the gas:

Step 1: Use the ideal gas law formula: \( PV = nRT \).
Step 2: Solve for \( n \): \( n = \frac{PV}{RT} \).
Step 3: Substitute the known values: \( n = \frac{(2 \, \text{atm})(10 \, \text{L})}{(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(300 \, \text{K})} \).
Step 4: Calculate the result: \( n = 0.81 \, \text{mol} \).

Ideal Gas Law for Different Gases

The ideal gas law can be applied to different gases, as long as they behave ideally, meaning the gas particles are small and interactions between them are negligible. For example, the behavior of oxygen and nitrogen gases can be modeled using the ideal gas law, but real gases may deviate slightly due to intermolecular forces and the volume of gas particles.

Example:

If the volume of \( 5 \, \text{mol} \) of oxygen gas is \( 40 \, \text{L} \) at a temperature of \( 350 \, \text{K} \), the pressure can be calculated using the ideal gas law formula:

Step 1: Use the formula \( PV = nRT \).
Step 2: Solve for \( P \): \( P = \frac{nRT}{V} \).
Step 3: Substitute the known values: \( P = \frac{(5 \, \text{mol})(0.0821 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(350 \, \text{K})}{40 \, \text{L}} \).
Step 4: Calculate the result: \( P = 3.60 \, \text{atm} \).

Real-life Applications of the Ideal Gas Law

The ideal gas law is widely used in many fields, including:

Calculating the behavior of gases in chemical reactions.
Designing pressurized systems, like gas cylinders and air compressors.
Predicting the behavior of gases in different environmental conditions (temperature and pressure).

Common Units for the Ideal Gas Law

SI Unit: The unit of pressure is pascal (Pa), volume is cubic meters (m³), temperature is kelvins (K), and the number of moles is mol.

The ideal gas law helps to predict and understand the behavior of gases in various practical and scientific applications.

Common Operations with the Ideal Gas Law

Solving for Unknown Variables: You can solve for any of the variables in the ideal gas law if you have the other values. For example, to find the volume, rearrange the formula to \( V = \frac{nRT}{P} \).

Dealing with Real Gases: The ideal gas law is a good approximation for many gases, but real gases may deviate from ideal behavior at high pressures or low temperatures. In such cases, the Van der Waals equation or other adjustments can be used.

Calculating Ideal Gas Law Examples Table
Problem Type	Description	Steps to Solve	Example
Calculating Pressure of a Gas	Finding the pressure of a gas given the volume, temperature, and amount of gas.	Identify the volume \( V \) of the gas (in liters). Identify the number of moles \( n \) of the gas. Identify the temperature \( T \) of the gas (in kelvin). Use the Ideal Gas Law: \( PV = nRT \), where \( R = 0.0821 \, \text{L} \cdot \text{atm}/\text{mol} \cdot \text{K} \).	If the volume of the gas is 10 L, the number of moles is 2 mol, and the temperature is 300 K, the pressure is \( P = \frac{(2)(0.0821)(300)}{10} = 4.926 \, \text{atm} \).
Calculating Volume of Gas	Finding the volume of a gas given the pressure, number of moles, and temperature.	Identify the pressure \( P \) of the gas (in atm). Identify the number of moles \( n \) of the gas. Identify the temperature \( T \) of the gas (in kelvin). Use the Ideal Gas Law: \( V = \frac{nRT}{P} \).	If the pressure is 2 atm, the number of moles is 3 mol, and the temperature is 350 K, the volume is \( V = \frac{(3)(0.0821)(350)}{2} = 43.07 \, \text{L} \).
Calculating Temperature of a Gas	Finding the temperature of a gas given the pressure, volume, and number of moles.	Identify the pressure \( P \) of the gas (in atm). Identify the volume \( V \) of the gas (in liters). Identify the number of moles \( n \) of the gas. Use the Ideal Gas Law: \( T = \frac{PV}{nR} \).	If the pressure is 1.5 atm, the volume is 5 L, and the number of moles is 2 mol, the temperature is \( T = \frac{(1.5)(5)}{(2)(0.0821)} = 91.3 \, \text{K} \).
Calculating Amount of Gas (Moles)	Finding the number of moles of a gas given the pressure, volume, and temperature.	Identify the pressure \( P \) of the gas (in atm). Identify the volume \( V \) of the gas (in liters). Identify the temperature \( T \) of the gas (in kelvin). Use the Ideal Gas Law: \( n = \frac{PV}{RT} \).	If the pressure is 3 atm, the volume is 10 L, and the temperature is 400 K, the number of moles is \( n = \frac{(3)(10)}{(0.0821)(400)} = 1.1 \, \text{mol} \).