David Chen, Ph.D. in Physical Chemistry, Specialist in Thermodynamics and Fluid Dynamics.
Use the Ideal Gas Law Calculator to quickly find the pressure (P), volume (V), amount of substance (n), or absolute temperature (T) of an ideal gas. Enter any three known variables, and the calculator will solve for the fourth.
Ideal Gas Law Calculator
Calculation Details
Ideal Gas Law Formula:
Formula Sources: LibreTexts Chemistry, Britannica – Ideal Gas Law
Variables:
- P (Pressure): The force exerted by the gas per unit area, typically measured in atmospheres (atm).
- V (Volume): The space occupied by the gas, typically measured in liters (L).
- n (Amount of Substance): The number of moles of gas particles.
- R (Ideal Gas Constant): A universal physical constant. For the units used here, R = 0.082057 L·atm/(mol·K).
- T (Temperature): The absolute temperature of the gas, which must be measured in Kelvin (K).
What is the Ideal Gas Law?
The Ideal Gas Law, often represented as $PV = nRT$, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It combines the empirical gas laws (Boyle’s, Charles’s, and Avogadro’s Law) into one comprehensive relationship.
The law mathematically links four state variables: pressure, volume, the number of moles, and absolute temperature. The Ideal Gas Constant ($R$) acts as a proportionality constant, ensuring the equation holds true across different units and scales. This law is fundamental in chemistry and physics for predicting how gases will respond to changes in their environment.
How to Calculate a Missing Variable (Example)
Let’s use the Ideal Gas Law ($PV = nRT$) to find the Volume (V) of 2.0 moles of gas at 3.0 atm and 300 K.
- Identify Known Variables:
- $P = 3.0 \text{ atm}$
- $n = 2.0 \text{ mol}$
- $T = 300 \text{ K}$
- $R = 0.082057 \frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}$ (Constant)
- Rearrange the Formula to Solve for V: $$V = \frac{nRT}{P}$$
- Substitute the Values: $$V = \frac{(2.0 \text{ mol}) \times (0.082057 \frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}) \times (300 \text{ K})}{3.0 \text{ atm}}$$
- Perform the Calculation: $$V \approx 16.4114 \text{ L}$$
- Result: The volume of the gas is approximately 16.41 L.
Frequently Asked Questions (FAQ)
What unit must temperature be in for the Ideal Gas Law?
Temperature (T) must always be in Kelvin (K). The Kelvin scale is an absolute temperature scale, meaning zero Kelvin represents zero molecular motion. Using Celsius or Fahrenheit will result in incorrect calculations.
What is the value of the Ideal Gas Constant (R)?
The value of R depends on the units used for pressure and volume. In this calculator, we use $R = 0.082057 \frac{\text{L}\cdot\text{atm}}{\text{mol}\cdot\text{K}}$. Other common values are $8.314 \frac{\text{J}}{\text{mol}\cdot\text{K}}$ (when P is in Pascals and V is in $m^3$).
Can I use this calculator if all four variables (P, V, n, T) are known?
Yes. If all four variables are entered, the calculator will perform a consistency check. It will calculate $PV$ and $nRT$ separately and report the percentage error to show how close the values are to satisfying the law.
What are the limitations of the Ideal Gas Law?
The law works best at low pressures and high temperatures. It becomes inaccurate under high pressure (where gas volume is significant) or low temperature (where intermolecular forces become significant).