Ideal Gas Law Calculator (Physics)
Calculate pressure, volume, temperature, or amount using PV = nRT.
Understanding Ideal Gas Law Calculator (Physics)
The ideal gas law relates pressure, volume, temperature, and amount of gas. It is an equation of state for an ideal gas.
$$PV = nRT$$
How to use this calculator
- Enter the known values for pressure, volume, temperature, and amount of gas.
- Choose the variable you want to solve for, such as pressure or volume.
- Make sure the temperature is in kelvin, because the formula uses absolute temperature.
- Read the result and the step by step work shown by the calculator.
The formula explained
The formula \(PV = nRT\) computes the relationship between pressure \(P\), volume \(V\), amount \(n\), temperature \(T\), and the gas constant \(R\). If one value is missing, you can rearrange the equation to solve for it.
- P = pressure
- V = volume
- n = amount of gas in moles
- R = ideal gas constant
- T = temperature in kelvin
Step by step method
- Start with \(PV = nRT\).
- Rearrange the equation for the unknown, for example \(P = \frac{nRT}{V}\) or \(V = \frac{nRT}{P}\).
- Substitute the known values, then calculate and include the correct units.
Worked example
Problem. A gas has \(n = 2.0\) mol, \(T = 300\) K, and \(V = 24.6\) L. Find the pressure.
- Use \(P = \frac{nRT}{V}\).
- Substitute the values with \(R = 0.0821\,\text{L}\cdot\text{atm}\,/\,(\text{mol}\cdot\text{K})\): \(P = \frac{(2.0)(0.0821)(300)}{24.6}\).
- Compute \(P \approx 2.00\) atm.
Answer. \(2.00\) atm
Tips and common mistakes
- Use kelvin for temperature, not Celsius, because \(PV = nRT\) requires absolute temperature.
- Keep units consistent with the value of \(R\), for example use liters with atmospheres or cubic meters with pascals.
Frequently asked questions
How do I use the ideal gas law calculator to solve for pressure, volume, temperature, or moles?+
Enter the three values you know for PV = nRT, then choose the variable you want to find. The calculator rearranges the formula automatically, for example P = nRT/V or T = PV/(nR).
What does each symbol in PV = nRT mean?+
P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is temperature in kelvin. The equation describes how these quantities are related for an ideal gas.
Why does the calculator require temperature in kelvin?+
The ideal gas law uses absolute temperature, so T must be in kelvin for the equation to work correctly. If you have Celsius, convert it first by adding 273.15.
What units should I use with the ideal gas law calculator?+
Use a consistent unit set, because R depends on the units you choose. Common choices are atm, liters, moles, and kelvin with R = 0.082057 L·atm/(mol·K), or pascals, cubic meters, moles, and kelvin with R = 8.314 J/(mol·K).
When does the ideal gas law give only an approximation?+
It works best for gases at low pressure and high temperature, where real gases behave more like ideal ones. At high pressure or near condensation, intermolecular forces and gas volume become important, so the result may differ from real behavior.
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