Ideal Gas Law Calculator

Solve for any variable in the Ideal Gas Law equation (PV = nRT). Enter three known values to calculate the fourth. Temperature must be in Kelvin or can be entered in Celsius for automatic conversion.

Ideal Gas Law: PV = nRT Where: • P = Pressure (atm, Pa, torr, etc.) • V = Volume (L, m³, mL, etc.) • n = Number of moles (mol) • R = Universal gas constant • T = Temperature (must be in Kelvin) Gas Constant Values: • R = 8.314 J/(mol·K) • R = 0.0821 L·atm/(mol·K) ← Used in this calculator • R = 62.36 L·torr/(mol·K) • R = 8.314 kPa·L/(mol·K) Solving for Each Variable: P = nRT/V V = nRT/P n = PV/(RT) T = PV/(nR) Temperature Conversions: K = °C + 273.15 °C = K - 273.15 °F = (°C × 9/5) + 32 Pressure Conversions: 1 atm = 101,325 Pa = 101.325 kPa 1 atm = 760 torr = 760 mmHg 1 atm = 14.696 psi Volume Conversions: 1 L = 1000 mL = 0.001 m³ At STP: 1 mol = 22.4 L
Example 1: Find Pressure Given: V = 2.5 L, n = 0.5 mol, T = 300 K P = nRT/V = (0.5)(0.0821)(300)/2.5 P = 4.926 atm ≈ 4.93 atm P = 499.3 kPa or 3,744 torr Example 2: Find Volume at STP Given: P = 1 atm, n = 2 mol, T = 273.15 K V = nRT/P = (2)(0.0821)(273.15)/1 V = 44.8 L (Note: 1 mol at STP = 22.4 L, so 2 mol = 44.8 L ✓) Example 3: Find Moles Given: P = 2 atm, V = 10 L, T = 350 K n = PV/(RT) = (2)(10)/(0.0821)(350) n = 0.696 mol Molecules = 0.696 × 6.022×10²³ = 4.19×10²³ Example 4: Find Temperature Given: P = 1.5 atm, V = 5 L, n = 0.3 mol T = PV/(nR) = (1.5)(5)/(0.3)(0.0821) T = 304.6 K = 31.4°C = 88.6°F Example 5: Real-World - Scuba Tank Tank: 12 L at 200 atm, T = 25°C (298 K) n = PV/(RT) = (200)(12)/(0.0821)(298) n = 98.1 mol of air Mass ≈ 2,841 g (using air MW = 28.97 g/mol)

What is the Ideal Gas Law?

The Ideal Gas Law (PV = nRT) describes the relationship between pressure (P), volume (V), number of moles (n), and temperature (T) for an ideal gas. R is the universal gas constant.

When does the Ideal Gas Law apply?

The law works best for gases at low pressure and high temperature where intermolecular forces are negligible. It's accurate for most gases at standard conditions but deviates for real gases at high pressure or low temperature.

What are the units for R?

R depends on your units: 8.314 J/(mol·K), 0.0821 L·atm/(mol·K), or 62.36 L·torr/(mol·K). This calculator uses 0.0821 L·atm/(mol·K) with Kelvin temperature, liters, and atmospheres.

How do I convert Celsius to Kelvin?

Add 273.15 to Celsius: K = °C + 273.15. Example: 25°C = 298.15 K. Always use Kelvin in gas law calculations as temperature must be absolute.

What pressure units can I use?

Common units: atm (atmospheres), Pa (pascals), torr, mmHg, psi. Conversions: 1 atm = 101,325 Pa = 760 torr = 760 mmHg = 14.7 psi. This calculator uses atm.

Can I calculate any variable?

Yes! The calculator solves for P, V, n, or T when you provide the other three variables. Simply select what you want to find and enter the known values.

What is STP?

STP (Standard Temperature and Pressure) is 0°C (273.15 K) and 1 atm. At STP, 1 mole of ideal gas occupies 22.4 L. This is useful for quick conversions and reference calculations.

Why do real gases deviate from ideal behavior?

Real gases have molecular volume and intermolecular attractions ignored by the Ideal Gas Law. At high pressure, molecular volume matters; at low temperature, attractions matter. Use van der Waals equation for better accuracy with real gases.