Gas equation with molecules calculator

Worked example

Find p, the pressure. Given: volume V = 0.0100 m³; number of molecules N = 2.50 × 10²³; temperature T = 300 K; Boltzmann constant kB = 1.38 × 10⁻²³ J/K.

1. Write the equation
   p V = N k_B T
2. Rearrange to make p the subject
   p = N k_B T / V
3. Constants used
   k_B = 1.38 × 10⁻²³ J/K
4. Substitute the values
   p = (2.5 × 10²³) × (1.38 × 10⁻²³) × 300 ÷ 0.01
5. Calculate
   p = 1.035 × 10⁵ Pa
6. Give the answer to 3 significant figures
   p = 1.04 × 10⁵ Pa

Symbols and units

Gas equation with molecules: rearranged

• To find pressure: p = N k_B T / V
• To find volume: V = N k_B T / p
• To find number of molecules: N = p V / (k_B T)
• To find temperature: T = p V / (N k_B)

Exam tip

N is the number of molecules, not moles. N = n × 6.02 × 10²³.

Common questions

What is the formula for gas equation with molecules?

The equation is p V = N kB T, where p is the pressure (Pa); V is the volume (m³); N is the number of molecules; T is the temperature (K); kB is the Boltzmann constant (J/K).

What units should I use for gas equation with molecules?

In SI units: pressure in Pa, volume in m³, number of molecules in no unit (a ratio), Boltzmann constant in J/K, temperature in K. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange p V = N kB T?

Rearranging gives these forms: to find pressure: p = N kB T / V. to find volume: V = N kB T / p. to find number of molecules: N = p V / (kB T). to find temperature: T = p V / (N kB).