Physics formulas: Molecular physics

Quick reference for school physics (molecular physics). Browse by topic or search by name.

Molecular physics

Amount of substance

n=mMn = \frac{m}{M}
Symbols
  • nn — amount of substance (number of moles), mol
  • mm — mass of the substance, kg (kilogram)
  • MM — molar mass, kg/mol
Molecular physics

Molar mass

M=mnM = \frac{m}{n}
Symbols
  • MM — molar mass, kg/mol
  • mm — mass of the substance, kg (kilogram)
  • nn — amount of substance, mol
Molecular physics

KMT equation via mean square molecular speed

p=13 nm0v2‾p = \frac{1}{3}\, n m_0 \overline{v^2}
Symbols
  • pp — gas pressure, Pa (pascal)
  • nn — molecular concentration (molecules per m³), m⁻³
  • m0m_0 — mass of one molecule, kg (kilogram)
  • v2‾\overline{v^2} — mean square of molecular speed, (m/s)²
Molecular physics

KMT equation via average translational kinetic energy

p=23 nEk‾p = \frac{2}{3}\, n \overline{E_k}
Symbols
  • pp — gas pressure, Pa (pascal)
  • nn — molecular concentration, m⁻³
  • Ek‾\overline{E_k} — average translational kinetic energy of a molecule, J (joule)
Molecular physics

Gas pressure vs. concentration and temperature

p=nkTp = nkT
Symbols
  • pp — gas pressure, Pa (pascal)
  • nn — molecular concentration, m⁻³
  • kk — Boltzmann constant, 1.38×10⁻²³ J/K
  • TT — absolute temperature (in kelvins), K (kelvin)
Molecular physics

Average translational kinetic energy vs. temperature

Ek‾=32 kT\overline{E_k} = \frac{3}{2}\, kT
Symbols
  • Ek‾\overline{E_k} — average translational kinetic energy of a molecule, J (joule)
  • kk — Boltzmann constant, 1.38×10⁻²³ J/K
  • TT — absolute temperature, K (kelvin)
Molecular physics

Root-mean-square speed vs. temperature

vrms=3kTm0v_{\text{rms}} = \sqrt{\frac{3kT}{m_0}}
Symbols
  • vrmsv_{\text{rms}} — root-mean-square speed of molecules, m/s
  • kk — Boltzmann constant, 1.38×10⁻²³ J/K
  • TT — absolute temperature, K (kelvin)
  • m0m_0 — mass of one molecule, kg (kilogram)
Also: v2‾=3kTm0\sqrt{\overline{v^2}} = \sqrt{\frac{3kT}{m_0}}.
Molecular physics

Clapeyron equation

pV=mMRTpV = \frac{m}{M}RT
Symbols
  • pp — gas pressure, Pa (pascal)
  • VV — volume of the gas, m³ (cubic meter)
  • mm — mass of the gas, kg (kilogram)
  • MM — molar mass of the gas, kg/mol
  • RR — universal gas constant, 8.31 J/(mol·K)
  • TT — absolute temperature, K (kelvin)
Molecular physics

Mendeleev–Clapeyron equation (ideal gas law)

pV=nRTpV = nRT
Symbols
  • pp — gas pressure, Pa (pascal)
  • VV — volume of the gas, m³ (cubic meter)
  • nn — amount of substance (moles), mol
  • RR — universal gas constant, 8.31 J/(mol·K)
  • TT — absolute temperature, K (kelvin)
Molecular physics

Boyle–Mariotte law

pV=constpV = \text{const}
Symbols
  • pp — gas pressure, Pa (pascal)
  • VV — volume of the gas, m³ (cubic meter)
At constant temperature: p1V1=p2V2p_1 V_1 = p_2 V_2.
Molecular physics

Gay-Lussac’s law

pT=const\frac{p}{T} = \text{const}
Symbols
  • pp — gas pressure, Pa (pascal)
  • TT — absolute temperature, K (kelvin)
At constant volume: p1T1=p2T2\frac{p_1}{T_1} = \frac{p_2}{T_2}.
Molecular physics

Charles’s law

VT=const\frac{V}{T} = \text{const}
Symbols
  • VV — volume of the gas, m³ (cubic meter)
  • TT — absolute temperature, K (kelvin)
At constant pressure: V1T1=V2T2\frac{V_1}{T_1} = \frac{V_2}{T_2}.