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Molar gas constant

R=8.31446261815324 J/(mol⋅K)R = 8.31446261815324\ \text{J/(mol}{\cdot}\text{K)}
Value8.31446261815324 J/(mol·K)
StatusExact by definition — no uncertainty
SourceSI Brochure, 9th edition (2019); CODATA 2022
CategoriesThermodynamicChemistryUniversal & Atomic
Molar gas constant in every molar entropy unit
joule per mole kelvin8.3144626 J/(mol·K)
joule per mole Celsius8.3144626 J/(mol·°C)
kilojoule per kilomole kelvin8.3144626 kJ/(kmol·K)
calorie per mole kelvin1.9872043 cal/(mol·K)
entropy unit1.9872043 e.u.
BTU per pound-mole Rankine1.9858753 BTU/(lb-mol·°R)
Boltzmann constant per particle1 kB/particle
kilojoule per mole kelvin0.0083144626 kJ/(mol·K)

Learning zone

The molar gas constant is the Boltzmann constant scaled up to laboratory quantities: R = k · NA. It is the constant of proportionality in the ideal gas law PV = nRT, the coefficient in the Nernst and Arrhenius equations, and the natural unit of molar entropy — which is why the site types it as J/(mol·K) and will convert it to BTU/(lb-mol·°R) or cal/(mol·K) for you.

Its value came out of nineteenth-century gas metrology, above all Henri Victor Regnault's obsessively careful measurements of gas densities and compressibilities in Paris in the 1840s, which Clausius and others folded into a single universal constant once Avogadro's hypothesis was accepted. For a century afterwards R was determined experimentally, usually by acoustic thermometry in argon; the best measurements agreed to a few parts per million and were the raw material for the 2019 redefinition. Now that both k and NA are fixed by definition, their product is exact: 8.31446261815324 J/(mol·K), full stop.

Used by 18 solvers

Activation Energy from an Arrhenius Plot

Ea=−R×slopeE_a = -R \times \text{slope}

Arrhenius Equation

k=A e−Ea/RTk = A\,e^{-E_a/RT}

Arrhenius Equivalent Age (Freiesleben Hansen and Pedersen)

te=t exp⁡ ⁣[−ER(1T−1Tr)]t_e = t \, \exp\!\left[ -\dfrac{E}{R} \left( \dfrac{1}{T} - \dfrac{1}{T_r} \right) \right]

Arrhenius Two-Temperature Form

ln⁡k2k1=EaR(1T1−1T2)\ln\frac{k_2}{k_1} = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)

Barometric Pressure with Altitude

P=P0 e−Mgz/RTP = P_0 \, e^{-Mgz/RT}

Clausius–Clapeyron Equation (Two-Point Form)

ln⁡ ⁣(P2P1)=−ΔHvapR(1T2−1T1)\ln\!\left(\frac{P_2}{P_1}\right) = -\frac{\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)

Compressibility Factor (Z = PV/nRT)

Z=PVnRTZ = \frac{P V}{n R T}

Gas Density from Molar Mass

ρ=PMRT\rho = \frac{PM}{RT}

Gas Volume at STP

V=n VmV = n\,V_m

Gibbs Free Energy and the Equilibrium Constant

ΔG∘=−RTln⁡K\Delta G^{\circ} = -RT\ln K

Graham's Law of Effusion

r1r2=M2M1\frac{r_1}{r_2} = \sqrt{\frac{M_2}{M_1}}

Ideal Gas Law

PV=nRTP V = n R T

Mach Number

Ma=vγRT/MMa = \frac{v}{\sqrt{\gamma R T / M}}

Nernst Equation

E=E∘−RTnFln⁡QE = E^{\circ} - \frac{RT}{nF}\ln Q

Norton Creep Law

ε˙=A σ nexp⁡ ⁣(−QRT)\dot{\varepsilon} = A \, \sigma^{\,n} \exp\!\left( -\dfrac{Q}{RT} \right)

Osmotic Pressure (Π = MRT)

Π=MRT\Pi = M R T

van 't Hoff Equation (K at Two Temperatures)

ln⁡K2K1=−ΔH∘R(1T2−1T1)\ln\frac{K_2}{K_1} = -\frac{\Delta H^{\circ}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)

Van der Waals Equation of State

(P+an2V2)(V−nb)=nRT\left(P + \frac{a n^{2}}{V^{2}}\right)\left(V - n b\right) = n R T