joule per mole kelvin

SI coherent derived unit whose name and symbol includes an SI coherent derived unit with a special name and symbol

Name	Symbol	Quantity	Base units
joule per mole kelvin	J/(mol K)	molar heat capacity, molar entropy	kg m² s⁻² K⁻¹ mol⁻¹
The joule per mole kelvin, symbol J/(mol K), is the SI coherent derived unit of molar entropy and of molar heat capacity. One joule per mole kelvin is equal to the molar heat capacity of a substance that requires one joule of heat energy to raise the temperature of one mole of the substance by one kelvin.
Definition			k N_A
$1 \mspace{4mu} \text{J} / (\text{mol} \mspace{4mu} \text{K}) \mspace{6mu} = \dfrac{1}{(1.380 \mspace{4mu} 649 \times 10^{-23})(6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23})} \mspace{6mu} k \mspace{4mu} N_A\\ \\ \\ 1 \mspace{4mu} \text{J} / (\text{mol} \mspace{4mu} \text{K}) \mspace{6mu} \approx 1.202 \mspace{4mu} 723 \mspace{4mu} 550 \mspace{4mu} 427 \mspace{4mu} 260 \mspace{4mu} 414 \times10^{-1} \mspace{6mu} k \mspace{4mu} N_A$

Molar heat capacity

The amount of heat energy needed to raise the temperature of an object by one kelvin depends on the object’s substance. The amount of energy needed is also directly proportional to the amount of substance.

To be able to make meaningful comparisons of the heat capacity of different substances, on the basis of their chemical nature, it is useful to measure the heat energy needed to raise the temperature of a standard number of particles of each substance. In the SI the standard number of particles used is the mole, or 6.022 140 76 × 10²³ particles.

The amount of heat energy needed to raise the temperature of one mole of a substance by one kelvin is equal to the molar heat capacity of the substance.

Ideal gas constant

The ideal gas law, also known as the general gas equation, is the equation of state of a hypothetical ideal gas. It approximates the behaviour of gases under many conditions.

Using SI coherent units,

$p V = n R T$

where:

p is the pressure in pascals, symbol Pa,
V is the volume in cubic metres, symbol m³,
T is the absolute temperature in kelvins, symbol K,
n is the amount of gas in moles, symbol mol,
R is the ideal gas constant in joules per mole kelvin, symbol J K⁻¹ mol⁻¹,

The ideal gas constant, R, also known as the molar gas constant, is the molar equivalent of the Boltzmann constant. It is equal to the product of two of the SI defining constants – the Boltzmann constant, k, and the Avogadro constant, N_A.

$R \ = k \mspace{4mu} N_A \\ \\ R \ = 1.380 \mspace{4mu} 649 \times 10^{-23} \mspace{6mu} \text{J K}^{-1} \ \times \ 6.022 \mspace{4mu} 140 \mspace{4mu} 76 \mspace{4mu} \times 10^{23} \mspace{6mu} \text{mol}^{-1} \\ \\ R \ = 8.314 \mspace{4mu} 462 \mspace{4mu} 618 \mspace{4mu} 153 \mspace{4mu} 24 \mspace{6mu} \text{J K}^{-1} \text{mol}^{-1}$

Inverting the definition for the ideal gas constant gives an exact expression for the joule per mole kelvin in terms of the Boltzmann constant, k, and the Avogadro constant, N_A :

$1 \mspace{4mu} \text{J K}^{-1} \text{mol}^{-1} \mspace{6mu} = \dfrac{1}{8.314 \mspace{4mu} 462 \mspace{4mu} 618 \mspace{4mu} 153 \mspace{4mu} 24} \mspace{6mu} k \mspace{4mu} N_A$

When used with regard to the ideal gas constant, the symbol for joule per mole kelvin is usually written in the form J K⁻¹ mol⁻¹.