kilogram per mole
Molar massexact by definition
The kilogram per mole is the coherent SI unit of molar mass, with a factor of 1 that is exact. It is a thousand times larger than the g/mol figure everyone actually uses, so water is 0.018015 kg/mol. It appears mainly inside SI-consistent equations, such as the ideal gas law written in terms of mass, where mixing g/mol into kg and joules is a reliable source of factor-of-1000 errors.
Watch out: Numerically kg/kmol and g/mol are identical, which is why chemical engineering handbooks working in kilomoles can quote 18.015 for water without changing anything.
| 1 | 1,000 |
About the kilogram per mole
The kilogram per mole is the molar mass that SI equations silently require, and most people first meet it when an equation misbehaves. The speed of sound in a gas is ; kinetic theory's mean molecular speed, Graham's effusion ratio and the scale height of an atmosphere all take M the same way, in kg/mol, because R is in joules. Feed them the periodic-table number instead and every answer is off by : the speed of sound in air comes out near 11 m/s, slower than a sprinting human, which is at least an error that announces itself.
The aerodynamicist's 287 is this unit in disguise. Air's specific gas constant, 287.05 J/(kg·K), is R divided by air's molar mass of 0.028965 kg/mol, and every compressible-flow table, along with the speed-of-sound solver on this site, carries that quotient. Water vapour's 461.5 J/(kg·K) is the same construction over 0.018015 kg/mol, and the ratio of the two is the 0.622 that runs through all of psychrometrics.
The caution on this page names the escape hatch: kg/kmol keeps the familiar digits for tabulation. This unit is for the moment the algebra goes fully coherent and the factor of 1000 has to be paid.
One kilogram per mole in every molar mass unit
| 1,000 | gram per mole (g/mol) | |
| 1,000 | kilogram per kilomole (kg/kmol) | |
| 1,000 | milligram per millimole (mg/mmol) | |
| 1,000 | pound per pound-mole (lb/lb-mol) | |
| 1,000 | dalton (as molar mass) (Da) | |
| 1 | kilogram per mole (kg/mol)this unit | |
| 1 | kilodalton (as molar mass) (kDa) |