The Freedom unit for molar energy: the foot-pound-force per pound-mole

## Friday, 9 October 2020

### The Freedom unit for molar energy: the foot-pound-force per pound-mole

In computational biochemistry the most commonly used unit is molar energy. The SI unit is kJ/mol (kilojoule per mole), but kcal/mol is also as frequently used —Google enumerates 5.3e6 and 3.8e6 pages for them respectively. Different programs use one or the other, GROMACS uses kJ/mol, while Rosetta uses kcal/mol. They differ by a factor of about 4, the latter has the advantage that 1 kcal/mol is the strength of a hydrogen bond and kBT/NA is 0.6 kcal/mol (25°C) or 1. kcal/mol (37°C), while the former being SI sounds more sciency ——and not in the overly obnoxious way as folk who use Kelvin for enzymology.

However, whereas it is not an SI unit, kcal/mol is still very metric and European, after all the unit calorie was introduced by a Frenchman. Therefore, a more American unit is clearly required. Hence the need for the foot–pound-force per pound-mole.

This unit is 100% freedom units and would make the founding father proud —okay, all except Benjamin Franklin, who was likely corrupted by the SI unit taint.

## foot–pound-force

The freedom/imperial unit of energy is not the joule, but the foot–pound-force.

A joule corresponds to a newton per meter, i.e. force per distance, where a newton is the force required to accelerate 1 kg for a second by 1 meter per second —for the sake of sanity it is best to pretend physics theory is on slippery ice (unless you have clocked over 100 hours in Kerbal Space Program and intuitively understand physics without friction). The freedom/imperial unit equivalent is the pound-force, which is the force that is subjected to a pound (mass, not coin) under Earth gravity. This differs from how the definition of a Newton and as a result for a similar definition you need to accelerate a "slug" by 1 foot per second per second, where one slug is 16 kilos —a mollusk as heavy as three bald eagles.

The freedom/imperial unit of energy is instead straightforward: one foot–pound-force is pound-force energy per foot. However, to quote Wikipedia, "Pound-force should not be confused with foot-pound, a unit of energy, or pound-foot, a unit of torque, that may be written as "lbf⋅ft"; nor should these be confused with pound-mass (symbol: lb), often simply called pound, which is a unit of mass.". Some confusion may also occur if you forget that the distance measurement is squares, so whereas 12 inches make a foot, 3 feet make a yard and 1760 yards make a mile, 144 inch–pound-force make a foot–pound-force etc.

## pound-mole

One mole of a compound that is n dalton (sum of number of protons and neutrons) big will have a mass of one gram. Whereas one pound-mole of a compound will weight one pound. A pound is some 450 grams (a UK pint weights 560 grams or 1.25 pounds making it more confusing), so a pound-mole will be a bigger amount of atoms, thus proving it to be better.

## foot-pound-force per pound-mole

Consequently, the foot-pound-force per pound-mole is a superior unit. Therefore to allow its use and widespread adoption here is a calculator:

kJ/mol
kcal/mol
ft·lbf/lbmol