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# Amagat

10th May 2019 @ 3 min read

Physical Chemistry

An amagat is a unit of number density. It is similar to Loschmidt constant which is the molecular density quoted at STP (T = 273.15 K, P = 1 atm). 1 amagat is defined as the number of molecules of an ideal gas per unit volume at STP. 1 amagat is equivalent to Loschmidt constant. The symbol used for amagat is amg or Am (rarely). It is a non-SI unit.

The number is named after Émile Hilaire Amagat. He was a French physicist and also known for Amagat’s law of additive volume.

## Definition

1 amagat equals the number of ideal gas molecules per cubic metre at STP (T = 273.15 K, P = 1 atm).

## Explanation

As mentioned earlier, Loschmidt constant n0 equals 1 amagat at STP.

1 amagat can easily be calculated from the ideal gas equation,

where:
P0 is the standard pressure, 101 325 Pa;
NA is the Avogadro’s constant, 6.022 140 6 × 1023mol−1;
R is the ideal gas constant, 8.314 459 8 J mol−1K−1;
T0 is the standard temperature, 275.15 K.

Let number density η be defined as:

where n is the molecular density at non-standard temperature T and non-standard pressure P, n0 is the molecular density at standard temperature T0 and standard pressure P0.

The molecular density using the ideal gas equation is defined as:

Inserting the molecular density equation into the number density equation, we get,

Using P0 = 101 325 Pa and T0 = 273.15 K, we get the below equation.

Here, P is pressure in pascal, T is temperature in kelvin.

From the above equation, we can calculate the number density at any pressure and temperature.

If we put P = P0 = 101 325 Pa, and T = T0= 273.15 K, we get number density equals 1 amg.

## Example

Calculate the number density in amg at pressure 2.0 × 104 Pa and temperature 300 K.

Using P = 2.0×104 Pa and T = 300 K,

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