# Clapeyron-Mendeleev equation. The relationship between the number of moles of gas, the temperature, volume and pressure.

Clapeyron-Mendeleev equation. The relationship between the number of moles of gas, the temperature, volume and pressure.

The calculator below is used for Clapeyron-Mendeleev equation or state of ideal gas equation problems. You can find the theory below the calculator. There are also some examples of typical problems below.

#### Clapeyron-Mendeleev equation problem examples

1. There is oxygen at 2.3 atmospheres and 23 degrees Celsius in a 2.6-liter flask.

2. Some amount of helium at 78 degrees Celsius and 45.6 atmospheres pressure occupies a volume of 16.5 liters.
Task: What's the volume of this gas at normal conditions? (Note that normal conditions are the pressure of 1 atmosphere and 0 degrees Celsius temperature.

We can enter this data in the calculator and choose what we want to find - a number of moles, new volume, temperature, or pressure, then input remaining data if needed and get a result.

#### Clapeyron-Mendeleev equation. The relationship between the number of moles of gas, the temperature, volume and pressure.

Digits after the decimal point: 2
moles

pressure 2

Volume 2

Temperature 2

Now some formulas

Clapeyron-Mendeleev equation
$PV=\frac{m}{M}RT$
where
P – gas pressure (e.g. in atmospheres)
V – gas volume (in liters);
T – gas temperature (in Kelvins);
R – gas constant (0,0821 l·atm/mol·K).
The gas constant is 8,314 J/K·mol if SI is used.

As m - the mass of gas is in (kg) and M - the molar mass of gas in kg/mol, then m/M - number of moles of a gas and you can write the equation as
$PV=nRT$
where n - number of moles

And it's easy to notice that the ratio
$\frac{PV}{T}=nR$
is a constant value for the same amount of moles.

And this dependence was empirically established before the conclusion of the equation. These are so-called gas laws - Boyle–Mariotte law, Gay-Lussac law, Charles law.

Boyle–Mariotte law says:
For a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional

Gay-Lussac law:
For a given mass m with a constant pressure P, the gas volume is linearly dependent on the temperature

Charles law:
For a given mass m with a constant volume V the gas pressure is linearly dependent on the temperature.

Looking at the equation, it is easy to verify the validity of these laws.

Clapeyron-Mendeleev equation and the experimental laws of Boyle–Mariotte, Gay-Lussac, and Charles are valid for a wide range of pressures, volumes, and temperatures. I.e., in many cases, these laws are suitable for practical use. But do not forget that when the pressure exceeds atmospheric pressure by 300-400 times or temperatures are very high, there are deviations in these laws.
Actually, the ideal gas is called "ideal" because it has no deviations from these laws.

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