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# 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.

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The calculator below is used for Clapeyron-Mendeleev equation or state of ideal gas equation problems. Some of theory is placed below the calculator. There is also some problem examples below.

### Clapeyron-Mendeleev equation problem examples

1. There is oxygen at 2.3 atmospheres and 23 degrees celsius in a 2.6-litre 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 1-celsius temperature.

We can enter these data in the calculator and choose what is needed to be counted (amount of moles, new volume, temperature of pressure) and input other 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
number of moles

pressure 2

Volume 2

Temperature 2

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Now some formulas

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

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

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

And this pattern was empirically established before the conclusion of the equation. This are so-called gas laws - Boyle–Mariotte law, Gay-Lussac's law, Charles's 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's law:
For a given mass m with a constant pressure P the gas volume is linearly dependent on the temperature

Charles's 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, as well as the experimental laws of Boyle–Mariotte, Gay-Lussac and Charles, are valid for a wide range of pressure, volume and temperature. 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 for this laws.