# Amount of Substance

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## The ideal gas equation

General

The volume of a given mass of any gas is not fixed. IT changes with pressure and temperature.

Equations

The product of pressure and volume is a constant as long as the temperature remains constant: PV= constant

The volume is proportional to the temperature as long as the pressure remains constant: V/T = constant

The pressure is proportional to the temperature as long as the volume remains constant: P/T = constant

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## The ideal gas equation

The ideal gas equation

If one mole of gas is taken, the constant is given the symbol R and is called the gas constant. For n moles of gas, this equation is correct: PV = nRT

The value of R = 8.31 JK^-1 mol^-1.

This is ideal gas equation. No gases obey it exactly but at room temperature and pressure it holds well for many gases. It's often useful to imagine a gas which obeys the equation perfectly, AKA an 'ideal gas'.

Units

Pressure must be in Pa             Volume must be in m^3            Temperature must be in K

R must be in JK^-1 mol^-1

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## The ideal gas equation

Using the ideal gas equation

Using the equation, the volume of one mole of gas at any temperature and pressure can be calculated. Since none of the terms of the equation refers to a particular gas, this volume will be the same for any gas.

It is the space between the gas molecules that accounts for the volume of a gas. Even the largest  gas particle is extremely small compared with the space in between the particles.

To find a volume: V = nRT/P

Example

If the temperature is 20.0 degrees C, pressure = 100,000 Pa and n=1 for one mole of gas:

V = (8.31JK^-1 mol^-1 * 293 K)/ 100,000 Pa

= 0.0243m^-3 = 0.0243 * 10^6 cm^3 = 24300 cm^3

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