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# The Gaseous State and the Gas Laws

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## The Gaseous State and the Gas Laws

**The kinetic theory of ideal gases makes 5 main assumptions:**

- The size of molecules is negligible compared with the mean intermolecular distance (i.e. they are widely spaced molecules).
- Molecules move with different speeds and in random directions.
- Standard laws of motion apply.
- Collisions between molecules are elastic. Translational kinetic energy is not converted into other forms of energy.
- There are no attractive intermolecular forces between molecules except during collision.

**Limitations of the theory**

**Assumption 1:** Real gaseous particles do have a volume.

Deviations large for large gas molecules (e.g. methane, carbon dioxide and ammonia). Deviations small for small gases (e.g. helium and hydrogen).

If the gas particles have a significant size compared to the total volume of the container, the volume of the remaining space in the container is reduced.

**The 'effective gas volume' is reduced.**

**Assumption 5: **Intermolecular forces of attraction do exist.

The larger the intermolecular force between the molecules the more they deviate from ideal behaviour. Van der Waal's forces increase with molecular size - as the molecular mass increases so does the size of the electron cloud.

**Real gases deviate from ideal behaviour at low temperatures and high pressure.**

Real gases behave more ideally at high temperature, due to the intermolecular forces been minimised due to an increase in the molecules' kinetic energy, and at low pressure, due to fewer particles per unit volume.

**The Kinetic Theory of Gases may be shown graphically:**

There are three Gas Laws, which set out the interdependence of the pressure(p), temperature (T) and volume (V) of a gas.

### Boyles law

**For a fixed mass of gas, the pressure is inversely proportional to the volume if the temperature remains constant.**

### Charles law

**For a fixed mass of gas, the volume is proportional to the absolute temperature if the pressure remains constant.**

### The pressure law

**For a fixed amount of gas, the pressure is proportional to the absolute temperature if the volume remains constant.**

**These three laws can be summarised as:**

- PV= constant
- V/T = constant
- P/T = constant.

**These can be combined to give:** PV/T = constant

The constant depends on the amount of gas, measured in moles (n). Therefore the constant may be written as nR, where R is the **molar gas constant**, which has the approximate value of 8.314JK^{-1}mol^{-1}.

So we can now write an equation that shows how pressure, volume and the temperature of a gas varies if conditions are altered. This is known as the ideal gas equation: PV = nRT

**The units must be SI.**

- P = Pa or Nm
^{-2} - V = m
^{3} - N = moles
- R = 8.314 JK
^{-1}mol^{-1} - T = K

If the pressure, volume and temperature of a gas change to new values because the gas has been processed, so that the initial pressure (P_{1}), final pressure (P_{2}) and similarly with V_{1} - V_{2} and T_{1} - T_{2}, then:

**P _{1}V_{1}/T_{1} = P_{2}V_{2}/T_{2}**

**Finding the Relative Molecular Mass (Mr) of a gas:**

Mr = mass (g) / no. of moles = gmol^{-1}

If we replace n in the equation with Mr/m we are given:

**Mr = m RT/PV**