# How does the pressure of an ideal gas change?

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An ideal gas is a physical model of gas. This model almost does not take into account the interaction of molecules with each other. It is used to describe the behavior of gases from a mathematical point of view. This model assumes the following properties of gas:

- the size of the molecules is greater than the distance between the molecules;
- molecules are round balls;
- The molecules are repelled from each other and from the vessel walls only after the collision. The collisions are perfectly resilient;
- Molecules are moving in accordance with Newton's laws.

There are several types of ideal gas:

- classical;
- quantum (considers an ideal gas in conditions of lowering the temperature and increasing the distance between the molecules);
- in the gravitational field (considers changes in the properties of an ideal gas in a gravitational field).

Below will be considered a classic perfect gas.

## How to determine the pressure of an ideal gas?

The fundamental dependence of all ideal gases is expressed using the Mendeleev-Clapeyron equation.

PV = (m / M) • RT [Formula 1]

Where:

- P - pressure. Unit of measure - Pa (Pascal)
- R = 8.314 is the universal gas constant. Unit of measurement - (J / mol • K)
- T - temperature
- V - volume
- m is the mass of gas
- M is the molar mass of a gas. Unit of measurement - (g / mol).

P = nkT [Formula 2]

Formula 2 shows that the pressure of an ideal gas depends on the concentration of molecules and temperature. If we take into account the features of an ideal gas, then n will be determined by the formula:

n = mNa / MV [Formula 3]

Where:

- N is the number of molecules in the vessel
- Na- Avogadro constant

Substituting formula 3 into formula 2, we obtain:

- PV = (m / M) Na kT [Formula 4]
- k * na= R [Formula 5]

The constant R is a constant for one mole of gas in the Mendeleev – Clapeyron equation (remember: at constant pressure and temperature, 1 mole of different gases occupies the same volume).

Now we derive the pressure equation for an ideal gas.

m / M = ν [Formula 6]

- where ν - quantities of a substance. Unit of measure - mole

We obtain the ideal gas pressure equation, the formula is given below:

P = νRT / V [Formula 7]

- where P is the pressure. Unit of measure - Pa (Pascal)
- R = 8.314 is the universal gas constant. Unit of measurement - (J / mol • K)
- T - temperature
- V is the volume.

## How to change the pressure of an ideal gas?

After analyzing equality 7, one can see that the pressure of an ideal gas is proportional to the change in temperature and concentration.

In the state of an ideal gas, changes are possible in all parameters on which it depends, and changes in some of them are possible. Consider the most likely situations:

- Isothermal process. This process is characterized by the fact that the temperature in it will be constant (T = const). If we substitute a constant temperature in equation 1, we see that the value of the product P * V will also be constant.
- PV = const [Formula 8]

Equality 8 shows the relationship between the volume of a gas and its pressure at a constant temperature. This equation was discovered experimentally in the 17th century by physicists Robert Boyle and Edmie Mariott. The equation was named in their honor the Boyle-Mariotte law.

- Isochoric process. In this process, the volume, mass of the gas and its molar mass remain constant. V = const, m = const, M = const. Thus, we obtain the pressure of an ideal gas. The formula is shown below:
- P = P0AT [Formula 9]
- Where: P - gas pressure at absolute temperature,
- P0- gas pressure at a temperature of 273 ° K (0 ° C),
- A is the temperature coefficient of pressure. A = (1 / 273.15) K-1

This dependence was discovered in the 19th century by experimenting physicist Charles. Therefore, the equation bears the name of its creator - the law of Charles.

An isochoric process can be observed if gas is heated at a constant volume.

- Isobaric process. For this process, the pressure, mass of gas and its molar mass will be constant. P = const, m = const, M = const. The equation of the isobaric process is:
- V / T = const or V = V0AT [Formula 10]
- where: v0- the volume of gas at a temperature of 273 ° K (0 ° C);
- A = (1 / 273.15) K-1.

In this formula, the coefficient A is the temperature coefficient for the volume expansion of the gas.

This dependence was discovered in the 19th century by the physicist Joseph Gay-Lussac. That is why this equality bears his name - the law Guy-Lussac.

If we take a glass flask connected to a tube, the opening of which will be covered with liquid, and heat the construction, then an isobar process will be observed.

It is worth noting that air at room temperature has properties similar to an ideal gas.