## Physical Properties of Gas Molecules

The physical **properties of gas** molecules have filled completely to any available space by the uniform density of gases. These physical properties of gases evident to the formation of Avogadro, Boyle’s, and Charles law and Gay Lussac laws which provide the relation between mass, pressure, volume, and temperature of gas molecules and the formula of ideal gas law.

Gas molecules have properties to move very large speeds because of the forces of attraction between them very low. Thus the gas molecules do not possess fixed volume, they move partially independent of one another.

### Boyle’s Law of Gases

Boyle’s law states as, at a constant temperature, the volume of a definite mass of a gas is inversely proportional to its pressure.

Therefore the volume of a given quantity of gases, at constant temperature decreases with the increase of pressure of gases.

At constant temperature and 1 atm pressure, a cylinder contains 10 ml of methane gas. If the pressure increases to 2 atm then according to this law volume decreases to 5 ml.

### Boyle’s Law of Gases Formula

According to the definition of Boyle’s law at a constant temperature

At constant T, V ∝ 1/P

∴ PV = K = constant for a gas

Therefore the value of gas constant depends on the properties and mass of the gas molecules.

For a given mass of gas, the volume V_{1} at pressure P_{1} and V_{2} at pressure P_{2}. Thus according to Boyle’s Law

P_{1}V_{1} = P_{2}V_{2}

### Pressure Volume Graph of Gas

The relation between pressure and volume of gas can be represented by an arm of a rectangular hyperbola graph given below.

- The value of gas constant changes with temperature. Thus there will be a separate curve for each fixed temperature. These curves plotted at different fixed temperatures are called isotherms.
- At constant temperature, a given mass of gas is the product of pressure and volume. If the product of pressure and volume of gas represents in Y-axis and pressure represents X-axis a straight line graph obtained parallel to X-axis.

### Relation between Gas Pressure and Density

Let at a constant temperature, M mass of gas has pressure P_{1} at volume V_{2} and pressure P_{2} at volume V_{2}.

According to Boyle’s law of gases formula

P_{1}V_{1} = P_{2}V_{2}

or, P_{1}/P_{2} = V_{2}/V_{1}

Let the density of the gas D_{1} at pressure P_{1} and D_{2} at pressure P_{2}.

Therefore, D_{1} = M/V_{1} and D_{2} = M/V_{2}

or, V_{1} = M/D_{1} and V_{2} = M/D_{2}

∴ P_{1}/P_{2} = V_{2}/V_{1} = D_{1}/D_{2
}or, P/D = constant

or, P ∝ D

Therefore, at a constant temperature, the density of a definite mass of gas proportional to its pressure.

### Relation between Gas Pressure and Volume

At constant pressure a given mass of gas, volume increases with the increasing temperature. Hence the volume of a given mass of gases at constant pressure is directly proportional to its kelvin temperature.

### Charles law of Gases formula

Charles law evident the physical properties of the volume of a fixed mass of gases at the various temperature at constant pressure.

At constant pressure, each degree rise in temperature of a definite mass of gas expands 1/273.5 of its volume at 0⁰C.

Let V_{0} = volume at 0⁰C, then 1⁰C rise of temperature the volume of the gas rise V_{0}/273.5 ml.

It is convenient to use the absolute temperature scale on which temperature is measured in Kelvin. Thus the reading on this scale obtained by adding 273 to the celsius value.

TK = 273 + t^{0}C

∴ V_{t} = (V_{0} × T)/273 = (V_{0}/273) × T

Since V_{0} = initial volume = constant at a given pressure, thus the above relation expressed as,

V_{t} = K_{2} T

where K_{2} = constant for a gas

∴ V ∝ T

According to the above formula, Charles law states as, at constant pressure, the volume of a given mass of gases is directly proportional to its kelvin temperature.

### Volume Temperature Graph

A typical property of the volume of gases with a change in its kelvin temperature a straight-line graph is obtained. These graphs are known as isobars. Thus the general term isobar, which means at constant pressure assigned to these plots.

### Absolute Zero Temperature of Gas Molecules

Since volume is directly proportional to its kelvin temperature. Thus the volume is theoretically zero at zero kelvin or – 273^{0}C.

This is hypothetical because the gas molecules have physical properties to form liquid and then solid before this low temperature of gases reached. In reality, no substance exists as gases at the temperature near kelvin zero.

### Relation between Gas Temperature and Density

Let at constant pressure, for M mass has volume V_{1} at temp T_{1} and V_{2} at temp T_{2}.

Charles law, V_{1}/V_{2} = T_{1}/T_{2}

Let density D_{1} and D_{2} at V_{2} and V_{1 }respectively

∴ T_{1}/T_{2} = V_{1}/V_{2} = D_{2}/D_{1}

D ∝ 1/T

Therefore at constant pressure, the density of a given mass of gases inversely proportional to its temperature.

### Combined Gas Laws Formula

Charles law, V ∝ 1/P when T constant.

Boyle’s law, V ∝ T when P constant.

Thus when all the variables are taken into account the variation rule states as

V ∝ T/P

or, PV/T = constant

∴ P_{1}V1/T_{1} = P_{2}V_{2}/T_{2}

or, PV = KT

Thus this ideal gas law state the physical properties, the product of the pressure and volume of a given mass of gases is proportional to its kelvin temperature.