Name: Graham's Diffusion Law
Uploaded: 2019-07-19
Duration: 9 min 43 s
Description: Gases diffuse at a different rate. Watch this video to understand Graham's diffusion law, which deals with the diffusion of gases. Have fun learning!

Question

Derive an equation for ‘

n

’ moles of an ideal gas. How can Charles’ law be explained in the light of kinetic theory of gases? Under what condition a real gas shows ideal behaviour?

Accepted Answer

An equation for $n$ moles of an ideal gas can be derived by the following,

According to Charles' law, the volume of a fixed mass of a gas is directly proportional to the absolute temperature of the gas at a constant pressure.

$V \propto T \frac{V}{T} = constant = k_{2}$

Where $k_{2}$ is an constant.

$\frac{V_{1}}{T_{1}} = \frac{V_{2}}{T_{2}}$

Boyle’s law states that under isothermal condition, pressure of a fixed amount of a gas is inversely proportional to its volume.

$P \propto \frac{1}{V} \frac{P_{1}}{P_{2}} = \frac{V_{2}}{V_{1}}$

We can derive the equation of state with the help of Boyle’s law and Charles’ law.

At constant temperature and moles, $V \propto \frac{1}{P}$ ( Boyle's law)

At constant pressure and moles, $V \propto T$ ( Charles' law)

At constant pressure and temperature, $V \propto n$ (Avogadro's Law)

After combining all three laws, we will get,

$V \propto \frac{nT}{P} V = R \frac{nT}{P}$

$PV = nRT$

The above equation is known as the ideal gas equation and $R$ is a constant that is known as the universal gas constant.

A real gas is a gas which does not adhere to ideal gas law. And, real gas behaves like ideal gas because they have intermolecular force of attraction between the molecules and these molecules do not have negligible volume as compared to the total volume of the gas. The volume compared to the total volume of gas is only negligible at low pressure and high temperature.

According to kinetic gas equation,

$PV = \frac{1}{3} {mnc}^{2}$

$PV$ $= \frac{2}{3} \times \frac{1}{2} {mnc}^{2}$ $= \frac{2}{3} \times \frac{1}{2} {Mc}^{2}$ ----(i) where, ( $M = m \times n$ , is the total mass of the gas).

But, kinetic energy $E_{k}$ $= \frac{1}{2} {Mc}^{2}$

Therefore, equation (i) becomes, $PV = \frac{2}{3} E_{k}$ .

According to one of the postulates of the kinetic theory of gases, $E_{k} \propto$ Absolute Temperature ( $T$ ) or $E_{k} = k T$ -----(ii), where, $k$ is the proportionality constant. On substituting the value of $E_{k}$ in equation (i), we get $PV = \frac{2}{3} \times kT$ -------(iii).

Equation (iii) can be written as, $\frac{V}{T} = \frac{2}{3} \times \frac{k}{P}$ ------(iv), $\frac{2}{3}$ and $k$ are constants hence, if $P$ is kept constant, according to equation (iv) $\frac{V}{T} = Constant$ , which is Charles' law.

Derive an equation for ‘ $n$ ’ moles of an ideal gas. How can Charles’ law be explained in the light of kinetic theory of gases? Under what condition a real gas shows ideal behaviour?

Important Questions on States of Matter : Gases and Liquids

Learn and Prepare for any exam you want !

Derive an equation for ‘n’ moles of an ideal gas. How can Charles’ law be explained in the light of kinetic theory of gases? Under what condition a real gas shows ideal behaviour?

Important Questions on States of Matter : Gases and Liquids

Learn and Prepare for any exam you want !

Derive an equation for ‘ $n$ ’ moles of an ideal gas. How can Charles’ law be explained in the light of kinetic theory of gases? Under what condition a real gas shows ideal behaviour?