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

Define Boyle’s law and Charles' law. Derive the combined gas equation from the two laws. Find out the value of gas constant

R

.

Accepted Answer

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

Boyle's law, Charles' law and Avogadro's law can be combined in a single equation called ideal gas equation. This equation can be derived as given below:

According to Boyle's law, $V \propto \frac{1}{P}$ (at constant $T$ and $n$ )---------(i)

According to Charles' law, $V \propto T$ (at constant $P$ ) and ----------(ii)

On combining equations (i) and (ii) we get, $V \propto \frac{T}{P}$

or $V = k \frac{T}{P}$ , where $k$ is proportionality constant.

or $\frac{PV}{T} = k$ ------------------(iii)

If $P_{1}$ , $V_{1}$ , and $T_{1}$ are the pressure, volume and temperature in the initial state respectively and $P_{2}$ , $V_{2}$ and $T_{2}$ are the pressure, volume and temperature in the final state respectively, then

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

This equation is known as combined equation. Using this equation we can determine the state of the gas in any unknown condition if the initial state is known.

Now from equation (iii), we can write
$PV = kT$
The value of $k$ depends on the amount of gas taken.
For $1$ mole of gas the value of $R$ is constant called universal gas constant $(R)$ .
i.e. $PV = RT$
For n mole of gas the equation becomes
$PV = nRT$ where $P$ is the pressure in atmospheres (atm), $V$ is the volume in liters $(L)$ , $n$ is the number of moles (mol) and $T$ is the temperature in kelvin $(K)$
This equation is called ideal gas equation.

If we set up the ideal gas law for the values of $1$ mole at Standard temperature and pressure $(STP)$ and calculate for the value of the constant $R$ , we can determine the value of the ideal gas law constant.

$P = 1$ atm
$V = 22.4 L$ (Avogadro's number)
$n = 1$ mol
$R =$ Constant
$T = 273 K (0 ° C)$

Rearranging and putting the aforementioned values

$R = \frac{PV}{nT} \Rightarrow \frac{1 \times 22.4}{1 \times 273} = 0.0821 L atm {mol}^{- 1} K^{- 1}$

Define Boyle’s law and Charles' law. Derive the combined gas equation from the two laws. Find out the value of gas constant $R$ .

Important Questions on States of Matter : Gases and Liquids

Learn and Prepare for any exam you want !

Define Boyle’s law and Charles' law. Derive the combined gas equation from the two laws. Find out the value of gas constant R.

Important Questions on States of Matter : Gases and Liquids

Learn and Prepare for any exam you want !

Define Boyle’s law and Charles' law. Derive the combined gas equation from the two laws. Find out the value of gas constant $R$ .