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**Hint:**While solving this question one should state the law and can give an explanation with the mathematical expression for this law corresponding to the ideal gas law and equation.

**Complete answer:**

1) First of all we will see the statement of Avogadro’s law where it is a gas law that states as the total number of atoms or molecules present in a gas are directly proportional to the volume that the gas occupies at the constant temperature and pressure.

2) This statement of Avogadro’s law can be expressed as,

${\text{V}} \propto {\text{n}}$

Where ${\text{V = }}$ the volume of the gas

${\text{n = }}$ the number of moles of gas.

We can write this equation by putting the constant as,

${\text{V = Kn}}$

Where K is the Avogadro's constant.

3) Now if we consider two gases of volume ${{\text{V}}_1}{\text{ and }}{{\text{V}}_2}$ and their number of moles as ${{\text{n}}_1}{\text{ and }}{{\text{n}}_2}$ respectively we can compare them by an equation,

$\dfrac{{{V_1}}}{{{V_2}}} = \dfrac{{{n_1}}}{{{n_2}}}$

As we took the value of K i.e. Avogadro's constant on both sides,

3) Now let's see the derivation by using the ideal gas law. According to the ideal gas law,

${\text{PV = nRT}}$

Where P is pressure

V is the volume of gas

N is the number of moles of gas

R is the universal gas constant

T is the absolute temperature of a gas

4) Now in order to get the equation for Avogadro’s constant, we need to compare it with the same value representation in the ideal gas equation. Hence, by rearranging the ideal gas equation we get,

$\dfrac{V}{n} = \dfrac{{RT}}{P}$

As we know $\dfrac{V}{n} = K$

We can say that $K = \dfrac{{RT}}{P}$

Therefore, from the above equation, the proportionality between the volume of a gas and the number of moles of gas is verified.

**Note:**

The graph which is drawn between the volume of gas and the number of moles of gas is a straight line which shows these two values are directly proportional to each other. Avogadro’s law is applicable to the ideal gases and it shows approximate values for the real gases. This law is very much applicable for light element gases such as hydrogen and helium than higher element gases.

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