Question

Q. No. 24: The equation of state for 7 g of nitrogen gas at a pressure P'and 1 point
temperature 'T' occupying a volume 'V' will be:​

Answer 1

To find:

The equation of state for 7 g of nitrogen gas at a pressure 'P'and temperature 'T' occupying a volume 'V' will be ?

Calculation:

In order to do the calculations easily, we need to consider nitrogen as an IDEAL GAS , such that it will follow the ideal gas equation:

$\sf\therefore \: PV = nRT$

• Here , "n" refers to the number of moles of ideal gas. The Equation can be rearranged as follows:

$\sf\implies\: PV = \bigg( \dfrac{given \: mass}{molar \: mass} \bigg)\times RT$

$\sf\implies\: PV = \bigg( \dfrac{7}{14 + 14} \bigg)\times RT$

$\sf\implies\: PV = \bigg( \dfrac{7}{28} \bigg)\times RT$

$\sf\implies\: PV = \bigg( \dfrac{1}{4} \bigg)\times RT$

$\sf\implies\: PV = \dfrac{ RT}{4}$

So, the required Equation will be:

$\boxed{ \bf{ \red{\: PV = \dfrac{ RT}{4}}}}$