Question

The value of $RT$ for $5.6{{ }}L$ of ideal gas at STP is reported to be $x$ times the value of PV. The value of $x$ is:
(A) $2$
(B) $0.25$
(C) $1$
(D) $4$

Answer 1

Hint : To solve this, we will use the ideal gas equation at STP conditions, and then we will calculate the number of moles for $5.6{{ }}L$ of ideal gas. After that we will solve for $x$ by comparing the equations at both the conditions.
Formula Used
The Ideal gas law is represented by;
$PV = nRT$
Where, $P =$ Pressure of the gas, $T =$ Temperature of the gas
$V =$ The volume of the gas, $n =$ No. of moles of gas and $R = 0.082$ (Gas Constant).

Complete step by step solution
According to the question;
$RT = x \times PV$
It will become;
$P = \dfrac{{RT}}{{xV}}.......(i)$
Now, according to ideal gas equation we have:
$PV = nRT$
It could be written as;
$P = \dfrac{{nRT}}{V}......(ii)$
On comparing (i) and (ii) we get;
$\dfrac{{RT}}{{xV}} = \dfrac{{nRT}}{V}$
$\Rightarrow x = \dfrac{1}{n}.......(iii)$
Now, we will calculate the number of moles in $5.6L$ of gas at STP. We know that at STP $22.6L$ contains one mole of gas.
Number of moles in $1L$ of gas $= \dfrac{1}{{22.4}}$
Number of moles in $5.6L$ of gas $= \dfrac{1}{{22.4}} \times 5.6 = 0.25$
Now we will put this value of $n$ in (iii) to calculate $x$ . It will be;
$\Rightarrow x = \dfrac{1}{n}$
$\Rightarrow x = \dfrac{1}{{0.25}} = \dfrac{{100}}{{25}} = 4$
$\Rightarrow x = 4$
Hence the value of $RT$ for $5.6{{ }}L$ of ideal gas at STP will be $4$ . Therefore, option (C) is correct.

Additional Information
In Ideal gas, the gas molecules are allowed to move uniformly in all directions, and the collision between them is said to be perfectly elastic which means there is no loss in the kinetic energy of the molecule. It always remains conserved. In ideal gases the collision is intermolecular.

Note
The molecules in an ideal gas are perfectly elastic and also there is no intermolecular force of attraction between them. An ideal gas is represented by four variables $P,{{ }}V\,and\,T$ as well as $n$ constant. Here $P$ represents pressure, $V$ volume, $T$ temperature as well as $n$ the number of moles.