For one mole of an ideal gas the slope of V vs. T curve at constant pressure of 2 atm is `XL*mol^(-1)*K^(-1)`. The value of the ideal universal gas constant 'R' in terms of X is-

Options

A. `XL*atm*mol^(-1)*K^(-1)`
B. `(X)/(2)L*atm*mol^(-1)*K^(-1)`
C. `2XL*atm*mol^(-1)*K^(-1)`
D. `2Xatm*L^(-1)*mol^(-1)*K^(-1)`

Answer

C

Explanation

`PV=nRT or, P((V)/(n))=RT`
or, `PV_(m)=RT[V_(m)=`molar volume] or, `V_(m)=(R)/(P)T`
At constant pressure for 1 mol of an ideal gas, `V_(m)=RT`
This relation represents a straight line equation passing through origin. So, for 1 mol of an ideal gas at constant pressure, the graph of `V_(m)` vs. T will be straight line with slope=K.
Given, `K=XL*mol^(-1)*K^(-1)o`
or, `(R)/(P)=XL*mol^(-1)*K^(-1) or, (R)/(2atm)=XL*mol^(-1)*K^(-1)`
`therefore R=2XL*atm*mol^(-1)*K^(-1)`.