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Question: Which one of the following is not the value of \(R\) ? A. \[1.99cal{K^{ - 1}}mo{l^{ - 1}}\] B. ...

Which one of the following is not the value of RR ?
A. 1.99calK−1mol−11.99cal{K^{ - 1}}mo{l^{ - 1}}
B. 0.0821litre−atm K−1mol−10.0821litre - atm{\text{ }}{K^{ - 1}}mo{l^{ - 1}}
C. 9.8kcalK−1mol−19.8kcal{K^{ - 1}}mo{l^{ - 1}}
D. 8.3JK−1mol−18.3J{K^{ - 1}}mo{l^{ - 1}}

Explanation

Solution

Hint : RR or gas constant is used in the kinetic theory of gases and its value is determined experimentally and the values turn out to be different for different units it is used in while writing the gas equations whether it is an ideal gas or a real gas.

Complete step by step solution :
As we know, what RR or gas constant is let’s analyse the given values one by one,
A. 1.99calK−1mol−11.99cal{K^{ - 1}}mo{l^{ - 1}} is the value for the gas constant as the experimental value for this unit is 2calK−1mol−12cal{K^{ - 1}}mo{l^{ - 1}} .
B. 0.0821litre−atm K−1mol−10.0821litre - atm{\text{ }}{K^{ - 1}}mo{l^{ - 1}} is the value for the gas constant as the experimental value for this unit is 0.0821litre−atm K−1mol−10.0821litre - atm{\text{ }}{K^{ - 1}}mo{l^{ - 1}} .
C. 9.8kcalK−1mol−19.8kcal{K^{ - 1}}mo{l^{ - 1}} is not the value for the gas constant as the experimental value for this unit is 2calK−1mol−12cal{K^{ - 1}}mo{l^{ - 1}} .
D. 8.3JK−1mol−18.3J{K^{ - 1}}mo{l^{ - 1}} is the value for the gas constant as the experimental value for this unit is 8.314JK−1mol−18.314J{K^{ - 1}}mo{l^{ - 1}} .
So, the value that does not belong to the gas constant is Option C.

Note : In the equation of state of an ideal gas we have the equation, PV=nRTPV = nRT , the value of the universal gas constant would depend totally on the units of measurement. The gas constant is independent of the nature of the gas, the pressure of the gas and the temperature of the gas. For example, as R has different values for different units:
R=R = 2calK−1mol−12cal{K^{ - 1}}mo{l^{ - 1}} , 0.0821litre−atm K−1mol−10.0821litre - atm{\text{ }}{K^{ - 1}}mo{l^{ - 1}} , 8.3JK−1mol−18.3J{K^{ - 1}}mo{l^{ - 1}} .