Question

The value of the universal gas constant (R) is the same for all gases. What is its physical gas significance?

Answer 1

Hint :A constant is a value or the term of constant of proportionality due to which one term can equate to another. According to the ideal gas equation, the product of pressure and volume is proportional to the product of number of moles and temperature i.e., $ PV\alpha nT $ . However, when we multiply one side with the constant of proportionality they are equal to one another i.e., $ PV = RnT $ .

Complete Step By Step Answer:
The units of any constants depend upon the various entities used for its calculation. The very first formula used for the determination of gas constant was the ideal gas equation. $ PV = nRT $ where p is pressure, v is volume, n is the number of gaseous moles, R is the universal gas constant, T is the temperature. On rearranging the equation we get, $ R = \dfrac{{PV}}{{nT}} $ . The S.I (Standard Internationally) unit of pressure is Pascal, volume is meter cube, number of moles is unitless and temperature is Kelvin.
So the unit of gas constant per mole is, $ R = Pa \times {m^3} \times {K^{ - 1}} \times mo{l^{ - 1}} $ . But the Pascal meter cube is equal to Joule. So the constant has the unit as $ R = J \times {K^{ - 1}} \times mo{l^{ - 1}} $ , as $ J $ is the unit of work done. Thus, we can say on the basis of units, that Gas constant is the work done by the gas per mole per Kelvin.

Note :
Today we have several constants for the constant of proportionality like Plank’s constant with S.I unit joules second, Decay constant with S.I unit per second, Rydberg’s constant with S.I unit per meter, Gas constant with S.I unit pascal meter cube per mole per Kelvin, wein’s constant with S.I unit meter Kelvin, and many more constants.