The SI unit of universal gas constant (R) is

Correct Answer: Joule K^-1 mol^-1

To find the SI unit of the universal gas constant (R), we can derive it from the ideal gas equation:

$PV=nRT$

Rearranging the equation to solve for R, we get:

$R=\frac{PV}{nT}$
Where:

• P represents pressure (SI unit: Pascal, Pa, or Newton per square meter, N m^-2)
• V represents volume (SI unit: cubic meter, m³)
• n represents the amount of substance (SI unit: mole, mol)
• T represents absolute temperature (SI unit: Kelvin, K)

Let us substitute the SI units of these variables into the expression for R:

The unit of the numerator (P × V) represents work or energy:

$\text{Unit of P}\times \text{Unit of V}={\text{N m}}^{-2}\times {\text{m}}^3=\text{N m}=\text{Joule (J)}$

The unit of the denominator (n × T) is:

$\text{mol}\times \text{K}$

Combining these, we get the SI unit of R as:

$\text{Unit of R}=\frac{\text{Joule}}{\text{mol}\times \text{K}}={\text{Joule K}}^{-1}{\text{mol}}^{-1}$

Thus, the SI unit of the universal gas constant (R) is Joule K^-1 mol^-1.