Question

determine the unit of R from dimensional ​

Answer 1

Answer:

Unit of R = kg m² mol⁻¹ K⁻¹ s⁻²

              = (Pa) (m³) (mol)⁻¹ (K)⁻¹              

Explanation:

From all the gas laws, we know that

$\boxed{PV = nRT}$

where, P is the pressure

            V is the volume

            n is the number of moles

            R is the universal gas constant

            T is the temperature

Rearranging the given equation we get,

$PV = nRT$

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

Hence,

Unit of R = [P][V] [n]⁻¹ [T]⁻¹

Unit of R = (kg m⁻¹ s⁻²) (m³) (mol)⁻¹ (K)⁻¹

Unit of R = kg m² mol⁻¹ K⁻¹ s⁻²

or

Unit of R = [P][V] [n]⁻¹ [T]⁻¹

Unit of R = (Pa) (m³) (mol)⁻¹ (K)⁻¹