Question

What is the dimensional formula of the universal gas constant with process?

A) [M^1 L^2 T^-2 K^-1]
B) [M^1 L^2 T^-2 K^-1 mol^-1]
C) [M^1 L^2 T^-2 K^-1 mol^-2]
D) [M^1 L^2 T^-2 K^-1 mol^2]

Answer 1

The dimensional formula of the universal gas constant R is [M^1L^2T^-2K^-1mol^-1], which corresponds to the units of R in SI units. The correct option is B) [M^1L^2T^-2K^-1mol^-1].

Step-by-step explanation:

The dimensional formula of the universal gas constant, denoted as R, is determined by analyzing the units it is expressed in. For the ideal gas law PV = nRT, where P is pressure, V is volume, T is temperature, and n is the amount of substance, the constant R has units that accommodate these quantities. When we consider the units (L*atm)/(mol*K) and convert atm to its basic units, we get that 1 atm = 101325 Pa = 101325 (kg/(m*s2)). Thus, we can express R in basic SI units as:

R = (101325 kg*m2)/(s2*mol*K)

This simplifies to R having the dimensional formula:

[M1L2T-2K-1mol-1]

Therefore, the correct option is B) [M1L2T-2K-1mol-1].