Which expression represents Avogadro’s number as the ratio of the ideal gas constant to Boltzmann’s constant?

• A. k/R
• B. R/k
• C. R^2/k
• D. R*k

Answer: (B)

The essential idea is that Avogadro’s number links macroscopic gas properties to microscopic particle properties. The molar gas constant R is related to the Boltzmann constant k by R = N_A × k. Since R uses per-mole quantities and k is per-particle, dividing R by k gives the number of particles per mole. Therefore Avogadro’s number is N_A = R / k.

Check the units to see why this makes sense: R has units of J/(mol·K), while k has units of J/K. Their ratio R/k then has units of 1/mol, which corresponds to a number of particles per mole. Numerically, R ≈ 8.314 J/(mol·K) and k ≈ 1.381×10^-23 J/K, so R/k ≈ 6.022×10^23 mol^-1, the familiar Avogadro’s number.

Other expressions don’t match the concept: taking the reciprocal would give a quantity with units of mol, not a particle count per mole; squaring or multiplying the constants produces different units and values.