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

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.

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.