The ratio of the ideal gas constant to Boltzmann's constant is a relation often discussed in chemistry. Which option expresses this correctly?

• A. Boltzmann constant divided by the ideal gas constant
• B. Ideal gas constant divided by Boltzmann's constant
• C. Product of the constants
• D. Sum of the constants

Answer: (B)

Understanding a ratio means comparing how many times one quantity contains another. The ratio of the ideal gas constant to Boltzmann's constant is expressed as R divided by k_B. The ideal gas constant R ties the macroscopic gas behavior to amount of substance through PV = nRT, where n is in moles. Boltzmann's constant k_B connects energy at the particle level to temperature, with relationships like E = k_B T and p = Nk_B T for a gas of N particles.

Forming R/k_B puts these scales together and yields units of 1/mol. More importantly, R/k_B equals Avogadro’s number, N_A, about 6.02×10^23 mol^-1, which is the number of particles in one mole. This is why this ratio is often discussed: it directly links per-mole quantities to per-particle quantities.

Taking the reciprocal would give k_B/R and changes the meaning to a per-particle-to-per-mole perspective, not the straightforward ratio of the two constants. Multiplying or adding the constants does not express a simple ratio between them.