For the reaction 3A → B, the dimensions of the rate constant are given as (L per gm-mole) per minute, i.e., (L·(gm-mole)^{-1})·min^{-1}. What is the reaction order?

Introduction / Context:Units of the rate constant reveal the reaction order when concentration units are specified. This is a staple skill in reaction engineering.

Given Data / Assumptions:

• Rate law form: r = k C^n for a single key species basis.
• Units of concentration: gm-mole per liter (gm-mole·L^-1).
• Units of k given: L·(gm-mole)^{-1}·min^{-1} = (concentration)^{-1}·time^{-1}.

Concept / Approach:For an nth order reaction, k has units (concentration)^{1-n} / time. Match the given units to solve for n.

Step-by-Step Solution:1) General: [k] = (conc)^{1-n} / time.2) Given: [k] = (conc)^{-1} / time.3) Equate exponents: 1 - n = -1 ⇒ n = 2.

Verification / Alternative check:Check typical patterns: first order has 1/time; second order has 1/(conc·time). The given matches second order.

Why Other Options Are Wrong:Zero/first/third/half orders have different unit patterns; only second order yields (conc)^{-1}/time.

Common Pitfalls:Using mass units instead of molar concentration; forgetting that the stoichiometric coefficient (3A → B) does not mandate the kinetic order.

Final Answer:Second order.