Final answer:
The correct rate expression for the reaction '[A]² → [B] + [C]' is rate = k[A]², confirming that it's second order with respect to A. Expressions for reactions 'b' and 'c' are correct, but 'd' is incorrect as it should be dependent on [A]², not [B].
Step-by-step explanation:
The rate expression for a chemical reaction indicates the relationship between the rate of the reaction and the concentrations of reactants.
For the reaction ‘a) [A]² → [B] + [C]’, the rate expression is given by rate = k[A]². By using the rate constant k and the concentrations of the reactants, this expression shows how the rate of the reaction depends on the concentration of reactant A raised to the second power, which signifies that the reaction is second order with respect to A.
The rate expressions for the other reactions are incorrect based on the information provided.
For reaction 'b) [A] + [B] → [C]', the correct rate expression would indeed be rate = k[A][B], which represents a reaction that is first order with respect to both A and B.
Conversely, for reaction 'c) [A] → [B] + [C]', the rate expression should be linked to the concentration of reactant A, not the product B, thus the correct rate expression should be rate = k[A], which is first order with respect to A.
Lastly, for reaction 'd) [A]² → [B] + [C]', the rate expression given as rate = k[B] is incorrect as it should be dependent on the concentration of reactant A squared, not on the concentration of product B.