If the rate of a reaction doubles when the concentration of reactant A is triple

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Question: If the rate of a reaction doubles when the concentration of reactant A is tripled, what is the order of the reaction with respect to A?

Options:

Correct Answer: 1

Solution:

If doubling the rate occurs when tripling the concentration, the reaction is first order with respect to A, as rate ∝ [A]^n implies 2 = 3^n.

If the rate of a reaction doubles when the concentration of reactant A is tripled, what is the order of the reaction with respect to A?

If the rate of a reaction doubles when the concentration of reactant A is tripled, what is the order of the reaction with respect to A?

Step 1: Understand that the rate of a reaction depends on the concentration of reactants. This relationship can be expressed as rate ∝ [A]^n, where n is the order of the reaction with respect to A.
Step 2: Identify the information given: the rate of the reaction doubles (becomes 2 times) when the concentration of A is tripled (becomes 3 times).
Step 3: Set up the equation based on the information: If the original rate is R and the original concentration of A is [A], then when the concentration is tripled, it becomes 3[A].
Step 4: Write the relationship for the rates: 2R = k(3[A])^n, where k is the rate constant.
Step 5: Compare the two rates: R = k[A]^n and 2R = k(3[A])^n.
Step 6: Divide the second equation by the first: 2 = (3^n) because the k and [A] terms cancel out.
Step 7: Solve for n: 2 = 3^n. To find n, take the logarithm or recognize that 3^1 = 3 and 3^0 = 1, so n must be 1.
Step 8: Conclude that the order of the reaction with respect to A is 1.

Rate of Reaction – The relationship between the concentration of reactants and the rate at which a reaction occurs.
Order of Reaction – The exponent to which the concentration of a reactant is raised in the rate law, indicating how the rate depends on that concentration.
Rate Law – An equation that relates the rate of a reaction to the concentration of reactants, typically expressed as rate = k[A]^n.