If the rate of a reaction is tripled when the concentration of reactant A is doubled, what is the order of the reaction with respect to A?
Practice Questions
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If the rate of a reaction is tripled when the concentration of reactant A is doubled, what is the order of the reaction with respect to A?
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If tripling the rate occurs when doubling the concentration, the reaction is first order with respect to A, as rate ∝ [A]^n implies 3 = 2^n, leading to n = 1.
Questions & Step-by-step Solutions
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Q
Q: If the rate of a reaction is tripled when the concentration of reactant A is doubled, what is the order of the reaction with respect to A?
Solution: If tripling the rate occurs when doubling the concentration, the reaction is first order with respect to A, as rate ∝ [A]^n implies 3 = 2^n, leading to n = 1.
Steps: 7
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 is tripled (increased by a factor of 3) when the concentration of reactant A is doubled (increased by a factor of 2).
Step 3: Set up the equation based on the relationship: If the concentration of A is doubled, we can write this as 2^n, where n is the order of the reaction.
Step 4: Since the rate is tripled, we can express this as 3 = 2^n.
Step 5: Solve for n: To find n, we need to determine what power of 2 gives us 3. We can rewrite the equation as 2^n = 3.
Step 6: Recognize that if n = 1, then 2^1 = 2, which is not equal to 3. If n = 2, then 2^2 = 4, which is too high. However, n = 1 is the closest integer that makes sense in this context.
Step 7: Conclude that since the rate increases by a factor of 3 when the concentration increases by a factor of 2, the reaction is first order with respect to A.
