Question:
For the reaction $2\mathrm{A} + 2\mathrm{B} \rightarrow 2\mathrm{C} + \mathrm{D}$, if the differential rate law is expressed as $r = k[\mathrm{A}]^2[\mathrm{B}]^0$, then the rate of the reaction is
For the reaction $2\mathrm{A} + 2\mathrm{B} \rightarrow 2\mathrm{C} + \mathrm{D}$, if the differential rate law is expressed as $r = k[\mathrm{A}]^2[\mathrm{B}]^0$, then the rate of the reaction is
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Whenever you see a reactant with a superscript zero ($0$) in a rate law, it indicates a zero-order dependency. You can mentally cross that entire reactant component out of the equation because its concentration has absolutely zero impact on how fast the reaction runs!
Updated On: Jun 18, 2026
- inversely proportional to the square of concentration of A
- independent of concentration of A
- independent of concentration of B
- directly proportional to concentration of B
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
We are given a specific chemical reaction and its experimentally derived rate law expression: $r = k[\mathrm{A}]^2[\mathrm{B}]^0$. We need to interpret the mathematical dependence of the reaction rate on the individual concentrations of reactants A and B.
Step 2: Key Formula or Approach:
In a chemical kinetics rate law expression $r = k[\mathrm{X}]^x[\mathrm{Y}]^y$, the exponent represents the partial order of the reaction with respect to that individual reactant. If an exponent is $2$, the rate is directly proportional to the square of that concentration. If an exponent is $0$, the rate is raised to the zeroth power, meaning changes to that concentration have absolutely no effect on the reaction speed.
Step 3: Detailed Explanation:
Let's analyze the given rate equation component by component:
$$r = k[\mathrm{A}]^2[\mathrm{B}]^0$$ Using the algebraic property where any non-zero term raised to the power of zero equals one ($[\mathrm{B}]^0 = 1$), the equation simplifies directly to:
$$r = k[\mathrm{A}]^2$$ Evaluating our simplified expression against the given choices:
The rate is directly proportional to the square of $[\mathrm{A}]$ (disproving options A and B).
Because the concentration of reactant B is completely absent from the final simplified rate equation, changing the concentration of B will not alter the overall velocity of the reaction. Thus, the rate is entirely independent of the concentration of B.
Step 4: Final Answer:
The rate of the reaction is independent of the concentration of B, corresponding perfectly to option (C).
We are given a specific chemical reaction and its experimentally derived rate law expression: $r = k[\mathrm{A}]^2[\mathrm{B}]^0$. We need to interpret the mathematical dependence of the reaction rate on the individual concentrations of reactants A and B.
Step 2: Key Formula or Approach:
In a chemical kinetics rate law expression $r = k[\mathrm{X}]^x[\mathrm{Y}]^y$, the exponent represents the partial order of the reaction with respect to that individual reactant. If an exponent is $2$, the rate is directly proportional to the square of that concentration. If an exponent is $0$, the rate is raised to the zeroth power, meaning changes to that concentration have absolutely no effect on the reaction speed.
Step 3: Detailed Explanation:
Let's analyze the given rate equation component by component:
$$r = k[\mathrm{A}]^2[\mathrm{B}]^0$$ Using the algebraic property where any non-zero term raised to the power of zero equals one ($[\mathrm{B}]^0 = 1$), the equation simplifies directly to:
$$r = k[\mathrm{A}]^2$$ Evaluating our simplified expression against the given choices:
The rate is directly proportional to the square of $[\mathrm{A}]$ (disproving options A and B).
Because the concentration of reactant B is completely absent from the final simplified rate equation, changing the concentration of B will not alter the overall velocity of the reaction. Thus, the rate is entirely independent of the concentration of B.
Step 4: Final Answer:
The rate of the reaction is independent of the concentration of B, corresponding perfectly to option (C).
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