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The rate constant is numerically the same for three reactions of first, second and third orders respectively. When concentration is less than unity, the rate of reactions are, in order:
- a)R1 > R2 > R3
- b)R3 > R2 > R1
- c)R3 > R1 > R2
- d)R2 > R3 > R1
Correct answer is option 'A'. Can you explain this answer?
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The rate constant is numerically the same for three reactions of first...
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The rate constant is numerically the same for three reactions of first...
Explanation:
Given that the rate constant is numerically the same for three reactions of first, second and third orders respectively. Let the rate constants be k1, k2, and k3 for the three reactions of first, second, and third order, respectively.
The rate law for each of the three reactions can be written as:
R1: Rate = k1[A]
R2: Rate = k2[A]^2
R3: Rate = k3[A]^3
Where [A] is the concentration of the reactant.
When the concentration of the reactant is less than unity, i.e., [A] < 1,="" the="" rate="" of="" reaction="" can="" be="" compared="" by="" calculating="" the="" values="" of="" the="" rate="" constants="" at="" some="" arbitrary="" concentration,="" say="" [a]="" />
For R1: Rate = k1[0.1]
For R2: Rate = k2[0.1]^2
For R3: Rate = k3[0.1]^3
Since the rate constants are numerically the same, the rate of the reaction would be directly proportional to the concentration of the reactant. Therefore, the order of the reactions with respect to the rate of reaction would be the same as the order of the reactions with respect to the order of the reaction.
Hence, the order of reactions in decreasing order of their rate is R1, R2, R3.
Therefore, the correct answer is option 'A'.
Conclusion:
The order of the reactions with respect to the rate of reaction would be the same as the order of the reactions with respect to the order of the reaction. For the given reactions, the order of reactions in decreasing order of their rate is R1, R2, R3.
Given that the rate constant is numerically the same for three reactions of first, second and third orders respectively. Let the rate constants be k1, k2, and k3 for the three reactions of first, second, and third order, respectively.
The rate law for each of the three reactions can be written as:
R1: Rate = k1[A]
R2: Rate = k2[A]^2
R3: Rate = k3[A]^3
Where [A] is the concentration of the reactant.
When the concentration of the reactant is less than unity, i.e., [A] < 1,="" the="" rate="" of="" reaction="" can="" be="" compared="" by="" calculating="" the="" values="" of="" the="" rate="" constants="" at="" some="" arbitrary="" concentration,="" say="" [a]="" />
For R1: Rate = k1[0.1]
For R2: Rate = k2[0.1]^2
For R3: Rate = k3[0.1]^3
Since the rate constants are numerically the same, the rate of the reaction would be directly proportional to the concentration of the reactant. Therefore, the order of the reactions with respect to the rate of reaction would be the same as the order of the reactions with respect to the order of the reaction.
Hence, the order of reactions in decreasing order of their rate is R1, R2, R3.
Therefore, the correct answer is option 'A'.
Conclusion:
The order of the reactions with respect to the rate of reaction would be the same as the order of the reactions with respect to the order of the reaction. For the given reactions, the order of reactions in decreasing order of their rate is R1, R2, R3.
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The rate constant is numerically the same for three reactions of first, second and third orders respectively. When concentration is less than unity, the rate of reactions are, in order:a)R1 > R2 > R3b)R3 > R2 > R1c)R3 > R1 > R2d)R2 > R3 > R1Correct answer is option 'A'. Can you explain this answer?
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