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For a hypothetical reaction ArarrB, it i...

For a hypothetical reaction `ArarrB`, it is found that the rate constant `= x s^(-1)`. By what factor the rate is increased if the initial concentration of `A` is tripled?

A

`1`

B

`2`

C

`3`

D

`4`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to analyze the effect of tripling the concentration of reactant A on the rate of the reaction A → B. ### Step-by-Step Solution: 1. **Identify the Reaction Order**: The problem states that the rate constant \( k = x \, s^{-1} \). The unit of the rate constant indicates that the reaction is first order with respect to A, since the unit \( s^{-1} \) corresponds to a first-order reaction. 2. **Write the Rate Expression**: For a first-order reaction, the rate \( r \) can be expressed as: \[ r = k [A]^1 \] Therefore, the initial rate \( r_1 \) can be written as: \[ r_1 = k [A] \] 3. **Calculate the New Rate with Tripled Concentration**: If the initial concentration of A is tripled, the new concentration becomes \( 3[A] \). The new rate \( r_2 \) can be expressed as: \[ r_2 = k [3A] = k (3[A]) = 3k [A] \] 4. **Relate the New Rate to the Initial Rate**: We can relate the new rate \( r_2 \) to the initial rate \( r_1 \): \[ r_2 = 3k [A] = 3r_1 \] 5. **Determine the Factor of Increase in Rate**: The factor by which the rate increases when the concentration of A is tripled is given by: \[ \text{Factor of increase} = \frac{r_2}{r_1} = \frac{3r_1}{r_1} = 3 \] ### Conclusion: The rate of the reaction increases by a factor of 3 when the initial concentration of A is tripled.
To solve the problem, we need to analyze the effect of tripling the concentration of reactant A on the rate of the reaction A → B. ### Step-by-Step Solution: 1. **Identify the Reaction Order**: The problem states that the rate constant \( k = x \, s^{-1} \). The unit of the rate constant indicates that the reaction is first order with respect to A, since the unit \( s^{-1} \) corresponds to a first-order reaction. 2. **Write the Rate Expression**: ...
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