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Diazonium salt decomposes as C(6)H(5)N...

Diazonium salt decomposes as
`C_(6)H_(5)N_(2)^(o+)Cl^(ɵ) rarrC_(6)H_(5)Cl+N_(2)`
at `10^(@)C`, the evolution of `N_(2)` becomes two first faster when the initial concentration of the salt is doubled. Thus, it is

A

A first order reaction

B

A second order reaction

C

Independent of the initial concentration of reactant

D

A zero order reaction.

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The correct Answer is:
To solve the problem regarding the decomposition of diazonium salt, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Reaction**: The decomposition of diazonium salt can be represented as: \[ C_6H_5N_2^+Cl^- \rightarrow C_6H_5Cl + N_2 \] Here, we are interested in the rate of evolution of \( N_2 \). 2. **Understanding Rate of Reaction**: The rate of a reaction can be expressed as: \[ \text{Rate} = k [C_6H_5N_2^+]^x \] where \( k \) is the rate constant, \( [C_6H_5N_2^+] \) is the concentration of the diazonium salt, and \( x \) is the order of the reaction. 3. **Effect of Doubling Concentration**: According to the problem, when the initial concentration of the diazonium salt is doubled, the rate of evolution of \( N_2 \) becomes two times faster. This can be mathematically expressed as: \[ \text{Rate}' = 2 \times \text{Rate} \] If we denote the initial concentration as \( [C_6H_5N_2^+] \), then when it is doubled, we have: \[ \text{Rate}' = k (2[C_6H_5N_2^+])^x \] 4. **Setting Up the Equation**: From the above, we can set up the equation: \[ k (2[C_6H_5N_2^+])^x = 2 \times k [C_6H_5N_2^+]^x \] Simplifying this gives: \[ k \cdot 2^x \cdot [C_6H_5N_2^+]^x = 2 \cdot k \cdot [C_6H_5N_2^+]^x \] 5. **Canceling Common Terms**: We can cancel \( k \) and \( [C_6H_5N_2^+]^x \) from both sides (assuming \( [C_6H_5N_2^+] \neq 0 \)): \[ 2^x = 2 \] 6. **Solving for x**: To find \( x \), we can equate: \[ 2^x = 2^1 \] This implies: \[ x = 1 \] 7. **Conclusion**: The order of the reaction is 1, meaning it is a first-order reaction. ### Final Answer: The order of the reaction is **1** (first-order reaction).

To solve the problem regarding the decomposition of diazonium salt, we can follow these steps: ### Step-by-Step Solution: 1. **Identify the Reaction**: The decomposition of diazonium salt can be represented as: \[ C_6H_5N_2^+Cl^- \rightarrow C_6H_5Cl + N_2 ...
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