To determine which chemical reaction follows an overall second-order rate law, we need to examine each given rate law and calculate the overall reaction order.
1. Rate Law: [tex]\( R = k[A]^2[B]^2 \)[/tex]
- The reaction order with respect to [tex]\( A \)[/tex] is 2.
- The reaction order with respect to [tex]\( B \)[/tex] is 2.
- The overall order of the reaction: [tex]\( 2 + 2 = 4 \)[/tex].
- This is a fourth-order reaction.
2. Rate Law: [tex]\( R = k[A][B] \)[/tex]
- The reaction order with respect to [tex]\( A \)[/tex] is 1.
- The reaction order with respect to [tex]\( B \)[/tex] is 1.
- The overall order of the reaction: [tex]\( 1 + 1 = 2 \)[/tex].
- This is a second-order reaction.
3. Rate Law: [tex]\( R = k \)[/tex]
- There are no concentration terms for [tex]\( A \)[/tex] or [tex]\( B \)[/tex]; hence, their exponents are 0.
- The overall order of the reaction: [tex]\( 0 + 0 = 0 \)[/tex].
- This is a zero-order reaction.
4. Rate Law: [tex]\( R = k[B] \)[/tex]
- The reaction order with respect to [tex]\( B \)[/tex] is 1.
- There is no [tex]\( A \)[/tex] term, indicating an exponent of 0 for [tex]\( A \)[/tex].
- The overall order of the reaction: [tex]\( 0 + 1 = 1 \)[/tex].
- This is a first-order reaction.
Among the given options, the rate law that represents an overall second-order reaction is:
[tex]\[ R = k[A][B] \][/tex]
Therefore, the correct answer is:
[tex]\[ R = k[A][B] \][/tex]
