Here's what I got.
First thing first, you mistyped the complex ion listed for option (2). More specifically, it's not
Now, the idea here is that you need to compare the equation given to you
#log(k/k_0) = -4 * 0.51 * sqrt(I)" " " "color(purple)((1))#
with this equation right here
#color(blue)(logk = logk_0 + 2 * Q * Z_AZ_B * sqrt(I))" "#, where
SIDE NOTE I will not go into the derivation for this particular equation, since I assume that you're familiar with the salt effect (both primary and secondary).
Before moving forward, it's important to note that for water at room temperature, i.3.
#Q = 0.509 ~~0.51#
So, rearrange the second equation to get
#logk - logk_0 = 2 * 0.51 * Z_AZ_B * sqrt(I)#
This is of course equivalent to
#log(k/k_0) = 2 * 0.51 * Z_AZ_B * sqrt(I)" " " "color(purple)((2))#
#-4 * color(red)(cancel(color(black)(0.51))) * color(red)(cancel(color(black)(sqrt(I)))) = 2 * color(red)(cancel(color(black)(0.51))) * Z_AZ_B * color(red)(cancel(color(black)(sqrt(I))))#
Therefore, you can say that
#Z_AZ_B = ((-4))/2 = -2#
Simply put, the product of the net charges carried by your ions must be equal to
Right from the start, you can conclude that your solution must feature both positively charged ions, or cations, and an odd number of negatively charged ions, or anions.
Any reaction that features a neutral molecule will have
#Z_AZ_B = 0 ->#rate constant is independent of ionic strength
By comparison, you can say that if
#Z_BZ_B > 0 ->#the rate of the reaction will increase with an increase in the solution's ionic strength
#Z_AZ_B < 0 ->#the rate of the reaction will decrease with an increase in the solution's ionic strength
In your case, the rate constant decreases upon the addition of an electrolyte.
So, take a look at you options. Option (4) features hydrogen peroxide,
For option (1), you have the peroxydisulfate anion,
#Z_AZ_B = (2-) xx (1-) = +2 != -2#
Option (3) features a neutral molecule as well, ethyl acetate,
This of course leaves you with option (2), for which you have a
#Z_AZ_B = (2+) xx (1-) = -2 color(white)(x)color(green)(sqrt())#