I just need that one question answered and do you work showed

Question

A chemist does a rate analysis on the following reaction:

 

C₃H₆Cl₂ + 3Br^-

⟶⟶

C₃H₆ + 2Cl^- + Br^- 

She gets the following data:

 

Trial	Initial Concentration of C3H6Cl2 (M)	Initial Concentration of Br- (M)	Instantaneous Reaction Rate (M/s)
1	0.080	0.080	0.116
2	0.160	0.080	0.232
3	0.160	0.160	0.232

a. Showing all the math work, what is the rate equation for this reaction (FILL IN the k with units)? 

b. Showing your work, what is k?  (use correct units!) 

c. What is the overall order? 

Answer 1

For reaction A + B->, the rate equation is r=k[A]^m[B]ⁿ where r is the reaction rate, k is the rate constant, and [A] and [B] are the concentrations of A and B, and m and n are the reaction orders for the given components of the reaction. For this reaction, the general form of the rate equation is r=k[C₃H₆Cl₂]^m[Br^-]ⁿ.

To find the exponents, look at how the reaction rate changes when we the reactant concentration changes. If the reaction rate changes by the same factor as the concentration of the reaction (for example, doubling the reactant doubles the rate), we call the reaction first order with respect to that reactant, and the exponent value is 1. If the reaction rate does not change when we change the concentration of a reactant, the exponent is 0 and we say the reaction is zero order with respect to that reactant.

For m, compare trials 1 and 2. When the concentration of C₃H₆Cl₂ doubles (0.08->0.16), the reaction rate doubles (0.116->0.232). Since the change in the concentration of C₃H₆Cl₂ and the change in reaction rate are the same (increase by factor of 2), this means that the reaction is first order with respect to C₃H₆Cl₂ and that m=1.

For n, compare trials 2 and 3. Br^- doubles from 0.08->0.16 and the reaction rate does not change. This means that the reaction is zero order with respect to Br^- and that n=0.

We have reached r=k[C₃H₆Cl₂]¹[Br^-]⁰. Since the concentration of Br^- does not affect the reaction, we can simplify the rate equation to r=k[C₃H₆Cl₂] (the exponent 1 is understood).

a. what is the rate equation for this reaction (FILL IN the k with units)? 

Since r is in units of M/s, the right side must be in M/s. This means k has units of s^-1

r=k(s^-1)[C₃H₆Cl₂]

b. What is k?

Plug trial values into rate equation and solve for k. Using trial 1, 0.116(M/s)=k(0.080M)

Dividing both sides by 0.08M yields k=1.45s^-1.

c. What is the overall order?

Add together the orders of all the reactants. 1+0=1. Therefore the overall order is 1.