Consider the reaction A + X products. Two trials are performed at the same temperature and using the same reaction medium. The initial rate is found to increase by a factor of 2.83 when the molar concentration of X is doubled and the molar concentration of A is unchanged.

(a) What is the order with respect to X?
(b) What can you determine about the order with respect to A from the information above?

rate 1 = 1 = k(X)a where a is the order of the reaction.

rate 2 = 2.83 = k(2X)a

Now take the ratio of equation 2 to equation 1 to obtain
2.83/1 = (2)a
Solve for a which is the order of the reaction. I don't get a whole number. Check my thinking. Check my work.

To determine the order with respect to X and A, we can use the method of initial rates. By comparing two trials where the concentrations of X and A are varied, we can analyze how these changes affect the initial rate.

(a) To find the order with respect to X, we compare two trials where only the concentration of X is changed while the concentration of A is kept constant. In one trial, the concentration of X is doubled, and in the other trial, it remains unchanged. The initial rate increases by a factor of 2.83 when the concentration of X is doubled. This suggests that the order with respect to X is approximately 2.

(b) From the information given, we can't directly determine the order with respect to A. The fact that the initial rate doesn't change when the concentration of A is kept constant doesn't provide any insight into the order with respect to A. We would need additional experiments where the concentration of A is varied to determine the order with respect to A.

To summarize:
(a) Based on the information, the order with respect to X is approximately 2.
(b) The information provided doesn't allow us to determine the order with respect to A.