Use the experimental data below to determine the order of the reaction with respect to [Cr(NH3)5Cl]^2+(aq)+OH^-(aq)-->[Cr(NH3)5(OH)]^2+(aq) +Cl^-(aq)

You must show your work for any calculations and/or sketch or include a printed graph showing how the equation of the line was found.

TABLE

Time,min.....Cr(NH3)6^2+,M
0............1.500
5............0.986
10...........0.648
15...........0.426
20...........0.279
25...........0.183
30...........0.121

To determine the order of the reaction with respect to [Cr(NH3)5Cl]^2+(aq) + OH^-(aq), we can use the method of initial rates. The rate of a reaction can be determined by comparing the change in concentration of a reactant over a given time period. By conducting multiple experiments with varying concentrations and observing how the rate changes, we can deduce the order of the reaction.

From the given table, we can calculate the initial rate of the reaction for each experiment by finding the change in concentration of [Cr(NH3)5Cl]^2+(aq) and dividing it by the time interval. Let's calculate the initial rates for each experiment:

Experiment 1 (0 - 5 min):
Initial concentration of [Cr(NH3)5Cl]^2+(aq) = 1.500 M
Change in concentration of [Cr(NH3)5Cl]^2+(aq) = 1.500 M - 0.986 M = 0.514 M
Time interval = 5 - 0 min = 5 min

Initial rate = (0.514 M) / (5 min) = 0.1028 M/min

You can calculate the initial rates for the other experiments in a similar way:

Experiment 2 (5 - 10 min):
Initial concentration = 0.986 M
Change in concentration = 0.986 M - 0.648 M = 0.338 M
Time interval = 10 - 5 min = 5 min

Initial rate = (0.338 M) / (5 min) = 0.0676 M/min

Experiment 3 (10 - 15 min):
Initial concentration = 0.648 M
Change in concentration = 0.648 M - 0.426 M = 0.222 M
Time interval = 15 - 10 min = 5 min

Initial rate = (0.222 M) / (5 min) = 0.0444 M/min

Experiment 4 (15 - 20 min):
Initial concentration = 0.426 M
Change in concentration = 0.426 M - 0.279 M = 0.147 M
Time interval = 20 - 15 min = 5 min

Initial rate = (0.147 M) / (5 min) = 0.0294 M/min

Experiment 5 (20 - 25 min):
Initial concentration = 0.279 M
Change in concentration = 0.279 M - 0.183 M = 0.096 M
Time interval = 25 - 20 min = 5 min

Initial rate = (0.096 M) / (5 min) = 0.0192 M/min

Experiment 6 (25 - 30 min):
Initial concentration = 0.183 M
Change in concentration = 0.183 M - 0.121 M = 0.062 M
Time interval = 30 - 25 min = 5 min

Initial rate = (0.062 M) / (5 min) = 0.0124 M/min

Now that we have calculated the initial rates for each experiment, we need to determine the order of the reaction. By comparing the initial rates for various experiments while keeping the concentration of OH^-(aq) constant, we can determine the order.

To find the order, we need to examine how the initial rate changes as the concentration of [Cr(NH3)5Cl]^2+(aq) changes while keeping the concentration of OH^-(aq) constant. One way to visualize this relationship is to plot the initial rate against the concentration of [Cr(NH3)5Cl]^2+(aq).

Let's create a graph with the initial rate (y-axis) and the concentration of [Cr(NH3)5Cl]^2+(aq) (x-axis):

Initial Rate (M/min) |
|
|
|
|
|________________________
0.0 0.5 1.0 1.5 2.0

Now, plot the points with the corresponding initial rate and concentration values:

(1.500 M, 0.1028 M/min)
(0.986 M, 0.0676 M/min)
(0.648 M, 0.0444 M/min)
(0.426 M, 0.0294 M/min)
(0.279 M, 0.0192 M/min)
(0.183 M, 0.0124 M/min)

Connect these points with a line. The equation of the line can be found using linear regression techniques in a graphing software or by calculating the slope and y-intercept using the least squares method. Once you have the equation of the line, you can determine the order of the reaction with respect to [Cr(NH3)5Cl]^2+(aq).

For example, if the equation of the line is y = mx + b, where y is the initial rate and x is the concentration of [Cr(NH3)5Cl]^2+(aq), then the order can be determined from the value of the exponent m. If m = 2, then the reaction is second order with respect to [Cr(NH3)5Cl]^2+(aq).

Remember that this is just a general method to determine the order of a reaction. The actual order can be a fraction or a non-integer value. The method of initial rates can be applied to other experiments as well to verify the order of the reaction.