A few chemistry problems I need help with

Question

A chemist ran a particular reaction at different temperatures to determine the activation energy of the reaction. The plot of his data displayed the following linear regression. Determine the activation energy of the studied reaction.

y = ax + b

a = -1449

b = 13.788

Determine the rate law and the value of the rate constant (k) from the data given below. Include units on the rate constant.  

Experiment	[A] (M)	[B] (M)	Initial rate (M/s)
1	0.50	0.60	2.0 x 10-3
2	1.00	0.60	4.0 x 10-3
3	0.50	1.80	6.0 x 10-3

Consider the dissolution of ammonium nitrate shown in the equation below.

NH4NO3 (s) → NH4+ (aq) + NO3- (aq)

1. Identify and explain one method a chemist could employ to increase the rate of the dissolution.

1. Identify and explain one method a chemist could use to measure the rate of this process.

Answer 1

For the first question, you neglected to mention what the plot was, or what the x and y axes were. I'll assume it was an Arrhenius plot of ln k vs 1/T according to the linear equation ln k = -Ea/R(1/T) + ln A in the form of y = ax + b.

a = slope = -Ea/R = -1449 where R = 8.314 J/mol-K

-Ea = (8.314)(-1449)

Ea = 12,047 but since you gave no units for the slope or the experiment in general, I can't assign units to this except that it is generally given in joules/mole.

For the next question, find the order of the reaction with respect to A and B:

Comparing Expt. 1 and 2 where [A] doubles and [B] remains the same, the rate doubles. This tells us that the reaction is FIRST ORDER WITH RESPECT TO A

Comparing Expt. 1 and 3 where [B] triples and [A] remains the same, the rate triples. This tells us that the reaction is FIRST ORDER WITH RESPECT TO B

We can now write the rate law as...

rate = k[A][B]

From the rate law and using any one of the experiments, we can find the value of k as follows:

using experiment 1, rate = 2.0x10^-3 M/s and we know that rate = [A][B], so...

2.0x10^-3 M/s = k[0.50 M][0.60 M]

k = 2.0x10^-3 M/s / [0.50 M][0.60 M]

k = 6.67x10^-3 M^-1s^-1

Finally, if you knew that the dissolution of NH4NO3 was/is endothermic, you would warm the solution in order to increase the rate of the reaction, i.e. to increase the rate at which the salt dissolved. You could also grind the solid NH4NO3(s) into finer particles to increase the rate of dissolution, or you could stir the solution during the dissolution process to increase the rate. As for determining the actual rate, this is difficult unless you use sophisticated methods (flow through, disc, etc.).

Answer 2

Look at initial rate data for 2 instances when A or B are held constant and solve

(A2/A1)ⁿ = r2/r1 for B constant where n is the order. In this case n = 1 for A and B

For EA , I assume the linear relationship is lnk2/k1 = (-EA/R)(1/T2 - 1/T1) or slope is EA/R R = 8.314 J/mole K