Question

1) For the reaction A ↔ B, equilibrium data is shown below. What is the value of kA that would satisfy the equation: rate of conversion of A to B = kA x number of A molecules?

Time	Number of A Molecules	Number of B Molecules	# of A reacting in next second	# of B reacting in next second	# of A formed in next second	# of B formed in next Second
0	40000	0	6000	0	0	6000
1	34000	6000	5100	2100	2100	5100
2	31000	9000	4650	3150	3150	4650
3	29500	10500	4425	3675	3675	4425
4	28750	11250	4313	3938	3938	4313
5	28375	11625	4256	4069	4069	4256
6	28188	11813	4228	4134	4134	4228
7	28094	11906	4214	4167	4167	4214
8	28047	11953	4207	4184	4184	4207
9	28023	11977	4204	4192	4192	4204
10	28012	11988	4202	4196	4196	4202

2) For the reaction A ↔ B, equilibrium data is shown below. What is the value of kB that would satisfy the equation: rate of conversion of B to A = kB x number of B molecules?

Time	Number of A Molecules	Number of B Molecules	# of A reacting in next second	# of B reacting in next second	# of A formed in next second	# of B formed in next Second
0	40000	0	6000	0	0	6000
1	34000	6000	5100	2100	2100	5100
2	31000	9000	4650	3150	3150	4650
3	29500	10500	4425	3675	3675	4425
4	28750	11250	4313	3938	3938	4313
5	28375	11625	4256	4069	4069	4256
6	28188	11813	4228	4134	4134	4228
7	28094	11906	4214	4167	4167	4214
8	28047	11953	4207	4184	4184	4207
9	28023	11977	4204	4192	4192	4204
10	28012	11988	4202	4196	4196	4202

Answer 1

ANSWER - Part A:

The equation

rate of conversion of A to B = (kA) x (# molecules of A)

it resembles a straight-line equation (y = mx +b) where

• y = rate of conversion of A to B
• m = slope = kA
• x = # molecules of A

Then, we need to plot the rate of conversion of A to B vs. the number of molecules of A:

• The rate of conversion of A to B is the data on the fourth column of table => # of A reacting in the next second = #molecules / s
• # molecules of A => data on second column of table
• Then, the plot is

From the plot we get

Then the value of kA is

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ANSWER - Part B:

It is similar to part A, but in this case the equation is

rate of conversion of B to A = (kB) x (# molecules of B)

where

• y = rate of conversion of B to A
• m = slope = kB
• x = # molecules of B

Then, we need to plot the rate of conversion of B to A vs. the number of molecules of B:

• The rate of conversion of B to A is the data on the fifth column of table => # of B reacting in the next second = #molecules / s
• # molecules of B => data on third column of table
• Then, the plot is

From the plot we get

Then the value of kB is