Question

Determine the rate law, including the values of the orders and rate law constant, for the following reaction using the experimental data provided.

Answer 1

Trial [Q] [X] Rate
1 0.12 M 0.10 M 1.5 × 10-3 M/min
2 0.24 M 0.10 M 3.0 × 10-3 M/min
3 0.12 M 0.20 M 12.0 × 10-3 M/min

Answer 2

do you know how to relate the reaction rate to the concentrations of the reactants?

Answer 3

to find the order of each reactant, find the ratio of the rates when the concentrations are changed.

I'm assuming the reaction is:\[Q + X \rightarrow QX\] so the starting concentrations of Q and X are given, as well as the initial rate

Answer 4

the equation for a rate law is:\[Rate = k*[Q]^m*[X]^n\]the value of k I don't know, and the values of m and n ARE NOT THE SAME AS THE BALANCED COEFFICIENTS (important to remember that)

Answer 5

I'm going to divide R2 by R1 and show you what I get

Answer 6

\[\frac{R_2}{R_1} = \frac{k*[0.24]^m*[0.10]^n}{k*[0.12]^m*[0.10]^n}\]

Answer 7

k[q][x]^3

Answer 8

no

Answer 9

oh ok

Answer 10

the exponents for the rate law have to be determined using data, so the powers of Q and X are unknown (so far). that's what i'm going to solve for

Answer 11

ohhh ok

Answer 12

in the equation i posted, the RATIO of rates is what's important

Answer 13

\[\frac{R_2}{R_1} = \frac{k*[0.24]^m*[0.10]^n}{k*[0.12]^m*[0.10]^n} = \frac{3.0*10^{-3}}{1.5*10^{-3}} = 2\]

Answer 14

see what happens to the K's? See what happens to the value of n?

Answer 15

ther whole #s

Answer 16

they cancel

Answer 17

the ns cancel?

Answer 18

the n's cancel because the concentrations of X are the same.

When you divide 0.1 by 0.1, you get 1.

You raise 1 to any power and you get 1, so the entire term of X^n cancels

Answer 19

ok so how do you find the final answer?

Answer 20

I don't have the final answer yet

Answer 21

you have to set it up so that all terms cancel except one at a time

Answer 22

\[\frac{R_2}{R_1} = \frac{k*[0.24]^m*[0.10]^n}{k*[0.12]^m*[0.10]^n} = \frac{3.0*10^{-3}}{1.5*10^{-3}} = 2\]so\[2 = \frac{[0.24]^n}{[0.12]^n} = 2^n\]

Answer 23

okkkk

Answer 24

the K's cancel because they're equal. the n's cancel because the concentrations of X are the same, so it's 1^n which always equals 1

Answer 25

the only terms left over simplify into 2^n = 2. There's only 1 number that makes that true.

Answer 26

ok

Answer 27

do you have the final answer?

Answer 28

what's the only possible answer for n, in this case?

Answer 29

n=2

Answer 30

no\[2^n = 2\]
n must equal 1

Answer 31

ohh

Answer 32

2^n=2

Answer 33

?

Answer 34

2^n = 2, so n must equal 1

Answer 35

do the same thing with R3/R1, to solve for the value of the other power

Answer 36

divide by 2 on the left

Answer 37

no.

write out the whole equations and see which parts cancel by taking R3/R1

Answer 38

can you show me?

Answer 39

do the same thing i did above doing R2/R1, but use the data from R3 on top instead of R2

Answer 40

\[r3=k*12*20\]

Answer 41

that's R3, now what's R3/R1? set it up like I did above

Answer 42

k*12*10

Answer 43

that's R1, now divide R3/R1\[\frac {R_3}{R_1} = \]

Answer 44

im not sure

Answer 45

okk,then what?

Answer 46

simplify and solve for n

Answer 47

how?

Answer 48

1

Answer 49

sorry, made a typo. it should be: \[\frac{R_3}{R_1} = \frac{k*[0.12]^m*[0.20]^n}{k*[0.12]^m*[0.10]^n} = \frac{12*10^{-3}}{1.5*10^{-3}}\]

the k's cancel, the m's cancel. all you're left with is\[\frac{R_3}{R_1} = \frac{[0.20]^n}{[0.10]^n} = \frac{12*10^{-3}}{1.5*10^{-3}}\]

Answer 50

how do we get past this part?

Answer 51

simplify and solve for n. algebra

Answer 52

can you help?

Answer 53

\[\frac{R_3}{R_1} = (\frac{[0.20]}{[0.10]})^n = \frac{12*10^{-3}}{1.5*10^{-3}} = 8\]

\[2^n = 8\]

Answer 54

thats not the final tho

Answer 55

that's true. what's the only value of n that makes that equation true?

Answer 56

umm? lol

Answer 57

4?

Answer 58

2x4 is 8, but 2 RAISED to the 4th is not 8

Answer 59

ok so? im not sure :/

Answer 60

\[2^1= 2\]\[2^2 = 2 * 2\]\[2^3 = 2*2*2\]\[2^4 = 2*2*2*2\]

Answer 61

oh okkk that mases sence

Answer 62

so what value of 2^n = 8?

Answer 63

2^4=8

Answer 64

?

Answer 65

2*2*2*2 = 8?

Answer 66

3

Answer 67

n = 3

Answer 68

oh okk so what would be the fnal answer?

Answer 69

What's the value of k? the powers of Q and X are now solved for, so find the value of k

Answer 70

okk so whats next?

Answer 71

plug in a set of values and solve for k. you've got 3 trials to pick from

Answer 72

how do we do yhat?

Answer 73

pick one of the trials. plug in numbers into the equation for rate. solve for k

Answer 74

can you set one up for me?

Answer 75

i think you should try setting it up first

Answer 76

Here is a chapter on kinetics that should be of interest to you, Jfraser seems to be able to help you at the moment im in lecture so I cant really be of help to you.

Answer 77

He has pretty much given you the answer just take a break and come back to it :) Im sure you can get it.

Answer 78

ive been trying lol

Answer 79

r=2*12*10 ?

Answer 80

\[R = k*[Q]^1*[X]^3\]\[1.5*10^{-3} = k*[0.12]^1*[0.10]^3\]

Answer 81

how do i know if its right

Answer 82

because i've done all the work. it's right

Answer 83

solve for k

Answer 84

10^-3 = -1000?

Answer 85

no. 10^-3 is 0.001

Answer 86

0.0015

Answer 87

0.0015=k*.00012

Answer 88

k=.08

Answer 89

no. you flipped it upside down

Answer 90

? how lol

Answer 91

oh i see the right side is positive 10^3

Answer 92

-.00012

Answer 93

-0.08 ?

Answer 94

it's upside down, not negative. If\[0.0015 = k*0.00012\]then\[k = \frac{0.0015}{0.00012}\] you flipped the fraction upside down

Answer 95

so it a whole #

Answer 96

k=12.5

Answer 97

it's not guaranteed to be a whole number, just larger than 1

k =12.5