SME
General Chemistry II · Problem type
Order and rate constant from initial rates
Use this for “With [B] held at 0.100 M, raising [A] from 0.100 M to 0.200 M raises the initial rate from 2.00 × 10⁻³ to 8.00 × 10⁻³ M/s. The reaction is first order in B. Find the order in A and k.”
Table
Concentration of A in run 1 ([A]₁)
(M)
Initial rate in run 1 (rate₁)
(M/s)
This is an example. Type your own values to start a new problem.
rate₂ (M/s)
=
rate₁ (M/s)
×
(
[A]₂ (M)
÷
[A]₁ (M)
)
[B]
Concentration of B, held in both runs
example · M
n
Order in B
example
k
Rate constant
calculated
Formulas
rate₂
=
rate₁
×
([A]₂ ÷ [A]₁)
m
0.008
=
0.002
×
(
0.2
0.1
)
2
rate₁
=
k
×
([A]₁)
m
×
([B])
n
0.002
=
2
×
(0.1)
2
×
(0.1)
1
Assumptions
•
The rate law is rate = k[A]ᵐ[B]ⁿ. Runs 1 and 2 change only [A], so [B]ⁿ and k cancel when one rate is divided by the other.
•
Each rate is an initial rate, measured before the concentrations have changed much.
•
The order in B, n, comes from another pair of runs that change only [B]; type it here.
•
k’s unit depends on the overall order m + n: M⁻¹s⁻¹ when it is 2, and M⁻²s⁻¹ when it is 3, as here with m = 2 and n = 1.
Step-by-step
WE KNOW
[A]₁ = 0.1 M, [A]₂ = 0.2 M, rate₁ = 0.002 M/s, rate₂ = 0.008 M/s, [B] = 0.1 M, n = 1
FIND
order in A (m), rate constant (k)
Step 1 · Find order in A (m)
Use rate₂ = rate₁ × ([A]₂ ÷ [A]₁)ᵐ
Divide
the
rates:
k
and
[B]ⁿ
cancel,
leaving
rate₂
rate₁
=
([A]₂
÷
[A]₁)ᵐ.
Take
logs,
then
divide
the
rate
change
by
the
[A]
change.
m
=
log(rate₂) − log(rate₁)
log([A]₂) − log([A]₁)
m
=
log(0.008) − log(0.002)
log(0.2) − log(0.1)
m
=
−2.097 − (−2.699)
(−0.699) − (−1)
m
=
0.602
0.301
m
=
2
Step 2 · Find rate constant (k)
Use rate₁ = k × ([A]₁)ᵐ × ([B])ⁿ
Put run 1 into the rate law and divide its rate by the concentration terms.
k
=
rate₁
÷
(
([A]₁)
m
×
([B])
n
)
k
=
0.002
÷
(
(0.1)
2
×
(0.1)
1
)
k
=
0.002
0.01 × 0.1
k
=
0.002
0.001
k
=
2
M⁻²
s
-1
Check
Put the numbers back in. Both sides should match.
0.008
=
0.002
×
(
0.2
0.1
)
2
✓
0.002
=
2
×
(0.1)
2
×
(0.1)
1
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Related lessons
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Main lesson
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