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Lesson: Rate Constants from Reaction Data

In this lesson, we will learn how to use measurements of concentration over time to deduce the rate constant of a reaction.

Worksheet • 12 Questions

Q1:

Compound A decomposes into compounds B and C : The rate of reaction of compound A was measured at three different reactant concentrations, as shown in the table.

[ A ] (M) 0.230 0.356 0.557
Rate (M/s) 4 . 1 7 × 1 0 − 4 9 . 9 9 × 1 0 − 4 2 . 4 4 × 1 0 − 3

Determine the order of this reaction.

Expressing concentrations in units of molars and times in units of seconds, estimate, to 2 significant figures, the numerical value of the rate constant for this reaction.

Q2:

Acetaminophen is removed from the body by a series of reactions. The rate of acetaminophen removal in the body of an average male was measured for three different blood acetaminophen concentrations, as shown in the table.

Concentration (μM) 6.620 4.171 1.752
Rate (μM/h) 1.835 1.156 0.4857

Determine the order of reaction of the removal of acetaminophen.

If times are expressed in hours and concentrations in micromolars, estimate, to 3 significant figures, the numerical value of the rate constant of the removal of acetaminophen.

Estimate the rate of acetaminophen removal of a blood concentration of 0.500 μM.

Estimate the acetaminophen concentration if the rate of removal is 2.35 μM/h.

Q3:

Compound A decomposes in solution. A solution of A decomposed at constant temperature, and the concentration of A was measured at regular time intervals, as shown in the table.

Time (s) 0 1 6 0 0 3 2 0 0 4 8 0 0 6 2 0 0
[ A ] (M) 1 . 0 0 × 1 0 − 2 5 . 0 4 × 1 0 − 3 3 . 3 7 × 1 0 − 3 2 . 5 3 × 1 0 − 3 2 . 0 8 × 1 0 − 3

By plotting suitable functions of the tabulated data, determine the appropriate unit for the rate constant of this reaction.

  • A L/mol⋅s
  • B L3/mol3⋅s
  • C s−1
  • D L2/mol2⋅s
  • E M/s

Expressing concentrations in molars and time in seconds, estimate, to 3 significant figures, the numerical value of the rate constant for this reaction.

  • A 6 . 1 4 × 1 0 − 2
  • B 2 . 8 2 × 1 0 − 1
  • C 7 . 2 9 × 1 0 − 2
  • D 1 . 0 7 × 1 0 − 4
  • E 2 . 4 6 × 1 0 − 4

Q4:

Nitrosyl chloride ( N O C l ) decomposes to chlorine and nitric oxide:

The rate of reaction of N O C l was measured at three different N O C l concentrations:

[ N O C l ] (M) 0.100 0.200 0.300
Rate (M/h) 8 . 1 1 × 1 0 − 1 0 3 . 2 4 × 1 0 − 9 7 . 3 0 × 1 0 − 9

Determine the rate law for this reaction.

  • A R a t e [ N O C l ] = 𝑘 2
  • B R a t e [ N O C l ] = 𝑘 ( ) 1 2
  • C R a t e [ N O C l ] = 𝑘
  • D R a t e [ N O C l ] = 𝑘 4
  • E R a t e [ N O C l ] = 𝑘 3

Expressing concentrations in units of molars and times in units of hours, estimate, to 2 significant figures, the numerical value of the rate constant for this reaction.

  • A 8 . 1 × 1 0 − 8
  • B 8 . 1 × 1 0 − 9
  • C 8 . 1 × 1 0 − 1 0
  • D 8 . 1 × 1 0 − 1 1
  • E 8 . 1 × 1 0 − 7

Estimate, to 2 significant figures, the rate of reaction when [ N O C l ] m M = 3 3 . 3 .

  • A 9 . 0 × 1 0 − 1 1 M/h
  • B 1 . 4 × 1 0 − 1 0 M/h
  • C 2 . 4 × 1 0 − 1 1 M/h
  • D 2 . 7 × 1 0 − 1 0 M/h
  • E 7 . 3 × 1 0 − 1 1 M/h

Estimate, to 2 significant figures, the value of [ N O C l ] when the rate of reaction is 1 . 5 0 × 1 0 − 8 M/h.

Q5:

A sample of hydrogen peroxide was decomposed in water at 4 0 ∘ C . The concentration of hydrogen peroxide was measured at regular time intervals, as shown in the table.

Time (h) 0 6 12 18 24
[ H O ] 2 2 (M) 1.000 0.500 0.250 0.125 0.0625

Expressing concentrations in molars and time in seconds, calculate, to 3 significant figures, the rate constant for this reaction.

  • A 3 . 2 1 × 1 0 s−1
  • B 1 . 8 7 × 1 0 s−1
  • C 1 . 0 4 × 1 0 L/mol⋅s
  • D 1 . 6 7 × 1 0 s−1
  • E 1 . 3 9 × 1 0 L/mol⋅s

Q6:

Compounds A and B react according to the equation: The rate of formation of compound C was measured at three different reactant concentrations, as shown in the table.

[ A ] (M) [ B ] (M) Rate (M/s)
0.221 0.350 6 . 2 5 × 1 0 − 3
0.442 0.700 2 . 5 0 × 1 0 − 2
0.077 1.400 8 . 3 3 × 1 0 − 3

Determine the order of reaction with respect to compound A .

Determine the order of reaction with respect to compound B .

Expressing concentration in molars and time in seconds, estimate, to 2 significant figures, the numerical value of the rate constant for the formation of C .

Q7:

Aqueous hydrogen peroxide decomposes to form oxygen and water. The concentration of a hydrogen peroxide solution was measured at regular time intervals during this reaction, as shown in the table.

Time (h) 0.00 6.00 12.00 18.00 24.00
[ H O ] 2 2 (M) 1.000 0.500 0.250 0.125 0.0625

By plotting suitable functions of the tabulated data, determine the appropriate unit for the rate constant of this reaction.

  • A h−1
  • B L3/mol3⋅h
  • C L/mol⋅h
  • D M/h
  • E L2/mol2⋅h

Expressing concentrations in molars and time in hours, estimate, to 3 significant figures, the numerical value of the rate constant for this reaction.

Q8:

Nitroglycerine decomposes via a first-order process. Solutions of nitroglycerine with different initial concentrations were heated to 1 6 0 ∘ C . After a certain time, the percentage of compound reacted was measured for each solution, as shown in the table.

Initial Concentration (M) Time (s) Nitroglycerine Reacted (%)
4.88 300 52.0
3.52 300 52.9
2.29 300 53.2
1.81 300 53.9
5.33 180 34.6
4.05 180 35.9
2.95 180 36.0
1.72 180 35.4

By calculating the rate constants for each of these reactions, estimate the mean rate constant for the decomposition of nitroglycerine at 1 6 0 ∘ C .

  • A 2 . 4 8 × 1 0 s−1
  • B 2 . 3 9 × 1 0 s−1
  • C 2 . 5 1 × 1 0 s−1
  • D 2 . 4 2 × 1 0 s−1
  • E 2 . 4 5 × 1 0 s−1

Q9:

Which of the following is not a possible unit for the rate constant of a reaction?

  • As/kg
  • B √ / m o l y
  • CPa/day
  • Dmol/L ⋅ h
  • E1/h

Q10:

Compound A undergoes an addition reaction to form compound B : The concentration of A was measured every 5.0 seconds, producing the data in the table.

Time (s) 0.0 5.0 10.0 15.0 20.0 25.0 35.0
[ A ] (M) 2.000 0.952 0.625 0.465 0.370 0.308 0.230

Estimate, to 2 significant figures, the average rate of reaction of A between 5.0 and 20.0 s.

By plotting appropriate graphs, determine the order of reaction with respect to A .

Determine, to 2 significant figures, the instantaneous rate of reaction of A at 22.5 s.

Determine, to 2 significant figures, the instantaneous rate of formation of B at 12.0 s.

Q11:

Compound A decomposes in solution. A solution of A decomposed at constant temperature, and the concentration of A was measured at regular time intervals, as shown in the table.

Time (s) 0 10 15 20 25 35
[ A ] (M) 0.952 0.625 0.465 0.370 0.308 0.230

By plotting suitable functions of the tabulated data, determine the appropriate unit for the rate constant of this reaction.

  • A L/mol⋅s
  • B L3/mol3⋅s
  • C s−1
  • D L2/mol2⋅s
  • E M/s

Expressing concentrations in molars and time in seconds, estimate, to 3 significant figures, the numerical value of the rate constant for this reaction. Outliers should be omitted from this calculation.

  • A 1 . 1 0 × 1 0 − 1
  • B 7 . 4 6 × 1 0 − 2
  • C 9 . 6 9 × 1 0 − 2
  • D 2 . 8 4 × 1 0 − 2
  • E 2 . 0 7 × 1 0 − 2

Q12:

Compound A reacts with compound B according to the following equation: The initial rate of reaction was measured at various initial concentrations of A and B , as shown in the table.

[ A ] (mM) [ B ] (mM) Rate (M/s)
2.44 3.95 6 . 0 5 0 × 1 0 − 4
2.44 7.90 1 . 2 1 0 × 1 0 − 3
7.32 1.58 2 . 1 7 8 × 1 0 − 3
9.76 7.90 1 . 9 3 6 × 1 0 − 2

Determine the order of reaction with respect to compound A .

Determine the order of reaction with respect to compound B .

Determine the appropriate unit for the rate constant of this reaction, 𝑘 .

  • A L2/mol2⋅s
  • B L/mol⋅s
  • C M/s
  • D L3/mol3⋅s
  • E s−1

Expressing concentrations in units of M and times in units of s, estimate, to 3 significant figures, the numerical value of the rate constant, 𝑘 .

  • A 2 . 5 7 × 1 0 4
  • B 1 . 1 9 × 1 0 5
  • C 1 . 5 9 × 1 0 4
  • D 3 . 1 8 × 1 0 4
  • E 7 . 9 5 × 1 0 3
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