IBChemistryDPHLRevision NotesHow Much, How Fast & How Far?How Fast? The Rate of Chemical ChangeThe Rate Constant (HL)

The Rate Constant (HL) (DP IB Chemistry): Revision Note

Caroline Carroll

Written by: Caroline Carroll

Reviewed by: Richard Boole

Updated on

The rate constant

How to calculate the rate constant 

  • The rate constant, k, of a reaction can be calculated using the initial rate and the rate equation

  • Consider the reaction of sodium carbonate with chloride ions (from hydrochloric acid) to form sodium chloride:

Na2CO3 (aq) + 2Cl- (aq) + 2H+ (aq) → 2NaCl (aq) + CO2 (g) + H2O (l)

  • The rate equation for this reaction is:

rate = k[Na2CO3][Cl-]

  • The rate constant, k , can be calculated using the initial concentrations and the initial rate of reaction:

Alternative text not available

  • The progress of the reaction can be followed by measuring the initial rates of the reaction using various initial concentrations of each reactant

Experimental results of concentrations & initial rates table

Measurement

[Na2CO3] /
mol dm-3

 [Cl–] /
mol dm-3

 [H+] /
mol dm-3

 Initial rate of reaction /
mol dm-3 s-1

1

0.0250

0.0125

0.0125

4.38 x 10-6

2

0.0375

0.0125

0.0125

6.63 x 10-6

3

0.00625

0.0250

0.0250

2.19 x 10-6

  • To find the rate constant, k:

    • Use the data from measurement 1:

      • rate = 4.38 × 10-6 mol dm-3 s-1

      • [Na₂CO₃] = 0.0250 mol dm-3

      • [Cl⁻] = 0.0125 mol dm-3

bold italic k bold space bold equals bold space fraction numerator bold 4 bold. bold 38 bold space bold cross times bold space bold 10 to the power of bold minus bold 6 end exponent over denominator bold 0 bold. bold 0250 bold space bold cross times bold space bold 0 bold. bold 0125 end fraction bold italic k bold space bold equals bold space bold 1 bold. bold 40 bold space bold cross times bold space bold 10 to the power of bold minus bold 2 end exponent

  • The values of measurement 2 or 3 could also have been used to find k

    • They all give the same result of 1.40 x 10-2 

Calculating the units of the rate constant

  • Rate constant calculations requires the correct units

  • Correct units can be deduced by:

    1. Substituting the units of each term into the rate equation

    2. Combining or cancelling any units

  • For example, to calculate the units for the above reaction:

Units of k = fraction numerator open parentheses up diagonal strike mol space dm to the power of negative 3 end exponent end strike space straight s to the power of negative 1 end exponent close parentheses over denominator up diagonal strike open parentheses mol space dm to the power of negative 3 end exponent close parentheses end strike space open parentheses mol space dm to the power of negative 3 end exponent close parentheses end fraction

Units of k = fraction numerator straight s to the power of negative 1 end exponent over denominator mol space dm to the power of negative 3 end exponent end fraction

Units of k = mol dm-3 s-1

  • The units of the rate constant, k, are dependent on the overall order of the reaction

Rate constant units by order of reaction

  • When the rate is measured per second:

    • Rate constant units of a zero order reaction are mol dm-3 s-1

    • Rate constant units of a first order reaction are s-1

    • Rate constant units of a second order reaction are mol-1 dm3 s-1

    • Rate constant units of a third order reaction are mol-2 dm6 s-1

How does temperature affect the rate constant, k?

  • Consider the following reaction:

A + B → C + D

Rate of reaction = k[A][B]

  • The rate equation shows that the rate of reaction depends on:

    • The rate constant, k

    • The concentration of the reactants, A and B

  • Temperature is one of the factors that affects the rate of reaction

  • Increasing the temperature increases the rate constant k

    • This speeds up the rate of reaction, if the concentrations remain constant

  • Important: A higher rate of reaction does not necessarily mean a greater yield

Effect of temperature on k

  • The rate constant k increases exponentially with temperature:

The graph of the rate constant, k, against the temperature shows an exponential relationship
Relationship between temperature and rate constant, k

  • The rate of reaction roughly doubles for every 10 °C increase in temperature

  • This value is approximate because:

    • The rate may double every 9 °C or 11 °C instead

    • The temperature interval for doubling the rate changes gradually as temperature rises

  • This general trend does not apply to all reactions

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Author
Reviewer
Caroline Carroll

Author: Caroline Carroll

Expertise: Physics & Chemistry Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.

Richard Boole

Reviewer: Richard Boole

Expertise: Chemistry Content Creator

Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.

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