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

Calculating the rate constant from the initial rate

• The reaction of sodium carbonate with chloride ions (from hydrochloric acid) to form sodium chloride will be used as an example to calculate the rate constant from the?initial rate?and?initial concentrations
• The reaction and rate equation are as follows:

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

• 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

• To find the rate constant (k):
• Substitute the values of one of the experiments to find?k?(for example?measurement 1)

• 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 units

• When you are asked to calculate the rate constant,?k, for a reaction you must also be able to deduce the units
• This is done by replacing the values in the rearranged rate equation with the units of that value
• The units can then be combined or cancelled as required
• For example, to calculate the units for the above reaction:

Temperature and the rate constant,?k

• The following general reaction and rate equation will be used to discuss the effect of temperature on the rate constant,?k:

A + B → C + D

Rate of reaction =?k[A][B]

• The rate equation shows that rate of reaction depends on the rate constant,?k, and the concentration of the reactants
  • As the rate of reaction increases the rate constant will increase
• Increasing the temperature of a reaction increases the rate of a chemical reaction
  • Remember: this does not necessarily increase the yield of a chemical reaction depending on whether a reaction is?endothermic?or?exothermic?according to Le Chatelier’s principle
• Therefore, increasing the temperature also increases the value of the rate?constant,?k, assuming that the concentration of the reactants remains unchanged

• An exponential relationship between the rate of reaction and temperature is observed when seen on a graph:

Relationship between temperature and rate constant, k

• The graph shows that the rate of reaction roughly doubles with an increase of 10?^oC
  • This general relationship does not apply to all reactions
  • Also, it is not necessarily every 10?^oC, the rate may double every 9 °C or 11 °C
  • The number of degrees needed to double the rate also changes gradually as temperature increases