# 7.1.1 Determining the Rate of Reaction

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## Understanding Rate of Reaction

1. Rate of reaction is defined as the change in the amount of reactant or products per unit time.
2. It is a measure of how fast a reaction occurs.
1. Fast Reaction = Rate of reaction is high.
2. Slow Reaction = Rate of reaction is low
3. A fast reaction took a shorter time for the reaction to complete.

Example of fast reaction

 Type of Reaction Example Combustion Combustion of magnesium in oxygen$2Mg + {O_2} \to 2MgO$Combustion of ethane (C2H6)${C_2}{H_6} + \frac{7}{2}{O_2} \to 2C{O_2} + 3{H_2}O$ Reaction between reactive metal and water Reaction between potassium and water$2K + 2{H_2}O \to 2KOH + {H_2}$ Reaction between metal carbonate and acid Reaction between limestone/ marble and sulphuric acid$\begin{gathered}CaC{O_3} + {H_2}S{O_4} \hfill \\\to CaS{O_4} + C{O_2} + {H_2}O \hfill \\\end{gathered}$ Ionic precipitation (Double decomposition) Precipitation of silver(I) chloride$AgN{O_3} + HCl \to AgCl + HN{O_3}$

Example of slow reaction

 Type of Reaction Example Photosynthesis $6C{O_2} + 6{H_2}O \to {C_6}{H_{12}}{O_6} + 6{O_2}$ Rusting $4Fe + 3{O_2} + 2{H_2}O \to 2F{e_2}{O_3} \bullet 2{H_2}O$ Fermentation ${C_6}{H_{12}}{O_6} \to 2{C_2}{H_5}OH + 2C{O_2}$

## Finding the Average Rate of Reaction

Rate of reaction is a measure of how fast a reaction occurs, or how much the reactant/product change in a period of time.
Rates of reaction = Quantity change of reactants/products Total time for the reaction

Example
In a chemical reaction, 2.5g of calcium carbonate react completely with excess hydrochloric acid to produce 600cm³ of carbon dioxide gas in 1.5 minutes. Find the rate of reaction in term of
a. decreasing mass of calcium carbonate
b. increasing volume of carbon dioxide gas produced

a.
Change of the amount of reactant=-2.5g Tima taken for the change=1.5minute=90s Rate of Reaction = -2.5g / 90s = 0.027gs-1

b.
Change of the amount of product
=600cm3 Tima taken for the change
= 1.5minute = 90s

Rate of Reaction
= 600cm3/90s
=6.7cm3s-1

## Finding the Average Rate of Reaction from Measurable Quantities

1. During a chemical reaction, two things happen
1. The quantities of reactants reduce.
2. The quantities of products increase.
2. Therefore, the rate of the reaction can be determined by
1. measuring the decrease in the amount of reactant over time.
2. measuring the increase in the amount of product over time.
3. However, the quantity (or change) of the reactants/product may be measurable or immeasurable.
4. The easily measured quantity changes include
1. Mass
2. Concentration (Conductivity)
3. Volume of gas

Example
The reaction between calcium carbonate and hydrochloric acid.

CaCO3 + 2HCl → CaCl2 + CO2 + H2O

The rate of the reaction can be determined by

1. Measuring the reduces of the mass of the calcium carbonate (reactants) over time
$\begin{gathered} {\text{Rate or Reaction }} \hfill \\ {\text{ = }}\frac{{{\text{Mass of CaC}}{{\text{O}}_3}}}{{{\text{Time Taken for Reaction}}}} \hfill \\ \end{gathered}$
2. Measuring the increases of the volume of the carbon dioxide gas produced over time.
$\begin{gathered} {\text{Rate or Reaction }} \hfill \\ {\text{ = }}\frac{{{\text{Volume of C}}{{\text{O}}_2}{\text{ Produced}}}}{{{\text{Time Taken for Reaction}}}} \hfill \\ \end{gathered}$

Example:
In a reaction, 5 g of calcium carbonate takes 250 seconds to completely react with the solution of hydrochloric acid. Calculate the average rate for this reaction in units
(a) g s-1 and
(b) mol s-1
[ Relative atomic mass: C 12; O, 16; Ca, 40]

a.
Rate of Reaction
= 5g/250s
=0.02gs-1

b. Relative Formula Mass of calcium carbonate (CaCO 3 )
=40+12+3(16) = 100

Number of mole of CaCO3
= 5g/100gmol-1
=0.05 mol

Rate of Reaction
= 0.05mol/250s
=0.0002mols-1

We shall discuss the immeasurable quantity (or changes) in next section.

## Finding the Average Rate of Reaction from Immeasurable Quantities

1. In some reaction, some changes are observable but difficult to be measured. For example
1. Change in colour
2. Precipitation
2. The time taken for the colour of a reactant to change or certain amount of precipitate to form can be used to measure the rate of reaction.
3. If the quantity change is immeasurable

$\begin{gathered} {\text{Rate or Reaction }} \hfill \\ {\text{ = }}\frac{1}{{{\text{Time Taken for the Reaction}}}} \hfill \\ \end{gathered}$

Example
When the aqueous of ethanadioic is mixed with acided potassium manganate(VII) , the reaction happen slowly at room temperature. The purple colour of the solution is bleached after 20 seconds. Calculate the average rate of reaction.