1.1 Rates of Reaction

The meaning of Rate of Reaction
■ Rate of reaction

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The change in amount of reactant or product against time.

■ Fast reaction

	►	A reaction that happens quickly and take a shorter time to complete.
	►	Examples: ○ Reaction between sodium carbonate and dilute hydrochloric acid. Na2CO3(s) + 2HCl(aq) → 2NaCl(aq) + CO2(g) + H2O(l) ○ Burning of magnesium ribbon in oxygen. 2Mg(s) + O2(g) → 2MgO(s) ○ Precipitation of argentum chloride when argentum nitrate solution is added to sodium chloride solution. AgNO3(aq) + NaCl(aq) → AgCl(s) + NaNO3(aq)

■ Slow reaction

	►	A reaction that happens slowly and take a longer time to complete.
	►	Examples: ○ Photosynthesis process 6CO2(g) + 6H2O → C6H12O6(s) + 6O2(g) ○ Rusting of iron 4Fe(s) + 3O2 + xH2O → 2Fe2O3•xH2O(s) ○ Precipitation of sulphur HCl(aq) + Na2S2O3 → 2NaCl(aq) + S(s) + SO2(g) + H2O(l)

■ This video contains information on the meaning of rate of reaction.

Measuring Rate of Reaction
■ Definition of rate of reaction: the change in the quantity of the reactants or products per unit time.

	►	$\text{Rate of reaction}\mathrm{=}\frac{\text{change in quantity}}{\text{time taken}}$
	►	Change in the quantity of the reactants per unit time. $\text{Rate of reaction}\mathrm{=}\frac{\text{amount of reactant used up}}{\text{time taken}}$
	►	Change in the products per unit time. $\text{Rate of reaction}\mathrm{=}\frac{\text{amount of product produced}}{\text{time taken}}$

■ This video contains information on the way of measuring the rate of reaction.

■ Ways to measure the rate of reaction.

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Reaction Rate of reaction Volume of gas given off: Magnesium and hydrochloric acid to produced hydrogen. $\mathrm{=}\frac{\text{volume of gas release}}{\text{time taken}}$ Precipitation: Reaction between dilute hydrochloric acid and sodium thiosulphate $\mathrm{\propto }\frac{\text{1}}{\text{time taken to precipitate}}$ Colour changes: Reaction between bromine chemical cells with iron (II) sulphate $\mathrm{\propto }\frac{\text{1}}{\text{time taken for bromine colour to change}}$

■ The rate of reaction can be measured as

	►	Average rate of reaction: the average rate that occurs in a given period of time. ○ $\text{average rate}\mathrm{=}\frac{\text{change in quantity}}{\text{time taken}}$
	►	Instantaneous rate of reaction: the rate of reaction at any given time. ○ $\text{instantaneous rate}\mathrm{=}\frac{\text{change of volume in y-axis}}{\text{change of volume in x-axis}}$
	►	The animation below shows the calculation method of average and instantaneous rate of reaction by using graph.
	►	The animation below shows the rates of reaction at different points.

Laboratory Activity 1.1.1: Measuring Rate of Reaction

Worked Example : Measurement of Rate of Reaction

✍ Worked-example 1.1(a) In an experiment, 5.0 g of calcium carbonate will need 250 seconds to react with excess dilute hydrochloric acid. Calculate the average rate of this reaction in the unit of: g s-1 mol s-1 [Relative atomic mass: C, 12; O, 16; Ca, 40] Solution: ► (a) Total time taken = 250 seconds $\text{average rate}\mathrm{=}\frac{\text{the mass of calcium carbonate reacted}}{\text{time interval}}$ $\text{average rate}\mathrm{=}\frac{\text{5g}}{\text{250s}}$ = 0.02g s-1 ► (b) $\text{Number of moles of calcium carbonate}\mathrm{=}\frac{\text{5}}{\text{40 + 12 +3(16)}}$ = 0.05 mol $\text{average rate}\mathrm{=}\frac{\text{the mass of calcium carbonate reacted}}{\text{time interval}}$ $\text{average rate}\mathrm{=}\frac{\text{0.05mol}}{\text{250s}}$ = 0.0002 mol s-1

✍ Worked-example 1.1(b) In an experiment, granulated zinc is added to dilute hydrochloric acid. The gas evolved is collected in a burette. Volume of gas collected is recorded at intervals of 20 seconds. The following table shows the results obtained. Time (s) 0 20 40 60 80 100 120 140 160 180 Volume of gas(cm3) 0 8.0 12.0 15.0 18.0 20.0 21.0 22.0 22.0 22.0 Draw a graph of total volume of gas against time on the graph paper. Based on the graph plotted, determine the average rate of reaction in the 50 seconds first 100 seconds Based on the graph plotted, determine the instantaneous rate of reaction at 30 seconds 80 seconds Solution: ► (a) ► (b)(i) The average rate of reaction in the first 50 seconds Time taken = 50 seconds $\text{average rate}\mathrm{=}\frac{\text{the volume of gas released}}{\text{time interval}}$ $\text{average rate}\mathrm{=}\frac{\text{14}}{\text{50s}}$ = 0.28cm3s-1 (b)(ii) The average rate of reaction in the first 100 seconds Time taken = 100 seconds $\text{average rate}\mathrm{=}\frac{\text{the volume of gas released}}{\text{time interval}}$ $\text{average rate}\mathrm{=}\frac{\text{20}}{\text{100s}}$ = 0.20cm3s-1 ► (c)(i) Instantaneous rate at 30 seconds ( A tangent was drawn at the 30 seconds gradient) $\mathrm{=}\frac{\text{20 - 5}}{\text{72 - 12}}$ = 0.25cm3s-1 (c)(ii) Instantaneous rate at 80 seconds ( A tangent was drawn at the 80 seconds gradient) $\mathrm{=}\frac{\text{25 - 15}}{\text{140-72}}$ = 0.15cm3s-1

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