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Exercise 7 ā 1: Thinking about reaction rates
1. Think about each of the following reactions (look at your Grade 11 textbook forĀ a reminder on these processes):- corrosion (e.g. the rusting of iron)
- photosynthesisĀ
- weathering of rocksĀ
- combustion
- For each of the reactions above, write a balanced chemical equation for theĀ reaction that takes place.
- Rank these reactions in order from the fastest to the slowest.
- How did you decide which reaction was the fastest and which was theĀ slowest?
- Think of some other examples of chemical reactions. How fast or slow isĀ each of these reactions, compared with those listed earlier?

Fe(s) + S(s)Ā ā FeS(s)
In this reaction, we can observe the speed of the reaction by measuring how long it takes before there is no iron or sulfur left in the reaction vessel.Ā In other words, the reactants have been used. Alternatively, one could see how quickly the iron sulļ¬de (the product) forms. Since iron sulļ¬de looks very different from either of its reactants, this is easy to do.
In another example: 2Mg(s) + O(g)Ā ā 2MgO(s) Ā In this case, the reaction rate depends on the speed at which the reactants (oxygen gas and solid magnesium) are used, or the speed at which the product (magnesium oxide)is formed. DEFINITION: Reaction rate The average rate of a reaction describes how quickly reactants are used or how quickly products are formed during a chemical reaction. The average rate of a reaction is expressed as the number of moles of reactant used, divided by the total reaction time, or as the number of moles of product formed, divided by the total reaction time.


Ā
Exercise 7 ā 2: Reaction rates
1. A number of different reactions take place. The table below shows the numberĀ of moles of reactant that are used in a particular time for each reaction.
a) Complete the table by calculating the average rate of each reaction. b) Which is the fastest reaction? c) Which is the slowest reaction?
2. Iron reacts with oxygen as shown in the balanced reaction:Ā2Fe(s) + O2(g) ā2FeO(s) 2 g of Fe and 0,57 g of O2 are used during the reaction. 2,6 g of FeO is produced. The reaction takes 30 minutes to go to completion. Calculate the average rate of reaction for:
a) the use of Fe. b) the use of O2. c) the formation of FeO.
3. Two reactions occur simultaneously in separate reaction vessels. The reactions are as follows:Mg(s) + Cl2(g) āMgCl(s) 2Na(s) + Cl(g) ā 2NaCl(s) After 1 minute, 2 g of MgCl2 has been produced in the ļ¬rst reaction.
a) How many moles of MgCl2Ā are produced after 1 minute? b) Calculate the average rate of the reaction, using the amount of product thatĀ is produced. c) Assuming that the second reaction also proceeds at the same rate, calculate:i. the number of moles of NaCl produced after 1 minute. ii. the minimum mass (in g) of sodium that is needed for this reaction toĀ take place for 1 min.
Reaction rates and collision theoryĀ It should be clear now that the average rate of a reaction varies depending on a numberĀ of factors. But how can we explain why reactions take place at different speeds underĀ different conditions? Collision theory is used to explain the rate of a reaction.Ā For a reaction to occur, the particles that are reacting must collide with one another.Ā Only a fraction of all the collisions that take place actually cause a chemical change.Ā These are called successful or effective collisions. Ā DEFINITION: Collision theory Reactant particles must collide with the correct energy and orientation for the reactants to change into products. Collision theory explains how chemical reactions occur and why reaction rates differĀ for different reactions. It states that for a reaction to occur the reactant particles must:- collide
- have enough energy
- have the right orientation at the moment of impact

- Oxalic acid ((COOH)2), iron(II) sulfate (FeSO), potassium permanganateĀ (KMnO4) and concentrated sulfuric acid (H2SO4)
- a spatula, two test tubes, a medicine dropper, a glass beaker and a glass rod.



It is the oxalate ions (C2O42-) and the Fe2+ions that cause the discolouration. It is clear that the Fe2+ions react much more quickly with the permanganate than the (C2O42-) Ā ions. The reason for this is that there are no covalent bonds to be broken in the iron ions before the reaction can take place. In the case of the oxalate ions, covalent bonds between carbon and oxygen atoms must be broken ļ¬rst. Conclusions: Despite the fact that both these reactants (oxalic acid and iron(II) sulfate) are in aqueousĀ solutions, with similar concentrations and at the same temperature, the reaction ratesĀ are very different. This is because the nature of the reactants can affect the average rateĀ of a reaction.Ā The nature of the iron(II) sulfate in solution (iron ions, ready to react) is very differentĀ to the nature of oxalic acid in solution (oxalate ions with covalent bonds that must be broken). This results in signiļ¬cantly different reaction rates. Surface area (of solid reactants) Experiment: Surface area and reaction rate Marble (CaCO) reacts with hydrochloric acid (HCl) to form calcium chloride, water and carbon dioxide gas according to the following equation: Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā Ā CaCO3(s) + 2HCl(l)Ā ā CaCl2(s) + H2O(l) + CO2(g) Aim: To determine the effect of the surface area of reactants on the average rate of the reaction. Apparatus:
- 2 g marble chips, 2 g powdered marble, concentrated hydrochloric acid (HCl)
- one beaker, two test tubes.


CaCO3(s) + 2HCl(aq) āĀ CaCl2(aq) + H2O(l) + CO(g)
Consider the solid calcium carbonate. If we react 1 g of CaCO3 we ļ¬nd that the reaction is faster if the CaCO3 is powdered when compared with the CaCO3 being large lumps. Explanation: The large lump of CaCO3 has a small surface area relative to the same mass ofĀ powderedĀ CaCO3. This means that more particles of CaCO3 will be in contact with HCl in the powdered CaCO3 than in the lumps. As a result, there can be more successfulĀ collisions per unit time and the reaction of powdered CaCO3 is faster. Increasing the surface area of the reactants increases the rate of the reaction. The following video shows the effect of surface area on the time an effervescent tabletĀ takes to fully dissolve. The tablet is fully dissolved once the bubbles (CO2 gas) stopĀ forming. Ā
- Prepare a solution of 1 part acid to 10 parts water (1:10). Label a test tubeĀ A and pour 10 cm3Ā of this solution into the test tube.
- Prepare a solution of 1 part acid to 20 parts water (1:20). Label a test tubeĀ BĀ andĀ Ā pour 10 cm3Ā of this solution into the test tube.

- Which of the two solutions is more concentrated, the 1:10 or 1:20 hydrochloricĀ acid solution?
- In which of the test tubes is the reaction faster? Suggest a reason for this.
- How can you measure the average rate of this reaction?
- Name the gas that is produced?
- Why is it important that the same length of magnesium ribbon is used for each reaction?
- Two effervescent tablets (e.g. Cal-C-Vita)
- An ice-bath, two test tubes
- Two balloons, two rubber bands


- particles moving faster means more collisions per unit time (collision theory)
- particles with higher kinetic energy are also more likely to react on collidingĀ as they have enough energy for the reaction to occur (see Section 7.4 on the mechanism of reaction).
- Ā 3% hydrogen peroxide (H2O2), manganese dioxide (MnO) powder, yeast powder
- Ā two beakers or large measuring cylinders

- Which chemical compounds are acting as catalysts in these reactions?
- What causes the bubbles that form in the reaction?
- Zinc granules, 0,1 mol.dm3 hydrochloric acid, copper pieces
- One test tube, a glass beaker, tongs

- Potassium iodide (KI), soluble starch, sodium thiosulfate solution (Na2S2O3),Ā dilute (around 0,2 mol.dm3) sulfuric acid (H2SO4), 3% hydrogen peroxide(H2O2) solution
- Five beakers, a measuring cylinder, a hotplate, an ice bath, a glass stirring rod, a stop-watch
- Preheat the hotplate to 40°C
- Label a beaker solution 1. Measure 75 ml H2SOinto the beaker. Add 25 mlĀ 3% H2O2. Remember to use dilute (0,2 mol.dm3) sulfuric acid.
- Ā Varying the concentration


- Varying the temperature

- Did beaker A or B have the faster reaction rate?
- Why did it have a faster reaction rate?
- Did beaker A, C or D have the fastest reaction rate? Why?
- Did beaker A, C or D have the slowest reaction rate? Why?
Zn(s) + HCl(aq)āZnCl2(aq) + H2(g)
Step 2: Balance the equation if necessary There are more chloride ions and hydrogen atoms on the right side of the equation. Therefore there must be 2 HCl on the left side of the equation.Zn(s) + 2HCl(aq)āZnCl2(aq) + H2(g)
Step 3: Think about the methods mentioned in this section that would increase reactionĀ rate- A catalyst could be added
- The zinc solid could be ground into a ļ¬ne powder to increase its surface area
- The HCl concentration could be increased


Note: On a graph ofĀ production against time, it is the gradient of the tangent toĀ the graph that shows the rate of the reaction at that time.Ā e.g.
Ā a) Use the data in the table to draw a graph showing the volume of gas that isĀ produced in the reaction, over a period of 10 minutes.Ā (Remember to label the axes and plot the graph on graphing paper) b) At which of the following times is the reaction fastest: 1 minute; 6 minutesĀ or 8 minutes. Explain. c) Suggest a reason why the reaction slows down over time. d) Use the graph to estimate the volume of gas that will have been producedĀ after 11 minutes. e) How long do you think the reaction will take to stop (give a time in minutes)? f) If the experiment was repeated using a more concentrated hydrochloric acidĀ solution: Ā Ā Ā Ā Ā Ā i. would the average rate of the reaction increase or decrease from theĀ one shown in the graph? Ā Ā Ā Ā Ā Ā ii. draw a line on the same set of axes to show how you would expect theĀ reaction to proceed with a moreĀ Ā Ā Ā Ā Ā Ā Ā Ā concentrated HCl solution.Html code here! Replace this with any non empty text and that's it.
How the average rate of a reaction is measured will depend on what the reaction
is, what the reactants are, and what product forms. Look back at the reactions that
have been discussed so far. In each case, how was the average rate of the reaction
measured? The following examples will give you some ideas about other ways to
measure the average rate of a reaction:
Measuring the volume of gas produced per unit time
The volume of gas produced
in a reaction may be measured by collecting the
gas in a gas syringe (Figure 7.4). As more gas is produced, the plunger is pushed out and
the volume of the gas in the syringe can be recorded.
Ā
By measuring the volume at set time intervals, we can graph the data (Figure 7.5) and
hence determine the rate of the reaction.
Ā
Examples of reactions that produce gas are listed below:
- Reactions that produce hydrogen gas:
When a metal reacts with an acid, hydrogen gas is produced. The hydrogen can
be collected in a test tube. A lit splint can be used to test for hydrogen. The
āpopā sound shows that hydrogen is present.
For example, magnesium reacts with sulfuric acid to produce magnesium sulfate
and hydrogen.
Mg(s) + H2SO4(aq) ā MgSO4(aq) + H2(g) - Reactions that produce carbon dioxide:
When a carbonate reacts with an acid, carbon dioxide gas is produced. When
carbon dioxide is passed through limewater, it turns the limewater milky. A
burning splint will also stop burning (be extinguished) in the presence of CO
gas. These are a simple tests for the presence of carbon dioxide.
For example, calcium carbonate reacts with hydrochloric acid to produce cal-
cium chloride, water and carbon dioxide.
CaCO3(s) + 2HCl(aq) ā CaCl2(aq) + H2O(l) + CO2(g) - Reactions that produce oxygen:
Hydrogen peroxide decomposes in the presence of a manganese(IV) oxide catalyst
to produce oxygen and water.
Ā
Ā
Experiment: Measuring reaction rates
Aim:
To measure the effect of concentration on the average rate of a reaction.
Apparatus:
- Solid zinc granules, 1 mol.dm3Ā hydrochloric acid (HCl)
- Two conical ļ¬asks, two beakers, two balloons, bunsen burner, splint of wood
Method:
WARNING!
Do not get hydrochloric acid (HCl) on your hands. We suggest you use gloves andĀ safety glasses whenever handling acids and handle with care.
1. Label a conical ļ¬ask A. Weigh 5 g zinc granules into Repeat with the second conical ļ¬ask but label it B.
2. Label a beaker 1. Pour 10 cm3 HCl into it.
Label the other beaker 2. Pour 5 cm3 H2O into it.
Add 5 cm3 HCl to this second beaker.
3. Quickly: Pour the liquid in beaker 1 into conical
ļ¬ask A and pour the liquid in beaker 2 into conical
ļ¬ask B. Attach one balloon ļ¬rmly to each conical ļ¬ask.
4. Note which balloon ļ¬lled more quickly.
5. Fill a test tube with the gas formed. Light only
the gas in the test tube. Keep open ļ¬ames away
from the balloons. The equation for this reaction is:
Zn(s) + 2HCl(aq) ā ZnCl2(aq) + H2(g)
Ā
Results:
- Which beaker contained the more concentrated solution of HCl?
- Which balloon ļ¬lled more quickly?
- What happened when you lit the gas in the test tube?
Conclusions:
The more concentrated solution led to a faster reaction rate (i.e. the balloon ļ¬lling
with H2 gas more quickly). The test for hydrogen gas would have resulted in a loud
pop when the lit splint was placed near the mouth of a test tube.
Precipitate reactions
In reactions where a precipitate is formed, the amount of precipitate formed in a period
of time can be used as a measure of the reaction rate. For example, when sodium
thiosulfate reacts with an acid, a yellow precipitate of sulfur is formed. The reaction is
as follows:
One way to estimate the average rate of this reaction is to carry out the investigation in
a conical ļ¬ask and to place a piece of paper with a black cross underneath the bottom
of the ļ¬ask. At the beginning of the reaction, the cross will be clearly visible when
you look into the ļ¬ask (Figure 7.6). However, as the reaction progresses and more
precipitate is formed, the cross will gradually become less clear and will eventually
disappear altogether. Measuring the time that it takes for this to happen will give an
idea of the reaction rate. Note that it is not possible to collect the SO2 gas that isĀ produced in the reaction, because it is very soluble in water.
Ā
Informal experiment: Measuring reaction rates
Aim:
To measure the effect of concentration on the average rate of a reaction.
Apparatus:
300 cm3 of sodium thiosulfate Na2S2O3 solution. (Prepare a solution of sodium
thiosulfate by adding 12 g of Na2S2O3 to 300 cm3 of water). This is solution āAā.
- 300 cm3 of water
- 100 cm3 of 1:10 dilute hydrochloric acid. This is solution āBā.
- Six 100 cm3 glass beakers, measuring cylinders, paper and marking pen, stopwatch or timer
Method:
WARNING!
Do not get hydrochloric acid (HCl) on your hands. We suggest you use gloves and
safety glasses whenever handling acids and that you handle with care.
One way to measure the average rate of this reaction is to place a piece of paper with
a cross underneath the reaction beaker to see how long it takes until the cross cannot
be seen due to the formation of the sulfur precipitate.
1. Set up six beakers on a ļ¬at surface and label them 1 to 6.
2. Pour 60 cm3Ā solution A into the ļ¬rst beaker and add 20Ā cm3Ā of water
3. Place the beaker on a piece of paper with a large black cross on it.
4. Use the measuring cylinder to measure 10 cm3Ā
HCl. Now add this HCl to theĀ solution that is already in the ļ¬rst beaker (NB: Make sure that you always clean
the measuring cylinder you have used before using it for another chemical).
5. Using a stopwatch with seconds, write down the time it takes for the precipitate
that forms to block out the cross.
6. Now measure 50 cm3Ā of solution A into the second beaker and add 30 cm3Ā
ofĀ water. Place the beaker over the black cross on the paper. To this second beaker,
add 10 cm3Ā Ā HCl, time the reaction and write down the results as you did before.
7. Continue the experiment by diluting solution A as shown below.
Ā
Ā
The equation for the reaction between sodium thiosulfate and hydrochloric acid is:
Na2S2O3(aq)+ 2HCl(aq) ā 2NaCl(aq) + SO2(aq) + H2O(l) + S(s)
Results:
- Calculate the reaction rate in each beaker. Remember that:
rate of the formation of product =moles product formed/reaction time (s)
In this experiment you are stopping each experiment when the same approximate
amount of precipitate is formed (the cross is blocked out by precipitate). So a
relative reaction rate can be determined using the following equation:
reaction rate =1/time (s) - Represent your results on a graph. Concentration will be on the x-axis and
reaction rate on the y-axis. Note that the original volume of Na2S2O3
can beĀ used as a measure of concentration. - Why was it important to keep the volume of HCl constant?
- Describe the relationship between concentration and reaction rate.
Conclusions:
The higher the concentration of the reactants, the faster the average reaction rate.Ā In some reactions there is a change in colour which tells us that the reaction is occuring. The faster the colour change the faster the reaction rate.
For example, when ethanoic acid (acetic acid) is titrated with
sodium hydroxide, an indicator such as phenolphthalein is
added. The solution is clear in an acidic solution and changes
to pink when the reaction is complete. If the concentration
of the base were increased, the colour change would happen
faster (after a smaller volume of base was added), showing that
a higher concentration of base increased the reaction rate.
Ā
CH3COOH(aq) + NaOH(aq)Ā ā Na+(aq) + CH3COO(aq) + H2O(l)
Changes in massĀ
For a reaction that produces gas, the mass of the reaction vessel can be measured over
time. The mass loss indicates the amount of gas that has been produced and escaped
from the reaction vessel (Figure 7.7).
Ā
Rational and Irrational Numbers
Rational Numbers
Irrational Numbers
Rational and Irrational Numbers
Q1
Rational and Irrational Numbers
Q1 Solutions
- Irrational, decimal does not terminate and has no repeated pattern.
- Rational, decimal terminates.
- Irrational, decimal does not terminate and has no repeated pattern.
- Rational, all integers are rational.
- Rational, decimal has repeated pattern.
- Rational, decimal has repeated pattern.