# Grade 12 Rate and Extent of Reaction

## Grade 12 Rate and Extent of Reaction

#### 2. Rates of Reaction and Factors Affecting Rate

Firstly, let’s think about some different types of reactions and how quickly or slowly they occur.

Exercise 7 – 1: Thinking about reaction rates

1. Think about each of the following reactions (look at your Grade 11 textbook for a reminder on these processes):
• corrosion (e.g. the rusting of iron)
• photosynthesis
• weathering of rocks
• combustion
1. For each of the reactions above, write a balanced chemical equation for the reaction that takes place.
2. Rank these reactions in order from the fastest to the slowest.
3. How did you decide which reaction was the fastest and which was the slowest?
4. Think of some other examples of chemical reactions. How fast or slow is each of these reactions, compared with those listed earlier?
You can see how quickly the fuel burns when spread over the table. Think about how much more fuel would be needed to cook a meal if you had it spread over a large surface area rather than kept in a container with a small surface area. What is a reaction rate?  In a chemical reaction, the substances that are undergoing the reaction are called the reactants, while the substances that form as a result of the reaction are called the products. The reaction rate describes how quickly or slowly the reaction takes place. So how do we know whether a reaction is slow or fast? One way of knowing is to look either at how quickly the reactants are used during the reaction or at how quickly the products form. For example, iron and sulfur react according to the following equation:

Fe(s) + S(s) → 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. In other words, the reactants have been used. Alternatively, one could see how quickly the iron sulﬁde (the product) forms. Since iron sulﬁde looks very different from either of its reactants, this is easy to do.

In another example: 2Mg(s) + O(g) → 2MgO(s)   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. Worked example 1: Reaction rates

Exercise 7 – 2: Reaction rates

1. A number of different reactions take place. The table below shows the number 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:

2Fe(s) + O2(g) →2FeO(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) →MgCl(s) 2Na(s) + Cl(g) → 2NaCl(s) After 1 minute, 2 g of MgCl2 has been produced in the ﬁrst reaction.

a) How many moles of MgCl2 are produced after 1 minute? b) Calculate the average rate of the reaction, using the amount of product that 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 to take place for 1 min.

Reaction rates and collision theory  It should be clear now that the average rate of a reaction varies depending on a number of factors. But how can we explain why reactions take place at different speeds under different conditions? Collision theory is used to explain the rate of a reaction. For a reaction to occur, the particles that are reacting must collide with one another. Only a fraction of all the collisions that take place actually cause a chemical change. These are called successful or effective collisions.   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 differ 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 permanganate (KMnO4) and concentrated sulfuric acid (H2SO4)
• a spatula, two test tubes, a medicine dropper, a glass beaker and a glass rod.
Method: WARNING! Concentrated H2SO4 can cause serious burns. We suggest using gloves and safety glasses whenever you work with an acid. Remember to add the acid to the water and to avoid snifﬁng the acid. Handle all chemicals with care.
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-)  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 ﬁrst. Conclusions: Despite the fact that both these reactants (oxalic acid and iron(II) sulfate) are in aqueous solutions, with similar concentrations and at the same temperature, the reaction rates are very different. This is because the nature of the reactants can affect the average rate of a reaction. The nature of the iron(II) sulfate in solution (iron ions, ready to react) is very different to the nature of oxalic acid in solution (oxalate ions with covalent bonds that must be broken). This results in signiﬁcantly 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:                               CaCO3(s) + 2HCl(l) → 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.
Method: WARNING! Concentrated HCl can cause serious burns. We suggest using gloves and safety glasses whenever you work with an acid. Remember to add the acid to the water and handle with care.   Figure 7.2: a) A large particle, b) small particles with the same volume as the large particle. c) The surface area of large particles (shown in blue) is much smaller than that of small particles (shown in red). Calcium carbonate reacts with hydrochloric acid according to the following reaction:

CaCO3(s) + 2HCl(aq) →  CaCl2(aq) + H2O(l) + CO(g)

Consider the solid calcium carbonate. If we react 1 g of CaCO3 we ﬁnd 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 of powdered 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 successful 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 tablet takes to fully dissolve. The tablet is fully dissolved once the bubbles (CO2 gas) stop forming.
Concentration (of solutions) As the concentration of the reactants increases, so does the reaction rate. Experiment: Concentration and reaction rate Aim: To determine the effect of reactant concentration on reaction rate. Apparatus:  Concentrated hydrochloric acid (HCl), magnesium ribbon  Two beakers, two test tubes and a measuring cylinder. Method: WARNING! Do not get hydrochloric acid (HCl) on your hands. We suggest you use gloves and safety glasses whenever handling acids and handle with care. 1. When diluting a solution remember that if you want a 1:10 solution (1 part original solution in 10 parts water) measure 10 cm3 of water in a measuring cylinder and pour it into a beaker, then add 1 cm3 of the original solution to the beaker as well. 2 parts concentrated acid to 20 parts water will also be a 1:10 solution. Remember to always add the acid to the water, and not the other way around.
• Prepare a solution of 1 part acid to 10 parts water (1:10). Label a test tube A and pour 10 cm3 of this solution into the test tube.
• Prepare a solution of 1 part acid to 20 parts water (1:20). Label a test tube B  and   pour 10 cm3 of this solution into the test tube.
2. Take two pieces of magnesium ribbon of the same length. At the same time, put one piece of magnesium ribbon into test tube A and the other into test tube B, and pay close attention to what happens. Make sure that the magnesium ribbon is long enough so that your hand is not close to the HCl.   Results: Write down what happened (what did you observe?) in each test tube. Questions and discussion:
• Which of the two solutions is more concentrated, the 1:10 or 1:20 hydrochloric 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?
Conclusions: The 1:10 solution is more concentrated and therefore this reaction proceeds faster. The greater the concentration of the reactants, the faster the average rate of the reaction. The average rate of the reaction can be measured by the rate at which the magnesium ribbon disappears. Explanation: The greater concentration of the reactant means that there are more particles of reactant (HCl) per unit volume of solution. Therefore the chance that HCl particles will collide with the Mg particles will be higher for the solution with the greater concentration. The number of successful collisions per unit time will be higher and so the rate of the reaction will be faster. Project: Concentration and rate Design an experiment to determine the effect of concentration on rate using vinegar and baking soda. Hint: mix water and vinegar to change concentration but keep the total volume constant. Pressure (of gaseous reactants) As the pressure of the reactants increase, so does the reaction rate. The higher the pressure, the more particles of gas per unit volume. Therefore there are more collisions per unit time. The number of successful collisions per unit time will be higher and so the rate of the reaction will be faster. Temperature If the temperature of the reaction increases, so does the average rate of the reaction. Experiment: Temperature and reaction rate Aim: To determine the effect of temperature on reaction rate. Apparatus:
• Two effervescent tablets (e.g. Cal-C-Vita)
• An ice-bath, two test tubes
• Two balloons, two rubber bands
Method: 1. Half ﬁll two large test tubes with water. Label them A and B. 2. Break two effervescent tablets in two or three pieces and place them in the two balloons. Fit one of these balloons tightly to test tube A and one to test tube B, being careful not to drop the contents into the water. You can stand the test tube in a beaker to help you do this. 3. Place only test tube A into an ice-bath and leave to equilibrate (come to the same temperature). Approximately 10 minutes should be enough. 4. At the same time lift the balloons on test tubes A and B so that the tablets go into the water.Do not shake either test tube. CO2 (g) is released during this reaction. Observe how quickly the balloons increase in size and write down your observations (which increases in size faster).         The higher the temperature, the greater the average kinetic energy of the particles, which means that the particles are moving faster. Therefore:
• particles moving faster means more collisions per unit time (collision theory)
• particles with higher kinetic energy are also more likely to react on colliding as they have enough energy for the reaction to occur (see Section 7.4 on the mechanism of reaction).
Catalyst Adding a catalyst increases the reaction rate by lowering the energy required for a successful reaction to take place. A catalyst speeds up a reaction and is released at the end of the reaction, completely unchanged. Experiment: Catalysts and reaction rate Aim: Hydrogen peroxide decomposes slowly over time into water and oxygen. The aim of this experiment is to determine the effect a catalyst has on the reaction rate. Apparatus:
•  3% hydrogen peroxide (H2O2), manganese dioxide (MnO) powder, yeast powder
•  two beakers or large measuring cylinders
Method: WARNING! Be careful when handling H2Oas it can burn you. We recommend wearing gloves and safety glasses. 1. Pour 30 cm3 H2O into two seperate containers. 2. Add a spatula tip of yeast to one container. 3. Time how long it takes for the bubbles to stop. 4. Repeat with MnO2 in the second container. 5. Compare the effect of the two catalysts. The balanced equation for this reaction is:            2H2O2(l) → 2H2O(l) + O2(g) This can also be written:  2H2O2(l)+ catalyst → 2H2O(l) + O2(g)+catalyst Results:
• Which chemical compounds are acting as catalysts in these reactions?
• What causes the bubbles that form in the reaction?
Conclusions: The bubbles that form are oxygen gas formed through the decomposition of hydrogen peroxide. This would happen over time without the presence of the catalyst. The manganese dioxide speeds up the reaction signiﬁcantly. The yeast speeds up the reaction, but not as much as the manganese dioxide. Experiment: Catalysts and reaction rate Aim: To determine the effect of a catalyst on the average rate of a reaction Apparatus:
• Zinc granules, 0,1 mol.dm3 hydrochloric acid, copper pieces
• One test tube, a glass beaker, tongs
Method: WARNING! Do not get hydrochloric acid (HCl) on your hands. We suggest you use gloves and safety glasses whenever handling acids. Be especially careful when removing the copper pieces from the test tube. 1. Place a few of the zinc granules in the test tube, using tongs. 2. Measure the mass of a few pieces of copper and, using tongs, keep them separatfrom the rest of the copper. from the rest of the copper. 3. Add 20 cm3 of HCl to the test tube. You will see that a gas is released. Take note of how quickly or slowly this gas is released (use a stopwatch or your cellphone to time this). Write a balanced chemical equation for the chemical reaction that takes place.chemical reaction that takes place. 4. Now add the copper pieces to the same test tube. What happens to the rate at which the gas is produced? 5. Carefully remove the copper pieces from the test tube (use tongs), rinse them in water and alcohol and then weigh them again. Has the mass of the copper changed since the start of the experiment? Results: During the reaction, the gas that is released is hydrogen. The rate at which the hydrogen is produced increases when the copper pieces (the catalyst) are added. The mass of the copper does not change during the reaction. Conclusions: The copper acts as a catalyst during the reaction. It speeds up the average rate of the reaction, but is not changed itself in any way. We will return to catalysts in more detail once we have explored the mechanism of reactions later in this chapter. Experiment: Temperature, concentration and reaction rate Aim: To determine the effect of temperature and concentration on the average reaction rate of the iodine clock experiment. This experiment is best done in groups. Apparatus:
• Potassium iodide (KI), soluble starch, sodium thiosulfate solution (Na2S2O3), 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
Method:
• Preheat the hotplate to 40°C
• Label a beaker solution 1. Measure 75 ml H2SOinto the beaker. Add 25 ml 3% H2O2. Remember to use dilute (0,2 mol.dm3) sulfuric acid.
The equations for what is occuring in this reaction are given below: H2O2(l) + 2KI(s) + H2SO4(l) →I2(s) +K2SO4(aq) + 2H2O(l) I2(s) +2Na2S2O3(aq) ! Na2S4O6(aq) + 2NaI(aq) It is good scientiﬁc practice to vary only one factor at a time during an experiment.Therefore, this experiment has two parts. First we will vary the concentration of KI, then we will vary the temperature:
•  Varying the concentration

• Varying the temperature
1. Weigh out 0,5 g of KI into a new beaker and label it C. 2. Add 20 ml Na2S2O3 to beaker C. 3. Add a spatula of soluble starch to beaker C and stir with a glass rod. 4. Measure 15 ml of solution 1 with the measuring cylinder. 5. Place beaker C in the ice bath. 6. Get your stopwatch ready. Pour the 15 ml of solution 1 into beaker C and 3 start timing. Stop timing when the solution starts to change colour. Write down your time in the table below. 7. Repeat steps 1 – 4 (label the beaker D). Place beaker D on the hotplate. Then repeat step 6     Beaker A has been included here because it has the same concentration as beakers C and D, but is at a different temperature. Results: Make a table with the information for all the beakers. Include columns for concentration, temperature, time, and reaction rate. Questions and discussion:
• 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?
Conclusions: You will notice that the faster reaction rate occurs in the beaker with the higher concentration of KI. You should also see that the higher the temperature, the faster the reaction rate. Worked example 2: Reaction rates QUESTION Write a balanced equation for the exothermic reaction between Zn(s) and HCl(l). Also name three ways to increase the rate of this reaction.  SOLUTION Step 1: Write the equation for zinc and hydrochloric acid The products must be a salt and hydrogen gas. Zinc ions have a charge of 2+ while chloride ions have a charge of 1-. Therefore the salt must be ZnCl2

Zn(s) + HCl(aq)→ZnCl2(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)→ZnCl2(aq) + H2(g)

Step 3: Think about the methods mentioned in this section that would increase reaction rate
• A catalyst could be added
• The zinc solid could be ground into a ﬁne powder to increase its surface area
• The HCl concentration could be increased
Exercise 7 – 3: Rates of reaction 1. Hydrochloric acid and calcium carbonate react according to the following equation: CaCO3(s) + 2HCl(l) → CaCl2(s) + H2O(l) + CO2(g) The volume of carbon dioxide that is produced during the reaction is measured at different times. The results are shown in the table below.

Note: On a graph of production against time, it is the gradient of the tangent to the graph that shows the rate of the reaction at that time. e.g.

a) Use the data in the table to draw a graph showing the volume of gas that is produced in the reaction, over a period of 10 minutes. (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 minutes 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 produced 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 acid solution:            i. would the average rate of the reaction increase or decrease from the one shown in the graph?            ii. draw a line on the same set of axes to show how you would expect the reaction to proceed with a more                  concentrated HCl solution.

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#### 3. Measuring Rates of Reaction

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.

By measuring the volume at set time intervals, we can graph the data (Figure 7.5) and
hence determine the rate of the reaction.

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
’pop’ sound shows that hydrogen is present.
For example, magnesium reacts with sulfuric acid to produce magnesium sulfate
and hydrogen.
Mg(s) + H2SO4(aq) → 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) → 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.

Experiment: Measuring reaction rates
Aim:
To measure the effect of concentration on the average rate of a reaction.
Apparatus:

• Solid zinc granules, 1 mol.dmhydrochloric acid (HCl)
• Two conical ﬂasks, 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 and safety glasses whenever handling acids and handle with care.

1. Label a conical ﬂask A. Weigh 5 g zinc granules into Repeat with the second conical ﬂask 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
ﬂask A and pour the liquid in beaker 2 into conical
4. Note which balloon ﬁlled more quickly.
5. Fill a test tube with the gas formed. Light only
the gas in the test tube. Keep open ﬂames away
from the balloons. The equation for this reaction is:
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)

Results:

• Which beaker contained the more concentrated solution of HCl?
• Which balloon ﬁlled 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 ﬁlling
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 ﬂask and to place a piece of paper with a black cross underneath the bottom
of the ﬂask. At the beginning of the reaction, the cross will be clearly visible when
you look into the ﬂask (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 is produced in the reaction, because it is very soluble in water.

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 ’A’.

• 300 cm3 of water
• 100 cm3 of 1:10 dilute hydrochloric acid. This is solution ’B’.
• 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 ﬂat surface and label them 1 to 6.
2. Pour 60 cm3 solution A into the ﬁrst beaker and add 20 cm3  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 cm3
HCl. Now add this HCl to the solution that is already in the ﬁrst 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 cm3 of solution A into the second beaker and add 30 cm3
of water. Place the beaker over the black cross on the paper. To this second beaker,
add 10 cm3  HCl, time the reaction and write down the results as you did before.
7. Continue the experiment by diluting solution A as shown below.

The equation for the reaction between sodium thiosulfate and hydrochloric acid is:
Na2S2O3(aq)+ 2HCl(aq) → 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 be 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. 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.

CH3COOH(aq) + NaOH(aq) → Na+(aq) + CH3COO(aq) + H2O(l)
Changes in mass
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).

#### Examples

Rational and Irrational Numbers
Rational Numbers

Irrational Numbers

#### Problems

Rational and Irrational Numbers
Q1

#### Solutions

Rational and Irrational Numbers
Q1 Solutions

1. Irrational, decimal does not terminate and has no repeated pattern.
2. Rational, decimal terminates.
3. Irrational, decimal does not terminate and has no repeated pattern.
4. Rational, all integers are rational.
5. Rational, decimal has repeated pattern.
6. Rational, decimal has repeated pattern.