Title: Energetics

Objective: To determine the enthalpy change of formation of calcium carbonate

Theory:

The enthalpy change of formation (ΔHf) is the enthalpy change of the reaction when one mole of a substance is formed from its constituent elements in their standard states under standard condition. Therefore the enthalpy change of formation of calcium carbonate (ΔHf[CaCO3(s)]) is the enthalpy change of reaction when one mole of calcium carbonate is formed from calcium, carbon and oxygen. It is noticed that the process may be exothermic or endothermic.

Another thing is that the standard enthalpy change of formation can be used to indicate the energetic stability of the compound.

However, the enthalpy change of formation of calcium carbonate cannot be determined directly by calorimetry experiments. It is because

There may be some side reactions and produce side products. It is difficult to control the extent of reaction The heat evolved cannot be separated into appropriate terms. Direct combustion of calcium can be violent.

Therefore, we should find out other ways to deal with the problem.

By Hess’s Law, the overall enthalpy change of a reaction depends on the initial and final states only and is independent of whether the reaction takes place through one stage or a series of stages. Thereby, the enthalpy change of formation of calcium carbonate can be broken down into a series of reactions that can be added together to give the formation of calcium carbonate. Therefore, the enthalpy change can be determined by the two reactions below:

(A) The reaction between calcium and hydrochloric acid Ca(s) + 2HCl(aq) CaCl2(aq) + H2(g)

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(B) The reaction between calcium carbonate and hydrochloric acid CaCO3(s) + 2HCl(aq) CaCl2(aq) + CO2(g) + H2O(l)

The enthalpy changes of reaction of the reactions above can be determined readily by relatively simple calorimetry.

For example in (A), 100 cm3 of 1 M hydrochloric acid at T1oC and about

1 g of calcium were mixed in an expanded polystyrene calorimeter. The maximum temperature was measured as T2

oC.

Then the temperature change can be obtained as ΔT = T2 – T1. Assume the density of the solution is 1 g cm-3. Therefore, the total volume of the mixture is 100 cm3, which has a mass of about 100 g.

By the formula, heat evolved = mcΔT (where m is the mass of the solution, c is the specific heat capacity of the solution which assume to be 4.18 J g-1 K-1).

Hence, the enthalpy change of reaction of (A)= heat evolved in the reaction / number of moles of calcium formed

Similarly, we can obtain the enthalpy change of reaction of (B).

After finding the enthalpy changes of the two reactions, an enthalpy diagram can be used to link the enthalpy changes of all the reactions,

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CaCl2(aq) + H2(g) + CO2(g) + H2O(g)

Ca(s) + C(s) + O2(g) + 2HCl(aq) + H2(g)

CaCO3(s) + 2HCl(aq) + H2(g)

△Hf[CaCO3(s)]

△H2

△H1 + △Hf[CO2(g)] + △Hf[H2O(l)]

En

thal

py

(KJm

ol-1)

or alternatively, an enthalpy cycle (Born-Haber Cycle) can be drawn.

CaCO3(s) + 2HCl(aq) CaCl2(aq) + CO2(g) + H2O(l) + H2(g)

Ca(s) + C(s) + O2(g) + H2(g) + 2HCl(aq)

Where △H1 is the enthalpy change of reaction between calcium and hydrochloric acid

△H2 is the enthalpy change of reaction between calcium carbonate and hydrochloric acid

This relates different equations involved in the reaction and shows the

relative enthalpy levels of different substances.

As stated before, by Hess’s Law, the overall change in enthalpy is equal to the algebraic sum of the enthalpy changes for each intermediate stage.

Hence, the enthalpy change of formation of calcium carbonate

= ΔH1 + ΔHf[CO2(g)] + ΔHf[H2O(l)] －ΔH2

(where ΔHf[CO2(g)] is the enthalpy change of formation of carbon dioxide C(s) + O2(g) CO2(g), given as -393 KJ mol-1;

ΔHf[H2O(l)] is the enthalpy change of formation of water

H2(g) + O2(g) H2O(l), given as -286 KJ mol-1)

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△H2

△Hf[CaCO3(s)] △H1 + △Hf[CO2(g)] + △Hf[H2O(l)]

Chemicals and apparatus500 ml beaker Polystyrene cupThermometer CottonStand and clamp Glass rodMeasuring cylinder Weighing bottleElectronic balance Calcium granulesCalcium carbonate Hydrochloric acid

Procedures:

(A)Determination of enthalpy change of reaction between calcium and hydrochloric acid

1. About 1g of pure calcium metal was weighed out accurately.2. A polystyrene cup was put into a 500 ml beaker which was insulated by

cotton wool. (Figure 1)

3. The measuring cylinder was used to measure 100 cm3 of approximately 1M hydrochloric acid into the polystyrene cup.

4. The temperature of the acid (T1) was measured and recorded.5. The weighed portion of calcium was added and the mixture was stirred

thoroughly with the glass rod until all the metal had been reacted.6. The maximum temperature (T2) attained was recorded.

(B)Determination of enthalpy change of reaction between calcium

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cotton

polystyrene

glass rod

cotton lid

thermometer

stand and clamp

beaker

Figure 1

carbonate and hydrochloric acid

1. About 2 to 3g of dry, powdered calcium carbonate was weighed out accurately into a clean polystyrene cup which had been insulated. (Figure 1)

2. 100 cm-3 of approximately 1M hydrochloric acid was measured and the temperature was recorded.

3. The acid was poured onto the carbonate, the mixture was stirred quickly and the maximum temperature (T2) reached by the solution was recorded.

Results:

M1 /g M2 /g ΔM /g T1 /oC T2 /oC ΔT /oCExpt (A):Ca + HCl

5.98 4.89 1.09 24.9 57.3 32.4

Expt (B):CaCO3 + HCl

11.09 8.80 2.29 24.5 25.8 1.3

where M1 is the mass of weighting bottle together with the sample, i.e. Calcium in Expt A; Calcium carbonate in Expt B, M2 is the mass of the weighting bottle used, ΔM is the mass of sample use

Calculation:

For the calculations below, the relative atomic mass of calcium, carbon and oxygen would be taken as 40.0, 12.0 and 16.0 respectively.

For experiment (A),Mass of the solution = volume × density

= (100) (1)= 100 g

Heat evolved = mcΔT= 100(4.18)(32.4)= 13543.2 J

No. of moles of calcium used = 1.09 ÷ 40= 0.02725

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Molar enthalpy change =ΔH1 = -13543.2 ÷ 0.02725= - 497.0 kJ mol-1

Similarly, for the experiment (B),

Heat evolved = 543.4 J

No. of moles of calcium carbonate used = 0.0229

Molar enthalpy change = ΔH2 = -23.7 kJ mol-1

By Hess’s Law, the enthalpy change of formation of calcium carbonate= -497.0 + (-393) + (-286) － (-23.7)= -1152.3 kJ mol-1

Conclusion:

The enthalpy change of formation of calcium carbonate is -1152.3 kJ mol-1.

Questions for discussion:

1. Equation for the standard enthalpy change of formation of calcium carbonate:

Ca(s) + C(s) + O2(g) CaCO3(s)

2. What interpretation can be made from the result obtained, i.e. the value of the enthalpy change of the formation of calcium carbonate?

Firstly, it is found that the enthalpy change of formation of calcium carbonate is negative. This implies that the reaction is exothermic. Also, the compound has a lower energy level than the constituent elements (calcium, carbon and oxygen), therefore the compound is more stable.

Since the value of the enthalpy change is quite highly negative, this implies that the bonds that form the compound, calcium carbonate, are strong and a lot of energy is needed to decompose the compound.

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3. Why is the exact concentration of hydrochloric acid not important?

It is because hydrochloric acid is in excess and would not involve in the calculations and affect the results. This can be explained by the following mathematics expression:

No. of moles of HCl(aq) present = molarity × volume= 1 × 100 × 10-3

= 0.1

No. of moles of Ca(s) used = 1.09 / 40= 0.02725

No. of moles of CaCO3(s) used = 2.29 / (40 + 12 + 16 × 3)= 0.0229

Since in both experiment, mole ratio of HCl to Ca / CaCO3 = 1 : 1Therefore, calcium and calcium carbonate were limiting agents, i.e. hydrochloric acid was in excess. Hence, only calcium and calcium carbonate were involved in the calculations.

4. There are some assumptions in the experiments:

The specific heat capacity of the solution is similar to that of water, i.e. 4.18 J g-1 K-1

The specific heat capacity of the thermometer, the glass rod, the polystyrene cup are so small that can be neglected

There is no heat loss to the surrounding. Both calcium and calcium carbonate dissolve and react in

hydrochloric acid quickly so that the energy is released quickly and the temperature rise reflects the amount of heat produced in the reaction. If the reaction takes place slowly, the energy released per time would be so small that energy would be lost to the surrounding as fast as it was produced as the apparatus were not well insulated.

The density of the solution is similar to water, i.e. 1 g cm-3. All the calcium is reacted in the hydrochloric acid in experiment (A)

and all the calcium carbonate is reacted in the acid in experiment (B) as well.

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The water produced in the reaction between calcium carbonate and hydrochloric acid is negligible.

All the gases produced would be escaped as fast as possible so that the gas bubbles would not affect the rate of reaction.

5. What are the sources of error in the experiments?

According to the data book, the standard enthalpy change of formation of calcium carbonate is -1207 kJ mol-1. However after the experiment, the calculated value is -1152.3 kJ mol-1. The value obviously is less negative than the exact value and by calculating the percentage error of the value obtained, we can find out how the calculated value is different to the exact value.

For the percentage error,

×100%

= - 4.53%

Form the percentage error calculated above, we can conclude that there is a loss in enthalpy value.

Hence, there are sources of error which lead to the difference in the value:

There is heat loss to the surrounding. Since the setup was not well insulated, heat could be lost through conduction, convection and evaporation.

The ‘dry’ calcium carbonate may not be completely dry, there may be some water molecule found in the salt.

The specific heat capacity of the solution is not the same as that of water, which would be larger and hence reduce the value of the enthalpy change of formation of calcium carbonate.

Heat will be absorbed by the polystyrene cup, the thermometer, the glass rod as well as the beaker and the cotton wool, which reduce the value obtained.

There may be impurities in the calcium carbonate, as stated in the label of the bottle, there are 0.01% of iron which may also react with the hydrochloric acid. Also the heavy metal presents like lead, the

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sulphate impurities present in the salt, will lower the minimum impurities, and hence reduce the value obtained.

During reactions, there are white fume produced, this will carry heat away and hence reduce the value obtained.

It was found that there is hissing sound presents during the two reactions, obviously some energy released through the reaction is converted into sound energy. This would lower the heat energy measured and hence the value of the enthalpy change of formation of calcium carbonate.

Actually, in the reaction between the calcium metal and the hydrochloric acid, calcium reacts quite slowly, this would make the heat loss larger and greatly reduce the value calculated.

The gas bubbles produced during the reaction between the calcium and the hydrochloric acid adhere on the surface of the metal making the sink calcium rise. This decreases the contact area between the metal and the acid and lowers the rate of reaction, making the rate of heat released is low and makes the heat loss larger, finally a decrease in value is obtained.

As stated on the label of the calcium carbonate, 0.01% of calcium carbonate cannot dissolve in hydrochloric acid. This make the number of moles of calcium carbonate reacted decreases, and hence the value obtained is lowered.

The thermometer used in the experiment is not precise enough as it can only precise to 0.1 oC.

The density of the solution cannot be exactly equal to that of water, i.e. 1 g cm-1

6. In order to make the experiments more accurate, the following improvements should be made:

Performing experiments to determine the specific heat capacity of the polystyrene cup, the thermometer and the glass rod. The value obtained should take into account in the calculation of the enthalpy change of formation of calcium carbonate.

A vacuum flask calorimeter should replace the polystyrene cup used so that a better insulating system can be achieved and the heat loss can be reduced to minimum.

A Beckmann thermometer can be used in the experiment (B), i.e. reaction between the calcium carbonate and hydrochloric acid to give

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a more accurate result (since it can only precise up to 0.001oC). While for the experiment (A), i.e. reaction between the calcium and the hydrochloric acid, a more precise thermometer (e.g. precise to 0.05) can be used (but not Beckmann thermometer as it can only measure at most 5 oC temperature change) to have a more accurate result.

The specific heat capacity of the solution should be found as it should not be equal to that of water.

The density of the solution should also be found so that a more accurate calculation can be done.

For the calcium metal used, using powder form would be better as this can increase the surface area for the reactions and increase the rate of reactions and the rate of heat released. However, calcium powder should be freshly prepared and quickly added to the acid, otherwise calcium would react with the oxygen in air and affect the result obtained.

It would be better if we heat the calcium carbonate slightly in an oven so that we can ensure there is no water inside the sample and keep in a desiccator.

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