РефератыИностранный языкScScience Investigation Essay Research Paper Science

Science Investigation Essay Research Paper Science

Science Investigation Essay, Research Paper


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Science InvestigationInvestigation:I have performed an experiment in order to see the


effects of varying the concentration of reactants on the reaction between


hydrochloric acid and marble chips. Planning: The experiment I have performed involved the


reaction between hydrochloric acid and calcium carbonate (marble chips) to


produce calcium chloride, water and carbon dioxide. The chemical equation for


this reaction is:?????????????????????? CaCO3? + 2HCl????????????? CaCl2


??+ H2 O + CO2Background Information:In order for a reaction to occur particles of the


reactants must collide with a certain minimal energy in order for products to


be produced.? This minimum energy must


be supplied in order to break the bonds in the reactants and allow new bonds to


be formed.There are a number of variables that will affect the


rate of a reaction.? In order to create


a fair investigation these variables must be examined and controlled so that


accurate results can be obtained and conclusions drawn.i)


Temperature-Increasing


temperature increases the kinetic energy of the particles.? This means that collisions between reactant


particles becomes more frequent and occurs with more energy.? Since a greater proportion of the particles


have sufficient energy to break the bonds in the reactants, more products can


be formed increasing the rate of reaction.??


In this investigation, temperature will be kept constant at room


temperature so that only the effect of concentration is being measured.ii)


Catalysts-Catalysts increase the rate of reaction by providing


an alternative pathway for the reaction to proceed that requires less energy


and therefore takes place more quickly.?


In this investigation, a catalyst will not be used since the reaction


should take place sufficiently quickly for accurate measurements to be taken. iii)


Surface Area-An increased surface area increases the number of


collisions between the reactants.? This


increases the number of collisions likely to be successful and therefore


increases the rate of reaction. In this investigation the size of marble chips


(used as a source of calcium carbonate) will be kept as constant as possible so


that only the effect of varying concentration is being measured. iv)


Concentration-Increasing


the concentration of reactants increases the number of particles available for


collisions and therefore the number of particles that can be converted in to


products, increasing the rate of reaction.Apparatus list: Marble chips (Calcium carbonate) Stop-clock Connection tube Retort stand Digital scales Boss and clamp Conical Flask Safety goggles Paper towels Mat Gas cylinder Rubber bung Hydrochloric acid Measuring cylinder Method:I first set up the apparatus as shown in the


diagram below. I used digital scales to weigh 6 sets of 15 ?medium?


chips individually at 3.0 grams and separated them into different beakers.


Then, using a measuring cylinder, I measured out 0.5, 1.0, 1.5 and 2.0M of


hydrochloric acid from the containers and into separate beakers. I then


collected the retort stand, boss and clamp and set them up in the correct


position. I collected a mat and conical flask, placing the flask on the mat in


front of the stand. I then collected a gas syringe and fixed it into the clamp


by tightening it at the middle of the syringe. I collected a rubber bung and


fixed the connection tube that comes with the gas syringe all the way through I


took the first set of 15 marble chips and tipped them into the conical flask. I


took the first beaker of (0.5M) hydrochloric acid, and poured the contents into


the conical flask, and then quickly fixed the connected bung into the top of


the flask, simultaneously starting the stop-clock. Then, every 10 seconds I


took a reading from the gas syringe of how much gas had been produced. I


continued for 3 minutes (180 seconds) or until the gas syringe has reached the


maximum volume, recording each result onto paper. I disconnected the bung from


the conical flask and then I reset the gas syringe to 0. I emptied the contents


of the conical flask into a container and rinsed the flask with water, drying


it thoroughly with paper towels. I placed the flask on the mat and repeated the


procedure until all the tests were complete. To remain safe while performing the different tests,


I wore safety goggles and an apron when using the hydrochloric acid. I also


ensured careful handling in all parts of testing.To keep the experiment fair throughout, I needed to


ensure the key variables remained constant throughout my experiment. This ensured


my chosen variable of concentration was isolated in the experiment; the results


are then more accurate and direct.For temperature, I realised that in washing the


conical flasks using tap water, the temperature of the flasks would vary


greatly. The first flask would not be washed, meaning it would not cool


significantly like the other flasks. As there were not enough flasks to use a


new one after each test, I washed the first conical flask and tried to get each


conical flask to the same dryness level, using paper towels. Another heat variable comes from moving the conical


flasks, prior to each test; the heat from my hands transfers to the flasks. To


minimise this I handled the conical flasks from the top. This means there is no


heat near the bottom of the flask, where the reaction takes place to affect it. For the key variable of catalysts, I ensured there


would be no necessary interference to the results by not using a catalyst in


any part of my experiment. For surface area, this applies to the marble chips.


I decided there were two factors, the number of chips, and the weight of the


chips. This only applies when the chips are roughly the same size, and means


the surface area will be as even as possible and there is the same amount of


each chip, i.e. density. To do this, for each experiment we used 15 ?medium?


sized chips and weighed each set to be 3.0 grams, using the sensitive digital


scales for the greatest accuracy.To be able to see the changes in each reaction


clearly and compare results, I tested 4 different moles of hydrochloric acid,


0.5, 1.0, 1.5, 2.0. To ensure the greatest degree of accuracy I tested each


mole twice, and then for plotting the results, I took the average for each


point. (Time against volume produced) I also chose to take a third test if the


two sets of results for one mole were significantly different, indicating an


unfair part to the test. I also chose to only time for 3 minutes as this would


be the maximum length of time I could allow due to the time available and


number of tests needing to be performed. This also gave me enough results in


order to see patterns in the graphs and compare more accurately.Other variables I was aware of and accounted for


were:Ø Any product gas escaping


between adding the hydrochloric acid to the marble chips and fitting the bung


in the conical flask. I minimised this by adding the acid at a steady flow each


time, and putting the bung in as soon as all the acid had been poured in. Ø


Shaking the flask to speed up the reaction. As I would


not be able to ensure the level of shaking or heat increase and what the


individual effect on each reaction would be, I decided that for all the tests I


would leave the flask untouched while the reaction took place.Ø


Resetting and checking the apparatus. This included


making sure the gas cylinder was reset fully after each test, and that the


apparatus was sealed properly prior to testing. Predictions:From the above and past scientific knowledge, i.e. a


preliminary experiment, I predict that the higher the concentration of acid,


the faster the rate of reaction. This is due to the concentration of reactants


being proportional to the rate of reaction. This knowledge can be demonstrated


by this example:If there are 100 particles of both reactants, A and


B. There is a certain chance of collisions that could then be successful. If


the particles of each reactant are doubled, the chance of collisions is


doubled. Therefore the rate of reaction is doubled.It is for these reasons that I predict that as


concentration increases, so does the rate of reaction. Prediction graph: Rate of Reaction ????????? ????? ????????????????????????????????????? Concentration I can also calculate the gas produced by the reaction: ???????????????????????????????? Moles?? =? Mass


(g) ?????????????????????????? ??????????????????????????M ????????? ????????????????????????????????????????????? =??? 3.0 ??????????????????????????????????????????????????? 100???????? =0.03 moles of CaCO3???????????????????


1 mole of CaCO3? produces 1 mole CO2????????????????


???Therefore 0.03 moles of CaCO3? produce 0.03 moles of CO2??????????????????????????????? 1 mole occupies 24 dm??????????????????????????????? 0.03 moles = 0.03 X 24?????????????????????????????? = 0.72 dm ????????????????????? ???????????????????


???????????= 720 cm??????????? Preliminary Experiment:To find out whether my method would be the most


suitable to receive accurate results I chose to perform a preliminary


experiment. I chose to use 15 ?medium? chips at 3.0 grams and


use 150ml of hydrochloric acid at 1.0M. ?????????????????????? Results table for


Preliminary Experiment ???????????????????? 1st ????????????????? 2nd ??????????? Average ? Time (seconds) Vol. of gas????????????? produced (cm3 ) ?Time (seconds) Vol. of gas produced


(cm3 ) ?Time (seconds) Vol. of gas produced.


(cm3 ) ?0 ??????????? 0 ??????????? 0???? ?????????? 0 ???????????? 0 ????????


0 10 ??????????? 3 ?????????? 10 ?????????? 5 ??????????? 10 ????????


4 20 ??????????? 5 ?????????? 20 ?????????? 5 ??????????? 20 ????????


5 30 ??????????? 7 ?????????? 30 ?????????? 7 ??????????? 30 ????????


7 40 ??????????? 9 ?????????? 40 ????????? 10 ??????????? 40 ???????


9.5 50 ?????????? 13 ?????????? 50 ????????? 14 ??????????? 50 ??????


13.5 60 ?????????? 18 ?????????? 60 ??????? ??21 ??????????? 60 ??????


19.5 70 ?????????? 25 ?????????? 70 ????????? 29 ??????????? 70 ???????


27 80 ?????????? 32 ?????????? 80 ????????? 34 ??????????? 80 ???????


33 90 ?????????? 39 ?????????? 90 ????????? 41 ??????????? 90 ??????


39.5 ???????? ????100 ?????????? 44 ????????? 100 ????????? 47 ?????????? 100 ??????


45.5 ???????????? 110 ?????????? 52 ????????? 110 ????????? 55 ?????????? 110 ??????


53.5 ???????????? 120 ?????????? 61 ????????? 120 ????????? 63 ?????????? 120 ???????


62 ??????? ?????130 ?????????? 69 ????????? 130 ????????? 71 ?????????? 130 ???????


70 ???????????? 140 ?????????? 77 ????????? 140 ????????? 79 ?????????? 140 ???????


78 ???????????? 150 ?????????? 82 ????????? 150 ????????? 85 ?????????? 150 ??????


83.5 ?????? ??????160 ?????????? 88 ????????? 160 ????????? 92 ?????????? 160 ???????


90 ???????????? 170 ?????????? 94 ????????? 170 ????????? 96 ?????????? 170 ???????


95 ???????????? 180 ?????????? 95 ????????? 180 ????????? 97 ?????????? 180 ???????


96 The experiment worked well and so I did not have to


change anything in the method for the actual testing. Graph ?A? shows the results for my preliminary


experiment and indicates the line of best fit and a straight average trend


line.From my results I could see that as time increased,


so did the gas being produced, indicating that the reaction was taking place


successful.Obtaining Evidence As I have previously mentioned, certain precautions were


taken and ensured throughout testing to certify safety.After recording the results, I needed to be able to


see, and thus understand them clearly in order to make graphs correctly and


accurately. ??????????????????????????????????? Results


table for 0.5M of acid ???????????????????? 1st ????????????????? 2nd ???? ???????Average ? Time (seconds) Vol. of gas????????????? produced (cm3 ) ?Time (seconds) Vol. of gas produced


(cm3 ) ?Time (seconds) Vol. of gas produced.


(cm 3) ?0 ??????????? 0 ??????????? 0???? ?????????? 0 ???????????? 0 ????????? 0 10 ?????????? 3.5 ?????????? 10 ?????????? 3 ??????????? 10 ???????? 3.5 20 ?????????? 3.5 ?????????? 20 ?????????? 3 ??????????? 20 ???????? 3.5 30 ??????????? 4 ?????????? 30 ????????? 3.5 ??????????? 30 ????????? 4 40 ????????? 4.5 ?????????? 40 ?????????? 4 ????? ??????40 ???????? 4.5 50 ??????????? 5 ?????????? 50 ????????? 4.5 ??????????? 50 ????????? 5 60 ??????????? 6 ?????????? 60 ?????????? 5 ??????????? 60 ????????

5.5 70 ??????????? 7 ?????????? 70 ????????? 5.5 ??????????? 70 ???????? 6.5 80 ????????? ??8 ?????????? 80 ????????? 6.5 ??????????? 80 ???????? 7.5 90 ??????????? 9 ?????????? 90 ??????????? 7 ??????????? 90 ????????? 8 ???????????? 100 ?????????? 10 ????????? 100 ??????????? 8 ?????????? 100 ????????? 9 ???????????? 110 ???????? 11.5 ??? ??????110 ??????????? 9 ?????????? 110 ??????? 10.5 ???????????? 120 ???????? 12.5 ????????? 120 ?????????? 10 ?????????? 120 ??????? 11.5 ???????????? 130 ???????? 13.5 ????????? 130 ?????????? 11 ?????????? 130 ??????? 12.5 ???????????? 140 ????????? 15 ????????? 140 ????????? 12.5 ?????????? 140 ??????? 13.5 ???????????? 150 ?????????? 17 ????????? 150 ?????????? 14 ?????????? 150 ??????? 15.5 ???????????? 160 ?????????? 19 ????????? 160 ?????????? 16 ?????????? 160 ??????? 17.5 ???????????? 170 ? ?????????22 ????????? 170 ?????????? 18 ?????????? 170 ???????? 20 ???????????? 180 ?????????? 25 ????????? 180 ?????????? 21 ?????????? 180 ???????? 23 To do this, I have arranged my results as follows: ??????????????????????????????????? Results


table for 1.0M of acid ???????????????????? 1st ????????????????? 2nd ??????????? Average ? Time (seconds) Vol. of gas????????????? produced (cm3 ) ?Time (seconds) Vol. of gas produced


(cm3 ) ?Time (seconds) Vol. of gas produced.


(cm3 ) ?0 ??????????? 0 ? ??????????0???? ??????????? 0 ???????????? 0 ????????? 0 10 ??????????? 5 ?????????? 10 ??????????? 4 ??????????? 10 ???????? 4.5 20 ??????????? 7 ?????????? 20 ??????????? 6 ??????????? 20 ???????? 6.5 30 ??????????? 9 ?????????? 30 ??????????? 8 ??? ????????30 ???????? 8.5 40 ?????????? 13 ?????????? 40 ?????????? 11 ??????????? 40 ???????? 12 50 ?????????? 15 ?????????? 50 ?????????? 14 ??????????? 50 ??????? 14.5 60 ?????????? 18 ?????????? 60 ?????????? 17 ??????????? 60 ??????? 17.5 70 ?????? ????23 ?????????? 70 ?????????? 22 ??????????? 70 ??????? 22.5 80 ?????????? 28 ?????????? 80 ?????????? 26 ??????????? 80 ???????? 27 90 ?????????? 34 ?????????? 90 ?????????? 32 ??????????? 90 ???????? 33 ???????????? 100 ?????????? 40 ????????? 100 ?????????? 38 ?????????? 100 ???????? 39 ???????????? 110 ?????????? 47 ????????? 110 ?????????? 44 ?????????? 110 ??????? 45.5 ???????????? 120 ?????????? 53 ????????? 120 ?????????? 50 ?????????? 120 ??????? 51.5 ???????????? 130 ?????????? 59 ?????? ???130 ?????????? 57 ?????????? 130 ???????? 58 ???????????? 140 ?????????? 67 ????????? 140 ?????????? 64 ?????????? 140 ??????? 65.5 ???????????? 150 ?????????? 74 ????????? 150 ?????????? 70 ?????????? 150 ???????? 72 ???????????? 160 ?????????? 79 ?????????


160 ?????????? 75 ?????????? 160 ???????? 77 ???????????? 170 ?????????? 84 ????????? 170 ?????????? 80 ?????????? 170 ???????? 82 ???????????? 180 ?????????? 89 ????????? 180 ?????????? 85 ?????????? 180 ???????? 87 ??????????????????????? ????????????Results table for 1.5M of acid ???????????????????? 1st ????????????????? 2nd ??????????? Average ? Time (seconds) Vol. of gas????????????? produced (cm3 ) ?Time (seconds) Vol. of gas produced


(cm3 ) ?Time (seconds) Vol. of gas produced.


(cm3 ) ?0 ??????????? 0 ??????????? 0???? ??????????? 0 ???????????? 0 ????????? 0 10 ??????????? 6 ?????????? 10 ??????????? 5 ??????????? 10 ??????? 5.5 20 ?????????? 10 ?????????? 20 ??????????? 9 ??????????? 20 ??????? 9.5 30 ?????????? 16 ?????????? 30 ?????????? 15 ??????????? 30 ?????? 15.5 40 ?????????? 22 ?????????? 40 ?????????? 21 ??????????? 40 ?????? 21.5 50 ?????????? 31 ?????????? 50 ?????????? 29 ??????????? 50 ??????? 30 60 ?????????? 38 ?????????? 60 ?????????? 36 ??????????? 60 ????? ??37 70 ?????????? 47 ?????????? 70 ?????????? 45 ??????????? 70 ??????? 46 80 ?????????? 57 ?????????? 80 ?????????? 55 ??????????? 80 ??????? 56 90 ?????????? 67 ?????????? 90 ?????????? 65 ??????????? 90 ??????? 66 ???????????? 100 ?????????? 76 ? ????????100 ?????????? 74 ?????????? 100 ??????? 75 ???????????? 110 ?????????? 84 ????????? 110 ?????????? 83 ?????????? 110 ?????? 83.5 ???????????? 120 ?????????? 97 ????????? 120 ?????????? 95 ?????????? 120 ??????? 96 ???????????? 130 ????????? 107 ????????? 130 ????????? 105 ?????????? 130 ?????? 106 ???????????? 140 ????????? 140 ?????????? 140 ???????????? 150 ????????? 150 ?????????? 150 ???????????? 160 ????????? 160 ?????????? 160 ???????????? 170 ????????? 170 ?????????? 170 ???????????? 180 ????????? 180 ?????????? 180 ??????????????????????????????????? Results


table for 2.0M of acid ???????????????????? 1st ????????????????? 2nd ??????????? Average ? Time (seconds) Vol. of gas????????????? produced (cm3 ) ?Time (seconds) Vol. of gas produced


(cm3 ) ?Time (seconds) Vol. of gas produced.


(cm3 ) ?0 ?????????? 0 ??????????? 0???? ?????????? 0 ???????????? 0 ????????? 0 10 ?????????? 7 ?????????? 10 ?????????? 9 ??????????? 10 ????????? 8 20 ????????? 12 ?????????? 20 ????????? 14 ??????????? 20 ???????? 13 30 ????????? 19 ?????????? 30 ????????? 22 ??????????? 30 ???????? 21 40 ????????? 26 ?????????? 40 ????????? 30 ??????????? 40 ???????? 28 50 ????????? 36 ?????????? 50 ????????? 37 ??????????? 50 ??????? 36.5 60 ????????? 48 ?????????? 60 ????????? 50 ??????????? 60 ???????? 49 70 ????????? 57 ?????????? 70 ????????? 58 ??????????? 70 ??????? 57.5 80 ????????? 68 ?????????? 80 ????????? 64 ??????????? 80 ??????? 65.5 90 ????????? 76 ?????????? 90 ??????? ??79 ??????????? 90 ???????? 78 ???????????? 100 ????????? 90 ????????? 100 ????????? 90 ?????????? 100 ???????? 90 ???????????? 110 ???????? 103 ????????? 110 ???????? 105 ?????????? 110 ??????? 104 ???????????? 120 ????????? 120 ?????????? 120 ?? ??????????130 ????????? 130 ?????????? 130 ???????????? 140 ????????? 140 ?????????? 140 ???????????? 150 ????????? 150 ?????????? 150 ???????????? 160 ????????? 160 ?????????? 160 ???????????? 170 ????????? 170 ?????????? 170 ???????? ????180 ????????? 180 ?????????? 180 Observations:When I reacted the marble chips with the


hydrochloric acid, I observed different effects taking place. In the first


instant that the two reactants made contact, I observed nothing occur. However once


the acid had settled inside the flask a second later fizzing began to occur,


producing bubbles that rose to the surface in a whitish mix, after travelling


upward through the acid while some bubbles that formed, stayed on the marble


chips for longer.? As this bubbling


occurred, there was an audible ?fizzing? sound I detected directly from where


the reaction was occurring. I did not observe a colour change different to the


marble chips, nor did I notice a visible gas rising through the already present


air in the flask.Graph ?B? shows the lines of best fit for the four


different concentrations of Hydrochloric acid.Graph


?C? shows the straight trend lines for the four different concentrations of


Hydrochloric acid.Rates


of reactions:To find out whether my predictions are correct, I need to


directly compare the concentration of Hydrochloric acid with the rates of


reaction on a graph. From this I can then make a straight trend line that will


clearly show me what the trend in my results are.To


find the different rates of reaction I divide the increase of gas by the time


in seconds for each Mole of Hydrochloric acid.0.5


= 23 ??????? 180?


=? 0.127 Concentration Rate ????????? 0.5 ???? 0.127 ????????? 1.0 ???? 0.483 ????????? 1.5 0.815384165 ??? ??????2.0 ?????? 0.9 1.0


= 87 ??????? 180?


=? 0.483?? 1.5


= 106 130


=? 0.8153846152.0


= 90 ??????? 100?


=? 0.9 Graph ?D? shows the trend line for concentration of Hydrochloric acid


against the rates of reaction.Analysing:From looking at graph B, I can see my results by looking at the line of


best fit. As time increases so does the volume of gas produced.? For all the moles of acid this increase


starts gradually before then building up to create a steeper part of the curve.


For 1.0M of acid, I can also see this curve begin to fall towards the


horizontal indicating that the gas produced is now decreasing. As for Moles 1.5


and 2.0 of acid, I can see the same pattern where the curve is steepest at


about half way through the test (90s). I expect that if the time were increased


for these two tests, I would see the same drop toward the horizontal. For 0.5M


of acid, the entire pattern is there, but as the results are only deviated a


little it is difficult to see clearly. From looking at graph ?C?, I can clearly see how different the results are


from each other as it shows a straight trend line for each M of acid. The


greatest difference can be seen between 0.5 and 1.0M, the second largest was


between 1.0 and 1.5 and the smallest difference was between 1.5 and 2.0M of


acid. I can also see that there is a pattern at the start of each test.Graph


?E? shows the graph for 1.0M of Hydrochloric acid.In Graph ?E? I have chosen to use a line of best fit as I


can see how some points are not in sync with it. I have also chosen to use 1.0M


of acid to demonstrate a pattern, as it is most prominent in these results. I


noticed that for each set of results, the first point on each line was above


the lines of best fit as indicated.? I realised


that this was occurring when I placed the bung in the conical flask. As I did


this, the air inside the conical flask would of compressed thus pushing air


through the connection tube into the gas syringe. The amount of increase in the


syringe would then be varied as the amount the bung was pushed in.From looking at graph ?D? I can see how concentration


affects the rate of reaction directly by use of a straight trend line. It is


clearly obvious that the rate of reaction is directly proportional to


concentration. Predictions:As I predicted in a statement and a graph, the rate of


reaction is directly proportional to the concentration. This is seen from graph


?D?, where each point for concentration is higher for the rate of reaction than


the previous. Again indicated by the straight trend line that shows positive


correlation. Conclusion:My prediction is correct because the concentration of


reactants is a critical factor that affects the rate of a reaction. This can be


explained by understanding how reactions occur and how different factors affect


them.For reactions to occur, particles must collide with a


sufficient force. The concentration of a reactant determines how many particles


of that particular reactant will be in a solution. If you increase the


concentration, thus increasing the number of reactant particles, then


collisions are more likely to occur. This can be demonstrated clearly by the


diagram below:If you increase the number of collisions between the


particles of reactants, you will consequently increase the rate of reaction.I can also demonstrate this by my rate of reaction


results:1.0M is half of 2.0M of Hydrochloric acid So the rate of reaction for 1.0M should be half the rate


of reaction for 2.0M of Hydrochloric acid1.0M = 0.4832.0M = 0.9As you can see, the rate of reaction is near to doubled,


from 1.0M to 2.0M Evaluation: For this investigation, I found repeated results were


similar to the first, indicating a good method with no substantial mistakes. I


also found my results to be similar to some other people?s, while exceeding the


standard of others. To have fair results in this investigation I needed to


ensure several factors remained constant throughout testing. However I can only


attain a level of accuracy depending on how fair my testing is. I feel, for the


equipment and materials we were allowed to use, I achieved a high standard of


accuracy that gave me excellent results with minimal anomalies.Here I will list the factors that may be the cause for


slight inaccuracies in my experiment. This will show how anomalies can be


accounted for:·


Scales not correctly read or set, giving different


measurements of calcium carbonate.·


Variations in pouring Hydrochloric acid, more or less


agitation of the marble chips, varying surface area.·


Arrangement of chips when placed in flask, varying


surface area for acid.·


Friction in the gas syringe moving at a minimal


pressure, i.e. not smoothly.·


Displacement of gas when inserting bung into flask.·


Calcium carbonate dust that is weighed and then not


used in the reaction.·


Marble chips not of equal surface area.·


Differences in water left from washing the conical


flask after each test.The only way a completely fair test could occur with the


most accurate results, would be to follow the following factors and to account


for the previous ones.§


A completely sterile and constant laboratory


environment. §


Exact Hydrochloric acid volumes or larger quantities of


acid and marble chips i.e. 500ml of acid and 10 grams of calcium carbonate thus


reducing surface area as a factor.? §


Exact chip number, weight and surface area. §


Pure Calcium Carbonate. §


Allow all of the reaction to occur irrespective of


time. §


Take an infinite number of tests and average exactly. &sect

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