Title: Investigating the Effect of Temperature on the Activation Energy
Planning

A. Hypothesis
I predict that as temperature rises, the faster are the rates of reaction. The reaction that will be studied in this experiment is between magnesium and sulphuric acid. This reaction is shown in the chemical equation below:
Mg (s) + H2S04 (aq) → MgS04 (aq) + H2 (g)
In this experiment, 0.4 grams of magnesium ribbon will be used, together with 100 cubic centimeters of sulphuric acid which is in excess. The variable that I will be changing is the temperature of the water baths where the reactants (sulphuric acid and magnesium ribbon) will be placed. The volume of the gas (hydrogen gas) to be collected at each varying water bath temperature is 100 cubic centimeters. The time it takes for to collect 100 cubic centimeters of the hydrogen gas will be measured to calculate the rate of reaction.
B. Background
The fundamental basis of the collision theory is the kinetic theory which describes the state of matter in terms of the energy of its particles, (Energex, 2006). According to Wilbraham and others (1997), “the kinetic theory says that the tiny particles in all forms of matter are in constant motion. When heated, the particles of the substance absorb energy, some of which is stored within the particles. This stored energy does not raise the temperature of the substance. The rest of the energy goes into speeding up the particles.” Particles lacking the necessary kinetic energy to react still collide but simply bounce back. Substances decompose to simpler forms, or form new substances when supplied with sufficient energy, called the “activation energy”. The activation energy is a barrier or an obstacle that the reactants must cross in order to decompose into simpler substances, or to combine and form new products.

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At higher temperatures, the particles of a substance move faster and become more energetic. Thus, increasing temperatures help speed up the reaction by first increasing the amount of collisions of particles and cross over the energy barrier. Wilbraham and others argue that “the main effect of increasing the temperature is to increase the number of particles that have enough kinetic energy to react when they collide. More colliding molecules are energetic enough to slip over the energy barrier to become products.” The frequency of high energy collisions between reactants increase, thus, products form faster.

The illustration above shows the basis for the postulate: “raising the temperature increases the rate of reaction because the added kinetic energy allows a larger fraction of reactants to go over the hill”, (Norton, 2003).
C. Risk Assessment
Sulphuric acid is a strong, corrosive substance. Therefore, care should be observed when performing the experiment. I will keep in mind the following safety precautions to ensure a safe experiment:

To protect the eyes from the strong acid, goggles should be worn.
Care in handling the sulphuric acid should be observed. I will not pipette acid by mouth.
The temperature of the water baths should be ascertained carefully to prevent scalding. The beaker with hot water bath should be set up carefully to prevent it from being knocked over.

D. Fair test
To ensure a fair test and high reliability of results from this experiment, I will observe the following measures:

All apparatus and equipment shall be cleaned after each time where the time it takes to collect 100 cc of hydrogen gas is obtained at each run of the experiment.
The reading for the volume of the sulphuric acid shall be made very carefully by reading from the lower meniscus of the 100 cubic centimeter mark.
The volume of the sulphuric acid and the weight of the magnesium ribbon will be measured very accurately for all time measurements at every temperature level at each run of the experiment.
The bung should be correctly and tightly placed to prevent the collected hydrogen gas from escaping.
In order to achieve a constant and stable temperature for each time measurement, after adding the magnesium ribbon to the sulphuric acid, I will wait for 20 seconds to make sure that the temperature is kept constant. .

Procedure of the experiment:

Materials needed:

For this experiment, the following are the materials that are to be used:
0.4 grams of Magnesium ribbon
100 cubic centimeters of 0.3 Molar sulphuric acid
100 cc gas syringe for the collection of the hydrogen gas (H2)
stopwatch for measuring the time it takes to collect 100 cubic centimeters of the H2 gas
Thermometer for measuring the temperature of the hot water baths
200 cc conical flask for the sulphuric acid
500 ml graduated cylinder for measuring the sulphuric acid
500 ml beaker for the water baths
water baths with the following temperatures: 18.5°C, 30°C, 40ºC, 50ºC, 60ºC, and 70ºC.
analytical balance for measuring 0.4 grams of magnesium ribbon

Procedure:

1. Set up the materials while making sure that they are clean and the reagents are not contaminated.
2. Using a graduated cylinder, measure 100 cc of 0.3 molar concentration of sulphuric acid.
3. Carefully weigh 0.4 grams of Magnesium ribbon using an analytical balance to make sure that the weight measurement is accurate.
4. Pour the water bath with the desired temperature into the beaker.
5. Carefully put the conical flask with the sulphuric acid and into the beaker with the water bath.
6. Put the 0.4 grams of magnesium ribbon into the conical flask.
7. Measure the time it takes to collect 100 cubic centimeters of hydrogen gas into the gas syringe.
8. Repeat steps 1-7 for every desired temperature.
10. Label the time recorded as run 1.
11. Make 2 more runs for this experiment.
IV. Results:
Data Gathered: The time measurements for each temperature of 18.5°C, 30°C, 40ºC, 50ºC, 60ºC, and 70ºC were obtained and tabulated below (Table 1).
Table 1. Temperature Measurements for the Three Runs or Trials

Temperature (°C)

First Run (Seconds)

Second Run (Seconds)

Third Run (Seconds)

18.5

96

86

95

30

70

68

65

40

50

46

45

53

61

59

58

60

50

50

48

70

48

45

44

The rates of reaction were obtained using the following formula below:
Reaction Rate = Volume of gas collected in cc / Time it takes to collect the gas in seconds
The calculated reaction rates (Volume / Time) for each set temperature for the three runs were tabulated below:
Table 2. Reaction Rate of Each Run

Temperature (°C)

First Run Reaction Rate
(cm³ / s)

Second Run reaction Rate(cm³ / s)

Third Run Reaction Rate(cm³ / s)

18.5

1.04

1.16

1.05

30

1.43

1.47

1.54

40

2.00

2.17

2.22

53

1.70

1.69

1.72

60

2.00

2.00

2.08

70

2.08

2.22

2.27

The tabulated data of reaction rates above were then graphed for all the three runs. The graph shows the same pattern for all the runs.
Graph 1: Reaction Rate Vs. Time Graph of the Three Runs

Using the same data, the average of all calculated reaction rates for each set temperature in every run were taken and tabulated below:
Table 3: Average Reaction Rate for Each run

Temperature (°C)

First Run Reaction Rate
(cm³ / s)

Second Run reaction Rate(cm³ / s)

Third Run Reaction Rate(cm³ / s)

Average Reaction
Rates (cm³ / s)

18.5

1.04

1.16

1.05

1.08

30

1.43

1.47

1.54

1.48

40

2.00

2.17

2.22

2.13

53

1.70

1.69

1.72

1.70

60

2.00

2.00

2.08

2.03

70

2.08

2.22

2.27

2.19

The average reaction rate of all the three runs are then graphed below:
Graph 2: Average Reaction Rate Vs. Temperature.

Determination of the Activation Energy:
The linear relationship between a rate constant or reaction rate and temperature is given in the equation:
In k = -Ea/R X 1/T + In A, which is obtained from the Arrhenius equation that relates temperature, rate constant and activation energy. To solve this equation, the rate constant or reaction rate at several temperature values obtained in the experiment are required. Activation energy can be calculated from the obtained temperature values and each respective rate constant by graphing In k versus 1/T. The In k values were obtained using a calculator, where for every value of reaction rate (k) entered into the calculator, the In function is pressed and the In k value was given. .
Table 4: In K and 1 /T Values with the Corresponding Time and Rate of the First Run

Temperature in Kelvin

Rate (Volume/Time in cm³ / s)

In k

1/T

291.65

1.04

0.0392

0.0034

303.15

1.43

0.3577

0.0033

313.15

2.00

0.6931

0.0032

326.15

1.70

0.5306

0.0031

333.15

2.00

0.6931

0.0030

343.15

2.08

0.7324

0.0029

After obtaining the In k and 1 / T values for the first run, they were graphed as shown below:
Graph 3: In k versus 1/T (First Run)

The slope of the In k versus 1/T graph for the first run was obtained the using a line of “best fit” through the points in the graph. A perpendicular line was drawn at points A and B. In the graph, A is equal to the distance between 0.6700 and 0.400 in the Y-axis and B is the distance between points 0.0033 and 0.0032 in the X-axis. So, to solve for the slope:
Line A = 0.6740-0.400 = 0.2740 and for line B = 0.0033-.00032= -0.0001
Slope = Line A / Line B = 0.02740 / 0.0001 = -2740
Graph 4: In k Versus 1/T showing the Slope

 
The relationship between slope and activation energy is: slope = -Ea/R. Hence, the activation energy for the reaction for the first run is:
-2740= -Ea/R
Ea = (-2740) (8.314J/mol)
Ea= 22780.36 J/mol
Similarly, data for the second run were obtained and tabulated as shown below:
Table 4: In K and 1 /T Values with the Corresponding Time and Rate of the Second Run

Temperature in Kelvin

Rate (Volume/Time in cm³ / s)

In k

1/T

291.65

1.16

0.1510

0.0034

303.15

1.47

0.3860

0.0033

313.15

2.17

0.7761

0.0032

326.15

1.69

0.5271

0.0031

333.15

2.00

0.6931

0.0030

343.15

2.22

0.7984

0.0029

The values of In k and 1/T for the second run were graphed as shown below:
Graph 5: In k – 1/T Graph for the Second Run

The slope of the above In k versus 1/T graph for the second run was determined by drawing a perpendicular line in the best fit points such as in the graph of the first run. For the second run, the slope is equal to: -1093.16
So, the activation energy for the second run is: -1093.16 = -Ea/R
-Ea = (-1093.16) (8.314 J/mol)
Ea = 9088.53 J/mol
Data for the In k versus 1/T graph for the third run are as follows were similarly obtained and tabulated as follows:

Temperature in Kelvin

Rate (Volume/Time in cm³ / s)

In k

1/T

291.65

1.05

0.0488

0.0034

303.15

1.54

0.4318

0.0033

313.15

2.22

0.7975

0.0032

326.15

1.72

0.5423

0.0031

333.15

2.08

0.7324

0.0030

343.15

2.27

0.8198

0.0029

The graph of the tabulated data above is shown below:

The slope of the above In k versus 1/T above is: -1274.70
So the activation energy for the third run is: -1267.89 = -Ea/R
-Ea = (–1267.89) (8.314 J/mol)
Ea= 10541.23 J /mol
Thus, the activation energy values for each run are the following:

First run : 22780.36 J/mol
Second run : 9088.53 J/mol
Third run : 10541.23 J /mol

V. Analysis
The data gathered clearly show that at higher temperatures, the rates of reactions increase up to a certain point, and then continue to slow down. This can be seen in the first 2 graphs, namely: Graph 1: Reaction Rate Vs. Time Graph of the Three Runs and Graph 2: Average Reaction Rate Vs. Temperature. This means that after sometime, the rate of reaction slows down because the products are already being formed. In the experiment, the plateaus in the graph correspond to the time that the hydrogen gas (H2) are already being formed.
The data also showed only one activation energy value for each run. Thus, it only shows that the activation energy in NOT temperature- dependent, NOR is there a direct relationship between the two, since its value does not change with changes in temperature. The relationship between temperature and activation energy as can be concluded in this experiment, is that the temperature increases the capacity of the system to overcome the activation energy needed to form the products. So, the higher the temperature, the faster are the rates or speed of reactions.
VI. Evaluation:
A. Experimental Uncertainty:
In the measurement of the different temperatures for the water baths, the following percentage errors were obtained:
For the reading of 18.5º C, the percentage error is: Plus or minus 0.5 / 18.5 x 100 = 2.7%
For 30º C, the percentage error is: Plus or minus 0.5 / 30 x 100 = 0.16%
For 40º C, the percentage error is: Plus or minus 0.5 / 40 x 100 = 0. 125%
For 53º C, the percentage error is: Plus or minus 0.5 / 53 x 100 = 0. 94%
For 60º C, the percentage error is: Plus or minus 0.5 / 60 x 100 = 0. 83%
For 70º C, the percentage error is: Plus or minus 0.5 / 60 x 100 = 0. 71%
In the use of a graduated cylinder with 1 cm scale, the percentage error is plus or minus 0.5 in every 10 cm scale. So, in this experiment, the percentage error can be calculated as:
0.50/100 X 100 = 0.5%.

Experimental Outcomes

The outcomes of the experiment exactly fit my hypothesis or prediction, that as the temperature rises, the faster is the rate of reaction.
However, I did not predict the outcome that the activation energy itself is NOT temperature dependent, since it does not change with the changes in temperature. This is shown in the experiment results, where there was only one activation energy value for all temperature measurements in each run of the experiment. The relationship between temperature and activation energy is based on the fact that the temperature increases the capacity of the system to overcome the activation energy needed to form the products.

Design of the Experiment

I believe that to improve the experiment, I may need to compare the reaction used in
this experiment to a reaction that uses a catalyst to investigate the effect of catalysts on the activation energy and speed of reactions.
References:
Activation Energy, 2006. http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch22/activate.html#act
[Accessed: February 28, 2006].
Collins, M. (1999), Activation Energy and the Arrhenius Equation. Abbey Newsletter, Vol.23, Number 3, 1999. http://palimpsest.stanford.edu/byorg/abbey/an/an23/an23-3/an23-308.html. [Accessed: February 29, 2006].
Energex, 2006. Kinetic Theory. http://www.energex.com/au/switched_on/project_info/electricity_production_glossary.html#K. [Accessed: February 29, 2006].
Norton, 2003. Key Equations and Concepts .Chemistry in the Science Context. http://www.wwnorton.com/chemistry/concepts/chapter14/ch14_5.htm [Accessed: February 27, 2006].
The Shodon Education Foundation, Inc. 1998. The Arrhenius Equation. http://www.shodor.org/UnChem/advanced/kin/arrhenius.html. [Accessed: February 27, 2006].
Wikipedia, 2006. Collision Theory. http://en.wikipedia.org/wiki/collision_theory. [Accessed: February 27, 2006].
Wilbraham, A. Stanley D., Matta, M., 1997. Chemistry. 4th edition. Menlo Park, California: Addison-Wesley. (pp.490-494).
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