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Reaction Kinetics: Order of Reaction of Sodium thiosulphate with Hydrochloric acid Name Sunway ID Monash ID Class Date of submission

: Captain America : 20034567 : 33224455 : Chem 2-1 : 19th March 2021

Aim Purpose: To investigate the reaction between sodium thiosulphate and hydrochloric acid using various concentrations respectively at constant temperature. Objectives: 1. To determine the order with respect to sodium thiosulphate and the order with respect to hydrochloric acid. 2. To determine the rate constant of the reaction between sodium thiosulfate and hydrochloric acid. 3. To determine the rate law of the reaction from the relationship between the concentrations of sodium thiosulphate and hydrochloric acid. To understand reaction kinetics is to understand how the rate of reaction relies on Collision Theory. According to the collision theory of reactivity, molecules are required to ‘effectively collide’ in order for a chemical change. For this to occur, the reactant molecules must be oriented correctly and reach a certain activation energy level to facilitate the breakdown or formation of bonds (Britannica, 2019). One of the factors that affect reactant rates is the temperature at which the reaction occurs. Although the minimum energy required (activation energy) does not change, an increase in temperature will increase the particle kinetic energy, thus increasing the reaction rate (Lumen, n.d.). The higher amount of kinetic energy would increase the frequency of fruitful collisions. Decreasing the temperature will lower the kinetic energy within a chemical reaction which would lead to less successful collisions. Altering the concentration of reactants can also affect the rate of reaction. This is due to a larger or smaller number of reacting molecules and ions present to form the reaction products. For example, if one in a million particles have the required activation energy, then in 100 million particles, only 100 will react. However, if you have 200 million particles, then 200 will react instead. Even so, there is a limit to be reached when increasing the concentration has little to no effect on the rate of reaction (Markgraf, 2021). In this experiment, the concentration of sodium thiosulphate and hydrochloric acid will be varied using a dilution of the chemical. This is the process of adding additional solvent like distilled water to decrease the concentration. The rate law is the mathematical relationship between reaction rate and reactant concentration. According to Key (2014), the relationship heavily relies on the concentration of one of the reactants and the resulting rate law may include some, or none, of the reactant species included in the reaction. Using the hypothetical reaction of: aA+bB→cC

The rate law can be expressed as: Rate = k[A]y[B]z The proportionality constant of ‘ k’, in the above reaction, is known as the rate constant, and it is independent of the concentrations of A and B. It is temperature-specific to the reaction, where the constant changes along with the temperature and its unit depend on the sum of the concentration term exponents in the rate law (Key, 2014). The values of ‘y’ and ‘z’ must be determined through experimental data and they do not correspond to the coefficients in the balanced chemical equation. The reaction order is the sum of the exponents of its respective reactants. Using the rate law, it can be used to understand the composition of the reaction mixture. This indicates the extent of the effect of concentration of a species on the reaction rate, as well as which species has the greatest impact. The exponents in a chemical reaction, in this example, the values of ‘ y’ and ‘z’. For instance, if y = 1, the reaction is first order with respect to A, and if y = 2, the reaction is of second order with respect to A. The overall reaction order is the sum of the orders with respect to the respective reactant. For example, if ‘y’ and ‘z’ is 1 and 1 respectively, the overall reaction order would be ( y + z = 1+1= 2) is of second order. Reaction order consists of zeroth, first, and second order.

Firstly, zero order reactions are independent of concentration. Therefore, increasing or decreasing the concentration of the reactant(s) will little to none effect on the reaction rate. The rate law for a zero order reaction will have a unit of concentration/time, M/s. This concept is graphed in Figure 1.

Figure 1: Zero order reaction (Xaktly, n.d.) First-order reactions have an exponent of 1 (order = 1), and has a rate proportional to the concentration of the reactions of the chemical equation. One common example of a first-order reaction is radioactive decay, it is the spontaneous process through which an unstable atomic nucleus would break into smaller fragments. The rate law for a first-order reaction will have a unit of M-2s-1. This concept can be graphed as:

Figure 2: First-order reaction (Xaktly, n.d.)

Second-order reactions have an exponent of 2 (order = 2), it has a rate proportional to the square of the concentration of a single reactant or the product of two reactants. The unit of the rate law is expressed as M-1sec-1. An example of the second-order graph is shown below in Figure 3.

Figure 3: Second-order reaction (Xaktly, n.d.)

In this experiment, the effect of different sodium thiosulphate concentrations on the reaction rate with hydrochloric acid, and the effect of different hydrochloric acid concentrations with sodium thiosulphate will be investigated. The chemical reaction produces an insoluble solid of sulphur, which will be used to measure the time taken for the mixture to become opaque. The results will be plotted into a graph to determine the order of reaction using the mathematical relationship between the reactant concentration and the reaction rate. This experiment aims to find the rate expression, as shown as: Rate = k[Na2S2O3]m[HCl] n

When sodium thiosulphate is mixed with a dilute acid such as hydrochloric acid, sulphur dioxide, sulphur and water is produced (Amrita Online Lab, 2013). According to Amrita Online Lab (2013), the sulphur produced appears as a white or pale yellow precipitation/colloid as it is insoluble in the mixture making the mixture looks opaque. As a result, the cross under the flask is expected to be masked out of sight due to the opaque appearance of the mixture (Amrita Online Lab, 2013). The reaction can be represented in the equation below: Na2 S2 O3 (aq) + 2HCl(aq) → 2NaCl(aq) + H2 Ol + SO2 (aq) + S(s) (Flinn Science, 2017). Once, the graph of 1/time against the concentration of sodium thiosulphate is plotted, it will show that 1/t is directly proportional to sodium thiosulfate hence, the reaction is a first order reaction directly proportional to the concentration of sodium thiosulfate (Amrita Online Lab, 2013). Whereas the order of reaction of hydrochloric acid will be zero order (Flinn Science, 2017).

Figure 4: A directly proportional graph of rate plotted against the concentration of sodium thiosulphate showing a first order reaction. (Amrita Online Lab, 2013)

In this experiment, it is expected that the reaction order with respect to Sodium thiosulphate will be first order. This means that the reaction rate will be directly proportionate to the concentration of Sodium thiosulphate, which is in line with Flinn Scientific, (2017). Therefore, a best fit straight-line which is a linear graph passing through the origin is expected. This can be seen in the figure above. Therefore, when the concentration of Sodium thiosulphate is doubled, the reaction rate is also doubled. As for Hydrochloric acid, a zero order is expected. This means that no changes in the reaction rate is expected when the Hydrochloric acid concentration is changed which is in line with Flinn Scientific, (2017). Therefore, a best fit straight-line graph which is horizontal is expected. This can be seen in the figure above. Hence, doubling the Hydrochloric acid concentration will not have any effect on the reaction.

Procedure: Refer to “Pre-Lab Summative Practical 1”. Safety precautions: Refer to “Pre-Lab Summative Practical 1”. Results: Part A Table 1: Concentration of sodium thiosulphate solution and the rate of reaction Set

Volume of sodium thiosulphate (ml)

1 2 3 4 5

5.0 10.0 15.0 20.0 25.0

Volume of distilled water (ml) 20.0 15.0 10.0 5.0 0.0

Volume of hydrochloric acid (ml)

Temperature (oC)

10.0 10.0 10.0 10.0 10.0

24.0 24.0 23.0 23.0 23.5

Concentration of sodium thiosulphate, [Na2S2O3] (mol L-1) 0.0500 0.100 0.150 0.200 0.250

Time, t (s)

1/Time, 1/t (s-1)

162 56.2 34.9 25.8 19.4

0.00616 0.0178 0.0287 0.0387 0.0516

Concentration of hydrochloric acid, [HCl] (mol L-1) 0.400 0.800 1.20 1.60 2.00

Time, t (s)

1/Time, 1/t (s-1)

52.6 51.5 48.3 45.8 43.6

0.0190 0.0194 0.0207 0.0219 0.0229

Part B Table 2: Concentration of hydrochloric acid and the rate of reaction Set

Volume of hydrochloric acid (ml)

Volume of distilled water (ml)

6 7 8 9 10

5.0 10.0 15.0 20.0 25.0

20.0 15.0 10.0 5.0 0.0

Volume of sodium thiosulphate (ml) 10.0 10.0 10.0 10.0 10.0

Temperature (oC)

23.5 23.5 23.0 23.0 23.0

Data Analysis: Part A - Determining order of reaction with respect to sedum thiosulphate The concentration of sodium thiosulphate solution used is calculated by using the formula:

M1V1 where

= M2V2

M1 = initial concentration of sodium thiosulphate solution (0.250M) M2 = final concentration of sodium thiosulphate solution after dilution V1 = initial volume of sodium thiosulphate solution

V2 = final volume of sodium thiosulphate solution after dilution (Solution Concentration, n.d.)

E.g., 0.250M (0.005 L) M2

= M2 (0.025 L) = 0.250M (0.005 L) ÷ 0.025 L = 0.0500M

The graph of rate of reaction, 1/t against concentration of sodium thiosulphate, [Na2S2O3] is then plotted to determine the order of reaction with respect to sodium thiosulphate graphically.

Graph of Rate of Reaction, 1/t against Concentration of Sodium Thiosulphate, [Na2S2O3] 0.06 y = 0.2094x - 0.0024

0.05

1/t, s-1

0.04 0.03 0.02 0.01 0 0

0.05

-0.01

0.1

0.15

0.2

0.25

0.3

[Na2S2O3], mol L-1

Figure 5: Graph of rate of reaction, 1/t against concentration of sodium thiosulphate, [Na2S2O3]

The rate law, concentrations of reactants and the rate of each set is used to perform manual calculations on the order of reaction with respect to sodium thiosulphate.

E.g., comparing Set 1 and Set 2

Rate, 1/t = Rate2 = Rate1

k [Na2S2O3]m[HCl]n {k [𝑁𝑎2 𝑆2 𝑂3 ]𝑚 [HCl]𝑛 }2 {k [𝑁𝑎2 𝑆2 𝑂3 ]𝑚 [HCl]𝑛 }1

0.0178 = 0.00616 2.89 = m =

k [0.100]𝑚 [2.00]𝑛 k [0.0500]𝑚 [2.00]𝑛 2m 1.53

The calculations above were conducted for all sets as listed in the table below and the m values were recorded:

Table 3: The m values of all sets compared and the average m value obtained Sets compared 1&2 1&3 1&4 1&5 Average

m value 1.53 1.40 1.33 1.32 1.40 ≈ 1

The time taken in Set 1 (162s) could be identified as an anomalous data as there is a drastic drop in the time taken for the cross to disappear from Set 1 to Set 2.

Part B - Determining order of reaction with respect to hydrochloric acid The concentration of hydrochloric acid used is calculated by using the formula:

M1V1 where

= M2V2

M1 = initial concentration of hydrochloric acid (2.0M) M2 = final concentration of hydrochloric acid after dilution V1 = initial volume of hydrochloric acid V2 = final volume of hydrochloric acid after dilution (Solution Concentration, n.d.)

E.g., 2.00M (0.005 L) = M2 (0.025 L) M2 = 2.00M (0.005 L) ÷ 0.025 L = 0.400M

The graph of rate of reaction, 1/t against concentration of hydrochloric acid, [HCl] is then plotted to determine the order of reaction with respect to hydrochloric acid graphically.

Graph of Rate of Reaction, 1/t against Concentration of Hydrochloric acid, [HCl] 0.2

1/t, s-1

0.16 0.12 0.08 0.04 0 0

0.5

1.5 y = 0.0026x + 0.0177 2

1

[HCl], mol

2.5

L-1

Figure 6: Graph of rate of reaction, 1/t against concentration of hydrochloric acid, [HCl]

The rate law, concentrations of reactants and the rate of each set is used to perform manual calculations on the order of reaction with respect to hydrochloric acid.

E.g., comparing Set 6 and Set 7 Rate, 1/t Rate7 Rate6 0.0194 0.0190 1.02 n

= = = = =

k [Na2S2O3]m[HCl]n {k [𝑁𝑎2 𝑆2 𝑂3 ]𝑚 [HCl]𝑛 n}7 {k [𝑁𝑎2 𝑆2 𝑂3 ]𝑚 [HCl]𝑛 n}6 k [0.250]𝑚 [0.800]𝑛 k [0.250]𝑚 [0.400]𝑛 2n 0.0286

The calculations above were conducted for all sets as listed in the table below and the m values were recorded: Table 4: The n values of all sets compared and the average m value obtained Sets compared 6&7 6&8 6&9 6 & 10 Average

n value 0.0286 0.0784 0.0868 0.118 0.312 ≈ 0

No anomalous data was identified as all the time taken for the cross to disappear followed the general decreasing trend and there are very small differences between the values obtained from one set and the subsequent set. Part C – Determining overall order of reaction, rate constant and rate law From the data analysis in Part A and Part B, m ≈ 1 and n ≈ 0. Therefore,

Overall order of reaction = m + n = 1+0 = 1 The reaction between sodium thiosulphate and hydrochloric acid is a first order reaction. Hence, the rate equation for the reaction is:

Rate

= k [Na2S2O3]

To determine the value of rate constant, k, the data of reaction rate and concentration of sodium thiosulphate of all experiment sets in Part A and Part B could be substituted into the rate equation, and an average of k value could be calculated.

E.g., using data in Set 1 of Part A,

0.00616 𝑘1

= 𝑘1 (0.0500) = 0.12

The calculations for k value were conducted for all sets of experiment in Part A and Part B and the kvalues obtained were recorded as follows:

𝑘1 𝑘2 𝑘3 𝑘4

= = = =

0.123 0.178 0.191 0.194

𝑘5 𝑘6 𝑘7 𝑘8 𝑘9 𝑘10

= = = = = =

0.206 0.0760 0.0776 0.0828 0.0876 0.0916

The average k-value was calculated:

Average k-value = 0.131 Hence, the rate constant, k is:

k

= 0.131 L mol-1 s-1

Rate

= 0.131 [Na2S2O3]

The rate equation is:

Discussion: The graph of rate of reaction, 1/t against concentration of sodium thiosulphate, [Na2S2O3] (Figure 5) is a linear increasing function which passes through the origin (0,0). This indicates that the reaction is first order with respect to sodium thiosulphate because according to Elsworth (2018), rate is directly proportional to the concentration of reactant for first-order reactions, given that temperature remains a constant.

In all sets in Part A of the experiment, the temperature of the reaction mixture was maintained relatively constant within the range of 1 degree Celsius (23.0 – 24.0 degrees Celsius). Thus, temperature change is not considered as the main factor of change in the rates of reactions in all sets. In fact, the only variable which was deliberately manipulated was the concentration of sodium thiosulphate, thus it could be concluded that the change in rates of reactions for different sets was mainly due to the change in concentration of sodium thiosulphate.

The inference obtained from the graphical analysis in Part A, i.e., the reaction is first order with respect to sodium thiosulphate is in line with the results of the manual calculations with the use of rate equation (Table 3), where m=1.40, which could be rounded-off to 1. The m-value obtained also meets the expected outcome of 1 as stated in the introduction (Flinn Scientific, 2017). Therefore, it can be inferred that the reaction is first order with respect to sodium thiosulphate, i.e., m=1.

The anomalous data identified (Set 1: 162s) occurred most likely because the concentration of sodium thiosulphate solution used is too low. According to Flinn Scientific (2017), concentration of sodium thiosulphate which is too low results in a more gradual onset of turbidity, thus making it more difficult to measure the time for the cross to disappear and thus is prone to errors in the observation of results. Besides, it could also have occurred due to the inconsistent rate of swirling of the reaction mixture in the conical flask, where the conical flask was swirled too gently in Set 1 as it was the first attempt. With a lower rate of swirling, there are less agitation made to the reaction mixture, the frequency of collision between the reactant molecules decreases, the frequency of successful collisions between reactant decreases and thus the rate of reaction decreases, resulting in a longer time taken for the cross to disappear (AUS-e-TUTE, n.d.).

The graph of rate of reaction, 1/t against concentration of hydrochloric acid, [HCl] (Figure 6) is a linear horizontal function which cut the y-axis (rate of reaction) at 0.0177 s-1. From the graph, the reaction order with respect to hydrochloric acid is likely to be zero order given the constant rate even with an increase in concentration of hydrochloric acid, which satisfies the characteristics of a graph of rate against concentration for a zero-order reaction under constant temperature (Elsworth, 2018).

In all sets in Part B of the experiment, the temperature of the reaction mixture was maintained relatively constant within the range of 0.5 degree Celsius (23.0 – 23.5 degrees Celsius). The only variable which was deliberately manipulated was the concentration of hydrochloric acid and thus the data collected can illustrate the relationship between the concentration of hydrochloric acid and the rate of reaction.

The inference obtained from the graphical analysis in Part B, i.e., the reaction is zero order with respect to hydrochloric acid is in line with the results of the manual calculations with the use of rate equation (Table 4), where n=0.0286, which could be rounded-off to 0. The n-value obtained also meets the expected outcome of 0 as stated in the introduction (Flinn Scientific, 2017). Therefore, it is inferred that the reaction is zero-order with respect to sodium thiosulphate, i.e., n=0.

Although the stoichiometric ratio of sodium thiosulphate and hydrochloric acid have the chemical equation of the reaction which is 1:2, the reaction order of sodium thiosulphate is 1 whereas that of hydrochloric acid is 0. This shows that reaction order cannot be determined by using stoichiometric ratio in the balanced chemical equation.

From the data obtained from this experiment, the overall order of reaction is first order with the rate equation of:

Rate

= 0.131 [Na2S2O3]

This indicates that the rate of reaction is directly proportional to the concentration of sodium thiosulphate and is not affected by the concentration of hydrochloric acid (Elsworth, 2018). Possible Errors As the results have shown obvious anomalies, it is clear that there was error conducted during the procedure, more specifically, the decrease in reaction time in the 4th trial when testing HCl. One of the factors that might have caused this anomaly is the uncontrolled variable of temperature. This is also why the temperature was recorded using the thermometer – to ensure that the temperature of ...