Lab Report on The Velocity of the Inversion of Sucrose in Acid Solution

The lab report below was submitted as part of the coursework for CM2102 Spectroscopic Applications. Please do not plagiarise from it as plagiarism might land you into trouble with your university. Do note that my report is well-circulated online and many of my juniors have received soft copies of it. Hence, please exercise prudence while referring to it and, if necessary, cite this webpage.

1. Aim

To show that the inversion of sucrose in acid solution is a reaction of the first order with respect to sucrose, to evaluate the rate constants of the reactions, k and to find out the degree of hydrolysis of urea hydrochloride.

2. Experimental

Preparation of solutions

20g of dry sucrose was made up to 100mL of water as Solution A. Using accurate dilution of 2M HCl (Solution B), a 100mL solution C of 1M HCl was prepared. Some urea was dried overnight over calcium oxide and 60.06g (constituting 0.1mol) was weighed out. Using the appropriate volume of solution B that contains 0.1mol HCl, the weighed urea was dissolved and made up to 100mL in a volumetric flask.

Measurement of Angle of rotation

25mL of each solution A and C were pipetted into separate dry flasks and the surrounding temperature was recorded. The polarimeter was set up. The stopwatch was started and both solutions A and C were mixed thoroughly by pouring back and forth a few times. As quickly as possible, a clean, dry polarimeter tube was filled with the mixed solution and the angle of rotation was measured and recorded. At the beginning, readings were taken at intervals of 5 minutes for 20 minutes. Subsequently readings were taken every 10 minutes. Three readings were taken at each time, and the average of the three readings was calculated. The experimental procedures were repeated, using Solutions A and D instead. The final readings at t=∞ for both sets of mixtures were taken after setting the reaction mixtures aside for 48 hours.

3. Results and Calculations

Preparation of solution A
Mass of sucrose added = 20.0096 g

Preparation of solution of C:
Concentration of stock HCl solution (solution B) = 2.100 M
To prepare 1 M HCl solution in 100 mL solution, V₁M₁=V₂M₂, vol. x 2.100 = 1 x 0.1
Volume of stock HCl solution needed = 0.1 / 2.100 = 0.04762 L = 47.62 mL

Preparation of solution of D:

Amount of dry urea required = 0.1 x 60.06 gmol^-1= 6.006 g

Mass of urea added = 6.0075 g

Temperature of surroundings = 25.0 ˚C

Table of polarimeter angle readings at different time for HCl solution (A&C):

Time t/min	6.0	11.0	16.0	21.0	26.0	31.0	41.0	51.0	61.0	71.0	81.0	91.0	∞
Polarimeter reading,  At	14.80	14.10	12.70	11.50	10.70	10.00	8.60	7.80	7.40	6.75	6.35	5.75	-4.40
ln (At–A∞)	2.955	2.918	2.839	2.766	2.715	2.667	2.565	2.501	2.468	2.411	2.375	2.317	--

For a 1st order reaction, ln(At–A∞) = -k t + ln(Ao–A∞) Gradient of the graphln (At–A∞) against time = -k = -0.0137 Rate constant, k = 0.0137 min-1

Table of average angle readings for urea HCl solution (A&D):

Time t/min	3.0	13.0	18.0	23.0	28.0	38.0	48.0	58.0	68.0	78.0	88.0	∞
Polarimeter reading,  At	12.60	11.60	10.70	10.40	9.80	8.90	7.80	6.90	5.30	4.60	2.80	-5.60
ln (At–A∞)	2.901	2.845	2.791	2.773	2.734	2.674	2.595	2.525	2.389	2.322	2.128	--

For a 1st order reaction,  ln(At–A∞) = -k t + ln(Ao–A∞) Gradient of the graphln (At–A∞) against time = -k = -0.0085 Rate constant, k = 0.0085 min-1

Degree of hydrolysis in urea hydrochloride =  =  = 0.620

4. Discussion

Optical activity

A polarimeter was used to determine the angle of optical rotation of plane-polarized light passing through a solution. Only chiral compounds are optically active compounds. Enantiomers of chiral compounds have identical atoms and bonds, but the two different forms have different optical properties. If plane polarized light is passed through a solution of a chiral compound, one enantiomer rotates the plane of polarization of the light clockwise and the other rotates the plane of polarized light anticlockwise. The extent of this rotation depends on the nature of the compound and the path length of the solution, as well as temperature and concentration. Since the angle of rotation due to any molecular species is proportional to its concentration, by measuring the angle of rotation for the solution, the progress of the reaction can be monitored.

A standard measure of the degree to which a compound is dextrorotary or levorotary is called the specific rotation. Dextrorotary compounds have a positive specific rotation, rotates the plane of plane polarized light clockwise, while levorotary compounds have negative specific rotation.

In this experiment, the rate of reaction between sucrose and water catalyzed by hydrogen ion can be determined by measuring the angle of rotation of polarized light passing through the solution.

A dilute acidic solution of sucrose is dextro-rotary with specific rotation=+66.5^o. When sucrose is converted into a laeve-rotary mixture of sucrose, fructose (with specific rotation = -92^o) and glucose (with specific rotation = +52.7^o).

Pseudo first order reaction

The reaction is:

C₁₂H₂₂O₁₁(sucrose) + H₂O + H⁺  à C₆H₁₂O₆(fructose) + C₆H₁₂O₆(glucose) + H⁺

As the sucrose is used up and the glucose-fructose mixture is formed, the angle of rotation clockwise becomes less and less, and finally the light will be rotated anticlockwise. 

For hydrolysis of sucrose, the rate equation is written as rate = k[H₂O]^a[H⁺]^b[C₁₂H₂₂O₁₁]^c.

No. of moles of sucrose used = (20.0096g/342.30 gmol^-1)/(100/1000 mL)x(25/1000 mL) = 0.0146mol

No. of moles of HCl present as catalyst = 1M x (25/1000 mL) = 0.025 mol

Concentration of water is approximated to be ≈ 55.5 M (large excess)

Acid was used as a catalyst and will be regenerated at the end of the reaction. Hence the concentration of acid can be assumed to be constant. Also, the concentration of water is very large, 55.5 M. Thus, changes in concentration of water will be insignificant. These results in a pseudo-first order reaction, since all other reactants apart from sucrose, are in large excess.

For a first order reaction, A  P, the rate equation is:  d[A]/dt = -k [A]

[A]_t = [A]₀e^(-kt)

ln([A]_t) = ln([A]₀) – kt

kt = ln([A]₀) – ln ([A]_t)

k = ln =   ln

or ln (A_t - A_¥) = -kt + ln (A₀ - A_¥),

where t is time, A_t is the polarimeter reading at time t, A₀ is the initial polarimeter reading and
A_¥ is the polarimeter reading at the end of the reaction.

From the graphs of ln (A_t–A_∞) against time, a linear relationship was shown by the r² value of lines to be very close to 1 for both solutions. Therefore, the inversion of sucrose in acid solution was a first order reaction with respect to sucrose.

The rate equation can be effectively written as rate = k’ [C₁₂H₂₂O₁₁]where k’= k[H₂O][H⁺]. We can therefore show that the reaction is overall a pseudo-first order, where only one of the reactant is not in excess while the others are.

Dissociation constants

The rate constant for the HCl solution was higher than the rate constant for the urea hydrochloride solution, this is expected because urea hydrochloride is a salt that weakly hydrolyses in aqueous solution to give a small amount of H⁺.  NH₂.CO.NH₃⁺ + H₂O ßà NH₂.CO.NH₂ + H₃O⁺.This incomplete dissociation to give H⁺ results in a lower concentration of H⁺ ions in the solution to act as catalysts for the inversion of sucrose. HCl is a strong acid which ionises completely to give H⁺ for the inversion of sucrose to occur. HCl + H₂O à H₃O⁺ + Cl^-. Since the velocity constant is directly proportional to the hydrogen ion concentration, the rate constant for the inversion of sucrose in urea hydrochloride is lower than that in HCl. Hence from the ratio of the rate constants, we can calculate the degree of dissociation of urea hydrochloride, which was found to be 0.87. Since the degree of dissociation is less than 1, this further confirms that there was incomplete dissociation. 

Sources of Errors & Improvements

There was some time lag in the mixing of solutions, transfer of the mixture into the polarimeter tube and adjusting to the angle of rotation. This resulted in loss of readings at the initial stage of the reaction when the angle changed rapidly as reaction occurs as soon as the mixtures were mixed. In addition, the reading of the angle of rotation from the polarimeter takes time as the scale is very small and the reading of the angle of rotation is taken when the degree and 1/10 degree coincide. However, sometimes there is not only one set of line that coincides, but rather, a few sets of line. Thus, the polarimeter reading may not reliable. Taking three readings of angle of rotation in quick succession and taking the average will reduce this error. Another way is to use computerized equipment that can record both the time and polarimeter reading simultaneously.

In addition, the temperature at which the experiment was conducted may be changing, especially for the reading at 48 hours later. Since the rate constant is dependent on the temperature according to the Arrhenius equation, the rate constant will be affected. Furthermore, the equilibrium between the reactants and products will be disturbed with fluctuations in temperature since by Le Chatelier’s principle, the equilibrium would shift to oppose any changes on the system, leading to changes in the concentration ratios of the mixture and affecting the angle of rotation. To improve this, the experiment could be conducted in an air-conditioned room instead to ensure that temperature is a constant.

5. Conclusion
The reaction for the inversion of sucrose was determined to be pseudo first order with respect to sucrose. The rate of reaction was also found to be proportional to H⁺ concentration. The rate constant for reaction in HCl was 0.0137 min^-1. The rate constant for inversion of sucrose in urea hydrochloride was 0.0085 min^-1. The degree of hydrolysis of urea hydrochloride was 0.620.

6. Exercise

1)      Explain the term ‘pseudo-first order’ by reference to the above reaction.

A pseudo-first order reaction is a reaction where all reactants except for one, are in large excess. The reaction in the experiment was

C₁₂H₂₂O₁₁ + H₂O + H⁺ => C₆H₁₂O₆ + C₆H₁₂O₆ + H⁺

Sucrose                            Glucose    Fructose

Hence, the rate equation can be written as:Rate = k[sucrose]^a[H₂O]^b[H⁺]^c, where[sucrose], [H₂O] and [H⁺] are concentrations in mol/L, k is the rate constant (unit dependent on the values of a, b and c) and  a, b and c are the orders of reaction to be determined from experiments with respect to sucrose, H₂O and H⁺ respectively.

The initial concentration of reactants, H₂O and H⁺ were much larger than the concentration of sucrose, with water present in large excess and acid in excess and acting as catalyst, would be regenerated after reaction to maintain a constant H⁺ concentration. Concentrations of these reactants remain fairly constant over time, thus the reaction can be considered pseudo-first order because it only depends on one reactant (the one that is not in excess as its concentration changes). Sucrose is relatively not in large excess, and the rate of reaction depending on the [sucrose] can be traced over time as the reaction proceeds. From graph 1 and 2, the rate of inversion of sucrose was found to be first order with respect to sucrose concentration, the rate equation can be written as: Rate = K_eff[sucrose], where K_eff = k[H₂O]^b[H⁺]^c.

With [H₂O] and [H⁺] remaining unchanged through the reaction, the rate equation appears to be first order with respect to only sucrose. Hence this reaction is pseudo-first order.

2) How would you expect the specific rate constant for this reaction to alter with the pH of the solution, for what reasons?

The specific rate constant is an experimentally determined (proportionality) constant, which is different for different reactions and changes with temperature, by the Arrhenius equation, k = A e^-Ea/RT, where A is the pre-exponential factor, Ea is the activation energy, R is the gas constant and T is the temperature. H⁺ acts as catalyst in the experiment, the presence of catalyst increases the rate of reaction by lowering the activation energy, more sucrose molecules will possess the minimum required energy for reaction to occur, thus the specific rate constant increases with H⁺ concentration at a given temperature. In addition, we have experimentally determined that the rate of inversion of sucrose increases with H⁺ concentration (from calculations). Since pH = - log₁₀[H⁺], when the pH of the solution decreases, [H⁺] increases. Since K_eff is proportional to [H⁺], an increase in [H⁺] (or decrease in pH) will result in an increase in rate in a pseudo first order reaction. An increase in pH on the other hand, will result in a decrease in rate.

7. References

·         Colby College (2008) Inversion of Sucrose. Website: http://www.colby.edu/chemistry/PChem/lab/InversionSucrose.pdf   

·         Retreived: 29 August, 2009.

·         Tel Aviv University. (2004) Inversion of Sucrose. Website: http://www.tau.ac.il/~phchlab/experiments/Sucrose/Sucrose.htm  

·         Retreived: 29 August, 2009.

·         Engineering Communication Centre, University of Toronto (2002) Laboratory Reports. Website: http://www.ecf.utoronto.ca/~writing/handbook-lab.html 

·         Retreived: 29 August, 2009.

·         Department of Energy, USA. Newton, Ask a Scientist. (2003) Pure Water Concentration. Website: http://www.newton.dep.anl.gov/askasci/chem03/chem03038.htm

·         Retreived: 29 August, 2009.

·         P.W. Atkins, Physical Chemistry, eighth edition, Oxford University Press, 2006, pp.794-797.

·         Clayden, Greeves, Warren and Wothers, Organic Chemistry, Oxford University Press, 2008, pp. 346-347.