Sharifi 1
Determining the Validity of Hess’s Law through Calorimetry SCH 4U1 Mrs. Bhardwaj By: Pooyan Sharifi
Sharifi 2 Introduction/ Background Info According to Albert Einstein’s equation (e=mc2) everything in the universe that has a mass contains energy. The constant c which is directly proportional to energy (e), represents the speed of light multiplied by itself indicating that even the smallest mass, contains exponential amounts of potential energy (Ex. Nuclear fission, nuclear fusion). Although we do not release energy to this scale in the experiment, the basis of releasing potential energy from matter is still investigated as well as its relation with the laws of thermodynamics. The properties and laws of energy dictate the flow of our everyday lives in the universe from the chemical reactions that occur in our bodies, to the nuclear reactions in our sun that release energy in order for life to exist on Earth. Although it is impossible to measure the energy constant of matter, chemists can measure the energy change or enthalpy (ΔH) from a reaction. By using calorimetric based experiments, one can measure the energy released (exothermic reaction) or energy absorbed (endothermic reaction) in a thermodynamic system. When studying energy transfer from chemical reactions it is important to distinguish between the substances undergoing change, which is called the system, and the surrounding environment which is called the surroundings. When energy is released/absorbed from a chemical reaction to its surroundings, it is in the form of heat represented by q, measured in joules in the equation q=mcΔT. The variable m represents the mass of the surroundings in grams that interacts with the energy transfer of the chemical reagents. The variable c represents the heat capacity of the surroundings in Joule/Gram •°Celcius), and ΔT represents the change in temperature of the surroundings. Through the use of this equation, the enthalpy of the system can be calculated by the equation ΔH = -q. Any energy gained by the surroundings, means energy has been released from the system, thus it will be a negative value. The ideal system for conducting a calorimetric based experiment is in an isolated system where energy and matter cannot escape. However, it is impossible to simulate an isolated system; therefore it is important to understand that some energy may escape the calorimeter. It is important to assume while calculating values from calorimetric based experiments that dilute solutions have the same density (1g/1ml) and heat capacity as water(4.18J/g•°C), no heat is transferred outside the calorimeter and any heat transfer by the parts of the calorimeter are negligible. Certain elements and compounds have indefinite enthalpy changes per quantity for each type of reaction. This is called molar enthalpy and can be calculated from the equation ΔH= nΔHx. The variable n represents the number of moles of the compound, and the variable ΔHx represents the molar enthalpy by type of reaction (x). Molar enthalpy of a substance can also be determined using Hess’s law which states that the sum of enthalpy change of a reaction only depends on the initial and final conditions of the process, and is the sum of the steps. Hess’s law also states that it does not matter how many steps it takes for a reactant to become a product, the enthalpy change will remain the same. The accepted molar enthalpy of the combustion of Magnesium is -601.6KJ/mol. Hypothesis If Hess’s law is used to calculate the molar enthalpy of combustion for magnesium using experimentally determined enthalpy values, then the final result will be accurate and near to the
Sharifi 3 accepted value (-601.6KJ/mol). This is because Hess’s law states that the sum of the enthalpy pages of the intermediate reactions, should equal the enthalpy change of the target reaction.
Table 1: Quantitative and Qualitative Data in the calorimetric study of the reaction of 1.00mol/L HCl with Mg and MgO in a Styrofoam calorimeter. Mg (solid ribbon) and MgO (powder) was immersed into a beaker of HCl solution.
Reactant to be immersed in 50.0mL +/- 0.05 of 1.00mol/L of HCl Magnesium Ribbon (Mg)
Mass Of Reactant +/0.01g
0.02g
Initial Temperature of HCl solution +/0.1°C 22.1°C
Final Temperature of HCl solution +/0.1°C 23.8°C
Magnesium Oxide Powder (MgO)
0.4g
22.1°C
26.1°C
Qualitative Observations of HCl solution
Before: Clear, transparent solution of HCl. Mg ribbon was shiny, smooth and malleable. During:-Bubbles formed around the Mg Ribbon rising out of the solution. After:-Ribbon completely dissolved into the solution. No qualitative change of solution. Before: MgO powder is white soft and very fine. HCl solution is clear and transparent. During: -Powder clumped at first. Solution became cloudy. While poured, MgO dust escaped into the air. After: -Solution turned transparent once stirred.
Sharifi 4 Data Analysis and Calculations b) Both reactions that occurred were exothermic as the final temperature of the HCl surrounding was greater than its initial temperature. Therefore the ΔT value would be a positive number in the equation q=mcΔT meaning the q value would also be positive. With a q value that is positive, this indicates that the heat was absorbed by the HCl solution from the release of heat of the reaction. Ultimately, proving that the reaction was exothermic. Sample Calculation to determine heat transfer using q=mcΔT. ΔT = ΔTf - ΔTi ΔTf = 100.0˚C ΔTi = 25.00 ˚C C= 4.18J/g•°C m = 50.0g q = (50g)(4.18J/g •°C)( 100.0˚C-25.0 ˚C) =+15.7KJ ∴ ΔTf > ΔTi, q value is positive and energy is released so it is exothermic.
c) Determine the heat transfer from the magnesium ribbon to the HCl solution. q=mcΔT q=? m = 50.0mL * (1.00g/1.00mL) = 50.0g c = 4.18J/g •°C ΔTf = 23.8˚C ΔTi = 22.1˚C ΔT = ΔTf - ΔTi = 23.8 - 22.1 = 1.70 ˚C
q = (50.0g)(4.18J/g •°C)(1.70 ˚C) = +355.3J
Sharifi 5 Energy absorbed from the surroundings ∴ that amount of energy has left the system and enthalpy of system is negative. ΔH = -q = -355.3J = -0.3553KJ Solve for ΔHr using the equation ΔH= nΔHr rearranged to ΔHr = ΔH / n ΔH = -0.3553KJ mMg= 0.02g MMg = 24.31g/mol n = mM n = (0.02g)/(24.31g/mol) = 0.000822707 mol ΔHr = (-0.3553KJ) / (0.000822707mol) = -4.32 x 102KJ/mol
∴ the enthalpy change per mole of Magnesium in this reaction is -4.32 x 102 KJ/mol. d) Mg(s) + 2HCl(aq) H2(g) + MgCl2(aq)
ΔH = -432KJ
e) Determine the heat transfer from the magnesium oxide powder to the HCl solution. q=mcΔT q=? m = 50.0mL * (1.00g/1.00mL) = 50.0g c = 4.18J/g •°C ΔTf = 26.1˚C ΔTi = 22.1˚C ΔT = ΔTf - ΔTi = 26.1 - 22.1 = 4.00 ˚C
Sharifi 6 q = (50.0g)(4.18J/g •°C)(4.00 ˚C) = +836J
Solve for ΔHr using ΔHr = ΔH / n ΔH = -q = -836J =-0.836KJ n = (0.4g) / (40.31g/mol) = 0.0099231mol
ΔHr = (-0.836KJ) / (0.0099231mol) = -84.2KJ/mol
∴ the enthalpy change per mole of Magnesium Oxide in this reaction is -84.2 KJ/mol. Thermochemical equation for the reaction of MgO in HCl MgO(s) + 2HCl(aq) H2O(l) + MgCl2(aq)
ΔH = -84.2KJ
f) Reference Equations: (A) Mg(s) + 2HCl(aq) H2(g) + MgCl2(aq) (B) MgO(s) + 2HCl(aq) H2O(l) + MgCl2(aq) (C) H2(g) + 1/2O2(g) H2O(l)
Formula for the combustion of Magnesium: Mg(s) + 1/2O2(g) MgO(s)
ΔH = -432KJ ΔH = -84.2KJ ΔH = -285.8KJ
Sharifi 7 1*(A): Mg(s) + 2HCl(aq) H2(g) + MgCl2(aq) ΔH = -432KJ -1*(B) H2O(l) + MgCl2(aq) MgO(s) + 2HCl(aq) ΔH = 84.2KJ Insert 1(C) to cancel out H2 and H2O: H2(g) + 1/2O2(g) H2O(l) ΔH = -285.8KJ
Mg(s) + 2HCl(aq) + H2O(l) + MgCl2(aq) + H2(g) + 1/2O2(g) H2(g) + MgCl2(aq) + MgO(s) + 2HCl(aq) + H2O(l) Mg(s) + 1/2O2(g) MgO(s)
∴ ΔHcomb = ΔH 1(A) + ΔH -1(B) + ΔH 1(C) = -432KJ + 84.2KJ + (-285.8KJ) = -633.6KJ/mol
(enthalpy change is per mole of Magenisum)
Table 2: Quantitative Results of Calculations from Experimental Data Reaction Mg(s) + 2HCl(aq) H2(g) + MgCl2(aq) MgO(s) + 2HCl(aq) H2O(l) + MgCl2(aq) Mg(s) + 1/2O2(g) MgO(s) Percent Error
Calculated Enthalpy Change per Mole of Magnesium -432KJ/mol -84.2KJ/mol -633.6KJ/mol 5.32% error
Sharifi 8 Evaluation and Conclusion The purpose of this lab was to determine the molar enthalpy of the combustion of magnesium using experimental values from reactions between magnesium and magnesium oxide in hydrochloric acid solution. The calculated molar enthalpy of the combustion of magnesium from this experiment was -633.6KJ/mol. This result was determined by immersing a known mass of magnesium metal as well as magnesium oxide powder into a known volume and concentration of HCl (aq). Knowing the initial temperature of the solution, the final temperature was measured and the change in temperature was calculated. The heat transfer between the reactant and the solution was calculated using the equation q=mcΔT. The energy value also represents the enthalpy change of the reaction which is ΔH = -q. Finally the known mass of the reactant was converted to moles to be used in the equation ΔHr = ΔH / n. Once the enthalpy change of the reference equations were calculated, Hess’s law was used in order to calculate the enthalpy change of the equation for the combustion of magnesium. However, the value calculated was not exactly equal to the accepted molar enthalpy of the combustion of magnesium. Referring to Table 2, the percent error was found to be 5.32% off from the accepted value. The experiment demonstrated evidence that calculated values were close to the accepted values. The procedure itself was generally simple to carry out and the possible sources of error would have no significant effect on the data. Considering the lack of a true calorimeter to prevent heat escape, as well as professional measuring instruments, the percent error is relatively minimal. This experiment did have some sources of error that resulted in the calculated value being unequal to the accepted value for the molar combustion of magnesium. One reason why the calculated value was inaccurate is because some heat may have transferred to the air in the Styrofoam cup or to the cup itself. If this occurred during the experiment, then not all of the energy released from the reaction would have been transferred to the solution. As a result, the calculated energy change (q) would have been less. Therefore, the enthalpy of the reaction would also be smaller than its true value. Ultimately, this would cause the molar enthalpy of combustion to be greater than the accepted value after the use of Hess’s law. This is seen in Table 2, where the calculated value has a +5.32% percent error. In addition, another source of error that affected the accuracy of the calculated value was that the magnesium ribbon surface had a coating of magnesium oxide. When pure magnesium is exposed to the air, it reacts oxygen to form magnesium oxide. Therefore, making the reactant in its respective equation, impure and therefore will yield inaccurate results. Impurity of the magnesium poses many problems in this experiment. For instance, because magnesium oxide is heavier than magnesium by itself, it will add weight to the mass of the ribbon. The measured 0.02g ribbon would not be purely 100% the mass of magnesium as the oxygen atom would also contribute to the mass. Therefore, there will be less magnesium to react and release energy so the enthalpy change of the reaction would be a smaller. The molar enthalpy of combustion of magnesium would be above the accepted value. Another source of error is from uncertainties from the imprecisions of lab equipment. In the experiment, values were measured for temperature and mass using a simple alcohol based
Sharifi 9 thermometer and a milligram balance. The thermometer was not digital and therefore temperature had to be rounded to the nearest marking. By referring to Table 1 and Table 2, you can see that the measures values are +/- 0.01 meaning they are not exact. Not having an exact measurement of the reactants could cause the calculated values to be inaccurate whether by measuring too much or too little. This could sway the final calculations in either direction. As well, another source of error is due to the fact that the reactants cannot completely be transferred from containers. In the experiment, hydrochloric acid was poured from a measuring beaker to a 100mL graduated cylinder. Not all of the solution could have been transferred as it would have remained on the measuring beaker as residue. Therefore there would be less volume present in the reaction and as a result the amount of heat generated would have been greater. This is because the less volume of a solution, the less energy is required to change its temperature (specific heat capacity is the number of joules required to raise the temperature of the substance by 1 degree Celsius). So the enthalpy change calculated for each equation would be greater than its true value. Another example of this source of error was observed in Table 1 under the Qualitative Observations header. When magnesium oxide powder was poured into the hydrochloric acid beaker, some of the powder escaped into the air in the form of dust. Therefore less of the recorded mass is used and ultimately there would be a smaller enthalpy change. Lastly, a source of error would be from the use of the stir rod. In the procedure, the stirring rod used is not cleaned after its use in the first reaction. Therefore the second reaction could have been contaminated with reactants or products from the first reaction. The effects of this source of error could vary depending on the reaction of the contaminants in the solution. If only hydrochloric acid residue was transferred, then more energy would have been required to increase the temperature. Therefore, the calculated enthalpy change would have been less and the molar enthalpy of combustion of magnesium would be a smaller negative number. Based off the evidence gotten from this experiment, it is clear that Hess’s law is an acceptable method to calculate enthalpies of reactions. Despite the many sources of error that potentially may have made the results inaccurate, Hess’s Law still proved to provide a result which was only 5.32% off from the accepted value. However, Hess’s law remains theoretically true and with accurate experimental data, the percent error could potentially be zero. Although it is difficult to measure enthalpy change accurately between many intermediate steps (the more steps the less accurate the result will be) Hess’s law still remains an acceptable method to calculate enthalpies of reactions. Some improvements that could be made to the procedure of this lab for future use would be to incorporate a step for rinsing the stirring rod and beakers used. This would prevent crosscontamination from occurring and increase the accuracy of results. Another improvement would be to use more professional equipment such as a digital thermometer and a true calorimeter. Heat is more likely to escape the system in a Styrofoam cup rather than a calorimeter. Another crucial improvement would be to have multiple trials of the reaction so that the average can be taken for the calculations. This would improve the accuracy of the final result for this experiment.
