LAB – Using Hess’ Law and calorimetery to determine the molar enthalpy of combustion of magnesium
Theory:
Thermochemistry is the study of energy changes accompanying chemical transformations and the change in enthalpy is a useful figure used by thermo-chemists. Enthalpy is defined as the total internal energy of a system plus the product of pressure and volume[4]. When pressure and volume are constant, Enthalpy can be defined as the total heat content or sum of all thermodynamic energies within a system. These energies include potential bond energies, potential nuclear energies as well as the sum of the kinetic energy of electrons. Chemists are unable to measure enthalpy because it is impossible to measure all of the energies in a system; however it is possible to determine the change in thermodynamic energy and thereby the change in enthalpy. The symbol associated with enthalpy is H and the symbol referring to a change in enthalpy is H.
Since H is defined as the change in thermal energy in a system and the 1st law of thermodynamics states that energy can neither be created nor destroyed, then the energy released by the surroundings when added to the energy lost by the system must equal 0 as seen in the equation below.
Esystem+ Esurroundings=0
Esystem= -Esurroundings
Since the change of internal energy of the system (Esystem) is also the change in enthalpy (H) and Heat (Q) is defined as the energy transferred to another body, such as the surroundings then this equation can be rewritten to:
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Hsystem= -Qsurroundings
Calorimetry is the technological process used by chemists to measure heat transfer. A calorimeter is a device that insulates and isolates a chemical transformation inside water. A thermometer and stirrer are also used to measure the temperature change and ensure even heat distribution respectively. By using a calorimeter to measure the change in temperature of the surroundings of a chemical or physical reaction one can determine the amount of heat leaving or entering a chemical system and thus the change in enthalpy. The following equation equates heat transfer in/out of the surrounding to the enthalpy change of the system being observed.
Hsystem= -Q= -(mass)(specific heat capacity)( in temperature)
These relationships make it possible to measure the energy change of a chemical transformation and thus, the change in enthalpy. This is useful for the study of thermochemistry because it can be used to determine the net energy that will be absorbed or released during a chemical transformation. This is even more valuable when expressed as a molar enthalpy (Joules per mole).
This can easily be calculated by dividing H by the number of moles (n).
n=mass(m)molar mass (M)=mM
H°= Hn or H=n× H°
In the process of applying these relationships, a scientist may encounter a reaction that cannot be safely conducted within a calorimeter because of large energy releases or difficulty in accurately measuring the heat transfer. However, in 1840, Dr. Henri Germain Hess published the following law that now carries his name:
“the heat evolved or absorbed in a chemical process is the same whether the process takes place in one or in several steps”[2]
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Hess’ Law can also be referred to as the law of heat summation. So in accordance to this law, one can calculate the change in enthalpy of a reaction by splitting it up into multiple steps, and then summing up the enthalpy changes of each reaction to find the overall enthalpy change for the entire process.
The equations are manipulated by reversing the equations and multiplying the stoichiometric co-efficients. In order to reverse multiply the equations enthalpy change by -1 and switch the reactants with the products. Also, when multiplying the co-efficients of an equation by a constant k, one must also multiply the enthalpy change by the same constant. After manipulating the equations in this way, one can add all the products and all the reactant substances. Then if a substance is found on both the reactant and product side of the net equation, it can be removed from the net equation. The enthalpy changes are also summed, and in this way, the total enthalpy change can be determined.
Hypothesis:
By breaking up the combustion of magnesium into 3 equations, finding the enthalpy of each reaction using calorimetry for 2 equations and using the given enthalpy of formation for the last reaction, dividing by moles to find the molar enthalpy and finally using Hess’ Law to sum up the molar enthalpies (for Mg and MgO respectively), the molar enthalpy of combustion of Magnesium derived with less than 15% error (due to lack of extremely precise equipment and controlled lab environment).
The 4 equations are as follows:
(1) Mg(s) + 12O2g MgO(s) Hcomb° = ?
(2) Mg(s)+2HClaq H2(g)+MgCl2(aq) Hr°= ?
(3) MgO(s)+ 2HCl(aq) H2O(l)+ MgCl2(aq) Hr°= ?
(4) H2(g)+ 12O2(g) H2O(l) Hf° = -285.8kJ
One can then manipulate Equations 2-4 to create equation 1. First once can reverse equation 2 and then cancel out all the redundant substance that show up on both sides of the arrows. For equation 2 multiply the experimental enthalpy by (-1)[1]. This is shown below:
(2) Mgs+2HClaq H2g+MgCl2aq
*Reversed* (3) H2O(l)+ MgCl2(aq) MgO(s)+ 2HCl(aq)[multiply H by -1 ]
(4) H2(g)+ 12O2(g) H2O(l)
Net equation : Mg(s)+ 12O2(g)→ MgO(s)
Hcombustion of magnesium = (H reaction 2)+ (-H reaction 3)+(H reaction 4)
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Purpose: The purpose of the lab is to safely and accurately measure the molar enthalpy of combustion of magnesium by splitting up the reaction into 3 steps, determining the molar enthalpy per mole of Mg and MgO respectively, summing them up using Hess’ Law and thus confirming our hypothesis that Hess’ Law can be used to determine the change in molar enthalpy of a reaction by splitting it into multiple steps.
Procedure:
Determine Hor for reaction (2)
1. Obtained a Styrofoam cup covered it with a piece of a cardboard with a hole and placed a thermometer through the hole into the cup to set up a simple calorimeter.
2. Used a graduated cylinder to measure approx. 100ml of HCl(aq) [1 mol/L] and poured into the calorimeter. Recorded the exact volume of HCl(aq) taken in milliliters.
3. Recorded the initial temperature of the HCl(aq) in degrees Celsius using thermometer.
4. Placed cup on electronic mass balance and then pressed button to set that weight to zero
5. Massed approximately 0.8g of MgO(s) powder while electronic mass balance believed cup had mass of 0. Recorded the exact mass taken in grams using electronic mass balance.
6. Poured MgO(s) powder into the calorimeter and closed lid and continually stirred solution with thermometer for 10mins
7. Measured highest temperature during reaction of final solution (or Tfinal) in degrees Celsius using thermometer.
8. Disposed of final solution by diluting with water to harmless concentration and pouring down the sink.
9. Cleaned and returned all lab equipment and supplies as well as wiping down lab workspace
Determining Hor for reaction (3)
1. Repeated steps 1 – 3 for Determining Hor for reaction (2)
2. Acquired approx. 0.4g of Mg(s) ribbon. Recorded the exact mass taken in grams using an electronic mass balance.
3. Sanded ribbon till shiny to remove dull oxide coat and measured exact mass taken.
4. Added the Mg(s) to the calorimeter containing HCl(aq) and closed lid. Continually stirred solution with thermometer for 10mins
5. Measured highest temperature during reaction of final solution (or Tfinal) in degrees Celsius using thermometer.
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6. Disposed of solution by diluting solution with water and pouring down the sink.
7. Cleaned and returned all lab equipment and supplies as well as wiping down lab workspace
Observations:
Change in Temperature of Solution inside simple Styrophoam, mercury thermomter and Cardboard Calorimeter with Mg(s) ribbon and MgO(s) powder reacting with HCl(aq) [1.0 mol/L] for 10 mins respectively
| MgO(s) | Mg(s) |
Mass of Solid Reactant (g)
| 0.810 | 0.360 |
Volume of HCL(aq) (mL)
| 98.2 | 100.0 |
Initial Temperature (˚C) of HCl
| 25.3 | 25.3 |
Final Temperature (˚C) of Solution
| 32.1 | 42.0 |
in Temperature (oC)
(Final Temp. – Initial Temp.) | 6.8 | 16.7 |
Calculations:
1. Calculate Number of Moles of Reactants for both Reactions and determine limiting reactants
nMgO=mM=0.81040.31=0.02009426941205656164723393698834 moles MgO(s)
nMg=mM=0.36024.31=0.01480872069107363225010283833813 moles Mg(s)
nHCl(MgO reaction)=C*V=1 molL*0.0982L=0.0982 moles HCl(aq)
nHCl(Mg reaction)=C*V=1 molL*0.1=0.1 moles HCl (aq)
nMgO*2 mol HClaq1 mol MgOs=0.04018853882411312329446787397668 mol HCl(aq)
MgO is the limiting reactant and HCl(aq) is in excess
nMg*2 mol HClaq1 mol Mgs=0.02961744138214726450020567667626mol HCl(aq)
MgO is the limiting reactant and HCl(aq) is in excess
2. Calculate Heat Transfer to Water inside Calorimeter
QSurroundings MgO=mcT=98.24.196.8= 2797.9144 J
QSurroundings Mg=mcT=100.04.1916.7= 6997.3J
3. Calculate Enthalpy
Hreaction 3°= -QSurroundingsMgO= -2797.9144J
Hreaction 2°= -QSurroundingsMg= -6997.3J
4. Calculate Molar Enthalpy
Hreaction 3°nMgO=-2797.9144J.02009426941205656164723393698834mol=-139239.41909135802469135802469136Jmol=-139kJmolMgO
Hreaction 2°nMg=-6997.3J0.01480872069107363225010283833813mol=-472512.11944444444444444444444452Jmol=-473kJmolMg
∴Mg(s)+2HClaq H2(g)+MgCl2(aq) Hr°= -473kJ
∴MgO(s)+ 2HCl(aq) H2O(l)+ MgCl2(aq) Hr°= -139kJ
5. Use Hess’ Law to determine Final H of Combustion of Magnesium
(2) Mgs+2HClaq H2g+MgCl2aq
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*Reversed* (3) H2O(l)+ MgCl2(aq) MgO(s)+ 2HCl(aq)[multiply H by -1 ]
(4) H2(g)+ 12O2(g) H2O(l)
Net equation : Mg(s)+ 12O2(g)→ MgO(s)
H = (H reaction 2)+ (-H reaction 3)+(H reaction 4)
H=-473+-(-139)+-285.8= -619.8 kJ
Potential Energy
Potential Energy
Reactants:
Mg(S) + 2HCl(aq)
Produts:
H2(g) + MgCl2(aq)
Products:
MgO(S) + 2HCl(aq)
Reactants:
H2O(l) + MgCl2(aq)
Reactants:
H2(g) + 1/2O2(g)
Product:
H2O(l)
Potential Energy
Hor =
-285kJ
Hor = -473kJ
Hor = 139kJ
Therefore Resulting Vector = -619.8kJ
Potential Energy
Potential Energy
Reactants:
Mg(S) + 2HCl(aq)
Produts:
H2(g) + MgCl2(aq)
Products:
MgO(S) + 2HCl(aq)
Reactants:
H2O(l) + MgCl2(aq)
Reactants:
H2(g) + 1/2O2(g)
Product:
H2O(l)
Potential Energy
Hor =
-285kJ
Hor = -473kJ
Hor = 139kJ
Therefore Resulting Vector = -619.8kJ
Hess’ Law Diagram
Analysis:
Firstly, 2 main assumptions have been made to simplify the above calculations.
One of the most significant is that the specific heat capacity and density used to calculate the heat gained by the surroundings is incorrect because it assumes that the remaining solution is composed entirely of water when we know that in both cases there will be a large amount of acid that will not be consumed as well as some Magnesium Chloride ions. The density of the solution will not be 1 for this reason and all the mass measurements based on 1g/1ml will be false. However in order to simplify the calculation we assume that both the intial and final solutions have the same density, mass and heat capacity as water.
The second main assumption made was that the calorimeter is a perfect insulator and so all the heat content transferred was absorbed by the surrouding water. However, since the system has many imperfections, heat would have been absorbed by the air through the hole, the thermometer and the calorimeter. If this was an accurate calculation, all of these factors would have to be considered and accounted for. However, in order to simplify calculations we assume that the loss to the air, calorimeter and thermometer is so minimal that it can be ignored.
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After completing the experiment, it was found that the accepted enthalpy of formation of Magnesium Oxide is 601.7kJ/mol[3]. This percentage error can be calculated using the following equation:
% Error=experimental value-theoretical valuetheoretical Value*100%
% Erorr=619.8- 601.7601.7*100%=3.008%
Sources of Error
(1) The mass balance has a very high uncertainty because it provides only 2 decimal places. This means that it has a minimum uncertainty of 0.005g. This is huge because it means that the number moles actually used could be off significantly because of the small sample being used. This could either increase or decrease the true value of the molar enthalpy in both reaction 1 and 2. A way to decrease this source of error might be to use a scale with 3 decimal places because that will reduce the uncertainty and the possibility of error during mole calculations or to increase the mass of reactants used in the reaction.
(2) Another source of error is that even after completely sanding the Magnesium ribbon, the ribbon will still react with the oxygen in the air before being placed into the calorimeter for the reaction to take place because of time lapses while setting up. This can affect calculations because the mass measured will be incorrect thereafter due to additional mass added by the additional oxygen. Furthermore, the oxide represents a contamination of the Mg that may affect its ability to completely react with the acid. This can be prevented by cleaning the magnesium directly before immediately dropping it into the calorimeter to prevent as much oxidation as possible.
(3) Another possible source of error may be the fact that the nature of the calorimeter does not allow the chemist to view the reaction without opening the calorimeter up and thus allowing heat and matter exchange with the outside environment. This prevents the chemist from making qualitative observations that do not affect the reaction. In the future, the amount of time the reaction should take should be made known so that the chemist can open the calorimeter confident that the reaction is over and that the temperature reading taken is the highest possible. Or perhaps using rates of reaction, the exact timing can be used.
(4) The highest temperature recorded is not precise because the temperature fluctuates throughout the reaction. A temperature probe should be used to digitally track all temperature fluctuations and then determine the highest temperature. A human being cannot accurately measure temperature continuously for 10mins. A digital probe will improve results because the heat transfer calculation will be more accurate. An incorrect temperature can either increase or decrease the change in enthalpy of a reaction and therefore increase or decrease the molar enthalpy of the same reactant.
Conclusion:
To conclude it is possible to safely and accurately measure the molar enthalpy of combustion of magnesium by splitting the single process into 3 separate steps, determining the molar enthalpy per mole of Mg and MgO respectively, summing them up using Hess’ Law and thus confirming the hypothesis that Hess’ Law can be used to determine the change in molar enthalpy of a reaction by splitting it into multiple steps within a 15% error margin. In order to prove this, Hess’ Law and the first law of thermodynamics were applied. The result of the lab is that the Molar enthalpy of combustion of Magnesium is -619.8kJ.
References
[1]http://www.science.uwaterloo.ca/~cchieh/cact/c120/hess.html
[2]http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Thermodynamisc_Cycles/Hess’_Law
[3]
[4] McGraw-Hill Ryerson Chemistry 12 Textbook ©2011
