Hess’s Law and the Molar Enthalpy of Combustion for Magnesium Purpose:The purpose of the lab ultimately is to find the molar enthalpy of magnesium. This is done by finding the enthalpy changes of reactions (2) and (3). The enthalpy changes of reactions (2) and (3) along with the enthalpy change given for reaction (4) can be used to arrive at a value of the molar enthalpy of combustion of magnesium by using Hess’s Law.
Hypothesis:By using Hess’s law to calculate the molar enthalpy of combustion using experimentally determined enthalpy change values (from reactions (2) and (3)) it is believed that the final calculated value will be similar to the accepted molar enthalpy of combustion of magnesium being 611kJ/mol. This should be the case because with Hess’s Law, the molar enthalpy change of magnesium is the sum of the enthalpy changes in reactions (2), (3), (4).
Materials:Apparatus of Materials: MgO(s) powder Mg ribbon Simple calorimeter Scoop 100 mL graduated cylinder Electron balance Thermometer Sandpaper/emery paper Styrofoam cup
Procedure:Part 1 (Determining the enthalpy change of Reaction 2):
Before the lab commences, a data table should be made to record mass and temperature data on. Obtain and set up a simple calorimeter. Add 100 mL of 1.00 mol/L HCL(aq) to the calorimeter using a 100 mL graduated cylinder. On the data table created in the first step, take note of and record the initial temperature of HCL(aq). Collect no more than 0.80 g of MgO(s) powder. Record the mass on the data table. A group member should then add MgO(s) powder to the calorimeter containing HCL(aq). Make sure to swirl gently. After a certain time when the temperature no longer rises, record the highest temperature reached.
Dispose of the solution as directed by teacher’s instructions before commencing part 2 of the lab.
Part 2 (Determining the enthalpy change of Reaction 3)
Create a data table to record the mass and temperature data on (exactly as first step in part 1). Using a graduated cylinder, add 100 mL of 1.00 mol/l HCL(aq) to the simple calorimeter Record the initial temperature of HCL(aq) on the data table. Gather a mass of magnesium that is close to 0.50 g (no more than that) and record the mass onto the data table. Make sure to sand the magnesium before proceeding with the experiment. Add Mg(s) to the calorimeter containing the HCL(aq). Once again gently swirl the solution. Take note of the temperature rising. When the temperature has stopped rising, record the highest temperature reached.
Dispose of the solution properly and return lab equipment to proper locations.
Observations:
Reaction (2) Observation Table Volume of HCL(aq)100 mL of 1.00 mol/L HCL(aq) Mass of MgO(s)0.80g Initial Temperature (T1)21.5°C Final Temperature (T2)25°C Change in Temperature (T2-T1)3.5°C
Reaction (3) Observation Table Volume of HCL(aq)100 mL of 1.00 mol/L HCL(aq) Mass of Mg(s)0.50g Initial Temperature (T1)21°C Final Temperature (T2)41°C Change in Temperature (T2-T1)20°C
Analysis:
Calculating the enthalpy change for reaction (2):
Q = mc∆T
Q = (m)(c)(T2-T1)
Q = (100g)(4.18J/g°C)(25°C – 21.5°C)
Q = 1500 J or 1.5 kJ
∆H = -Q
∆H = -1.5 kJ
Finding moles of Magnesium oxide:
nMgO = mMgO / MMgO
nMgO = 0.80g / 40.3044g/mol
nMgO = 0.0198 mol
∆Hr = ∆H / n
∆Hr = -1.5 kJ / 0.0198 mol
∆Hr = -75.57 kJ/mol
Therefore the enthalpy change of reaction (2) is -75.57 kJ/mol.
Calculating the enthalpy change for reaction (3):
Q= = mc∆T
Q = (m)(c)(T2-T1)
Q = (100g)(4.18J/g°C)(41°C – 21°C)
Q = 8400 J or 8.4 kJ
∆H = -Q
∆H = -8.4 kJ
Finding moles of Magnesium:
nMg = mMgO / MMg
nMg = 0.50g / 24.305g/mol
nMg = 0.02057 mol
∆Hr = ∆H / n
∆Hr = -8.4 kJ / 0.02057 mol
∆Hr = -408.324 kJ/mol
Therefore the enthalpy change of reaction (3) is -408.324 kJ/mol.
It was assumed that there was a closed system because no liquid would escape. Also it assumed that the mass of HCL(aq) is 100 g since for water 1 g/mL or 1 g = 1 mL. Essentially we assumed HCL had the same heat capacity of water.
Reaction (2): MgO(s) + 2HCL(aq) -> MgCl2(aq) + H2O(l) + 75.57 kJ Reaction (3): Mg(s) + 2HCL(aq) -> MgCl2(aq) + H2(g) + 408.324 kJ
(2) MgO(s) + 2HCL(aq) -> MgCl2(aq) + H2O(l) -75.57 kJ (3) Mg(s) + 2HCL(aq) -> MgCl2(aq) + H2(g) -408.324 kJ (4) H2(g) + 1/2O2(g) -> H2O(l)-258.8 kJ
Mg(s) + 1/2O2 -> MgO(s) ∆Hcomb =?
To find the molar enthalpy of combustion of magnesium, manipulate coefficients. An individual reaction can be reversed or be multiplied by a constant to obtain the value.
(2) MgCl2(aq) + H2O(l) -> MgO(s) + 2HCL(aq) -75.57 kJ*-1 (3) Mg(s) + 2HCL(aq) -> MgCl2(aq) + H2(g) -408.324 kJ (4) H2(g) + 1/2O2(g) -> H2O(l)-258.8 kJ
Mg(s) + 1/2O2 -> MgO(s)-618.55 kJ Equation (2) was manipulated by reversing the reaction, and in response the enthalpy change value of -75.57 kJ became positive 75.57 kJ. All enthalpy changes are then added with the sum being the molar enthalpy of combustion of magnesium. Therefore, the molar enthalpy of combustion of magnesium is -618.55 kJ/mol.
Mg(s) + 1/2 O2(g)
MgO(s)
The value obtained from calculations is bigger than the value accept value of the enthalpy change of combustion of magnesium. The two respective numbers being 618.55 kJ (calculated) and -611 kJ (accepted). Percent Error = (Experimental Value-Accepted Value)/(Accepted Value) * 100%
Percent Error = (-618.55-(-611))/(-611) * 100%
Percent Error = 1.235679214
Percent Error = 1.2
Therefore the percent error is 1.2%
There were many sources of errors during the procedure. When swirling the solution, it could have been done aggressively in contrast to actually swirling gently. The final temperature recorded could have been wrong as the temperature could have kept increasing, the group members just did not see it. Another source of error could have been forgetting to/not sanding the magnesium ribbon so when the mass is recorded, there is uncertainty of maybe +/- 0.01 g. When the HCL was transferred from the graduated cylinder to the simple calorimeter, some residue could have been left in the cylinder which would mean there would be less of it (volume wise) during the actual reaction which affects the data as the mass is used to find heat released.
The enthalpy value calculated from reactions (2) and (3) could therefore be greater than their true values. A main issue is simply the fact that simple calorimeters were being used in this experiment which can account for the 1.2% off from the accepted value. Another significant source of error could have been rounding temperatures or masses recorded. Also rounding calculated enthalpy changes can be considered a source of minor error when arriving to the molar enthalpy of combustion of magnesium. Some improvements that could be made are using digital thermometers for reading/recording temperatures and using actual calorimeters instead of just Styrofoam cups.
To obtain the molar enthalpy of combustion of magnesium, Hess’s law was used to arrive at the value. The enthalpy changes of reactions (2), (3), and (4) were added. However before that, equations were rearranged. The thermochemical equation for reaction (2) was reversed with the products becoming the reactants and reactants becoming the products. By doing this, the thermochemical equation for reaction (1) can be arrived at. Then simply add the enthalpy changes. Essentially, since this lab is carried out in numerous individual steps, the molar enthalpy change of combustion of magnesium is equal to the sum of the enthalpy changes (values obtained from individual steps). By using Hess’s law, the molar enthalpy of combustion value for magnesium obtained for the thermochemical equation that corresponds to reaction (1) is -618.55 kJ/mol.
Conclusion:To begin with, the purpose of this lab was to find a value for the molar enthalpy of combustion of magnesium using calculated experimental enthalpy changes from reactions (1) and (2). With the experimental values and using Hess’s law, the value for the molar enthalpy of combustion of magnesium calculated was -618.55 kJ/mol. To arrive at the experimental values, the heat transfer (between reactants and products) of reactions (2) and (3) were calculated by using the equation Q = mc∆T.
The value of the heat transfer also can represent the enthalpy change of the reaction using the equation ∆H = -Q. With the known mass being recorded on the data table, for reactions (2) and (3), the known masses can be converted into moles. The moles are then used in the equation ∆Hr = ∆H / n to find the experimental enthalpy change values for each reaction. Using these experimental values, Hess’s law was utilized to ultimately find the molar enthalpy of combustion of magnesium. The accepted value of molar enthalpy of combustion for magnesium was in fact -611 kJ/mol. The percent error calculated was 1.2%. This evidence supports the hypothesis stated beforehand as the calculated experimental molar enthalpy of combustion of magnesium is very close to the accepted value. Considering the circumstances of the lab and all the possible sources of error, the percent error is actually very small.
