At this point, Hess’s law can be applied to determine the molar heat of formation of MgO by using the data collected in the lab and the literature value for the heat of formation of H2O. The equation is as follows: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) + 1/2O2(g) + H2O(l) To combine the three equations above and create the stoichiometric equation that shows the formation of MgO, we can cancel out the common species on both sides of the equations: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) + 1/2O2(g) + H2O(l) 2HCl(aq) + MgO(s) → MgCl2(aq) + H2O(l) H2(g) + 1/2O2(g) → H2O(l) By adding these equations together, we get: Mg(s) + MgO(s) → MgCl2(aq) + H2(g) + 1/2O2(g) To determine the experimental heat of formation of MgO using Hess’s law, we need to calculate the enthalpy change for the reaction: ΔH_MgO = ΔH_1 + ΔH_2 + ΔH_3 where ΔH_1, ΔH_2, and ΔH_3 are the enthalpy changes for the three equations above.
At this point, Hess’s law can be applied to determine the molar heat of formation of MgO by using the data collected in the lab and the literature value for the heat of formation of H2O. The equation is as follows: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) + 1/2O2(g) + H2O(l) To combine the three equations above and create the stoichiometric equation that shows the formation of MgO, we can cancel out the common species on both sides of the equations: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) + 1/2O2(g) + H2O(l) 2HCl(aq) + MgO(s) → MgCl2(aq) + H2O(l) H2(g) + 1/2O2(g) → H2O(l) By adding these equations together, we get: Mg(s) + MgO(s) → MgCl2(aq) + H2(g) + 1/2O2(g) To determine the experimental heat of formation of MgO using Hess’s law, we need to calculate the enthalpy change for the reaction: ΔH_MgO = ΔH_1 + ΔH_2 + ΔH_3 where ΔH_1, ΔH_2, and ΔH_3 are the enthalpy changes for the three equations above
The Correct Answer and Explanation is:
To correctly determine the molar heat of formation (ΔH_f°) of magnesium oxide (MgO) using Hess’s Law, we must understand how to apply this principle to experimentally derived enthalpy data and known literature values. Below is the corrected approach and a comprehensive 1000-word explanation of the theory, methodology, chemical equations, and calculation process.
✅ Correct Approach Using Hess’s Law
Step 1: Understand the Goal
We want to determine the enthalpy of formation of MgO (ΔH_f° for MgO): Target equation: Mg(s) + 12O2(g)→MgO(s)\text{Target equation: } \text{Mg(s) + } \frac{1}{2}\text{O}_2(g) \rightarrow \text{MgO(s)}
This reaction forms 1 mole of solid MgO from its elements in their standard states. This is the definition of enthalpy of formation.
Step 2: Identify the Experimental Reactions
In the lab, we perform two reactions:
Reaction 1 (R₁): Magnesium metal in hydrochloric acid
Mg(s) + 2HCl(aq) → MgCl2(aq)+H2(g)(ΔH1)\text{Mg(s) + 2HCl(aq) } \rightarrow \text{ MgCl}_2(aq) + H_2(g) \quad (\Delta H_1)
Reaction 2 (R₂): Magnesium oxide in hydrochloric acid
MgO(s) + 2HCl(aq) → MgCl2(aq)+H2O(l)(ΔH2)\text{MgO(s) + 2HCl(aq) } \rightarrow \text{ MgCl}_2(aq) + H_2O(l) \quad (\Delta H_2)
Reaction 3 (R₃): Hydrogen gas combusting to form water (known from literature)
H2(g)+12O2(g)→H2O(l)(ΔH3=−285.8 kJ/mol)\text{H}_2(g) + \frac{1}{2}O_2(g) \rightarrow \text{H}_2O(l) \quad (\Delta H_3 = -285.8 \text{ kJ/mol})
Step 3: Combine the Reactions Using Hess’s Law
To derive the formation equation for MgO, manipulate and combine the above reactions so that their sum gives the target equation:
Step-by-step addition:
From R₁: Mg(s) + 2HCl(aq)→MgCl2(aq)+H2(g)\text{Mg(s) + 2HCl(aq)} \rightarrow \text{MgCl}_2(aq) + H_2(g)
From R₂ (reverse this reaction): MgCl2(aq)+H2O(l)→MgO(s) + 2HCl(aq)(−ΔH2)\text{MgCl}_2(aq) + H_2O(l) \rightarrow \text{MgO(s) + 2HCl(aq)} \quad (-\Delta H_2)
From R₃: H2(g)+12O2(g)→H2O(l)\text{H}_2(g) + \frac{1}{2}O_2(g) \rightarrow \text{H}_2O(l)
Add these equations:
- R₁: Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)
- Reverse of R₂: MgCl₂(aq) + H₂O(l) → MgO(s) + 2HCl(aq)
- R₃: H₂(g) + ½O₂(g) → H₂O(l)
Add them together:
Left side:
Mg(s) + 2HCl(aq) + MgCl₂(aq) + H₂O(l) + H₂(g) + ½O₂(g)
Right side:
MgCl₂(aq) + H₂(g) + MgO(s) + 2HCl(aq) + H₂O(l)
Cancel species common on both sides:
- 2HCl(aq), MgCl₂(aq), H₂(g), H₂O(l)
Final net reaction: Mg(s) + 12O2(g)→MgO(s)\text{Mg(s) + } \frac{1}{2}\text{O}_2(g) \rightarrow \text{MgO(s)}
This is our target equation. Thus, by Hess’s Law: ΔHf∘(MgO)=ΔH1−ΔH2+ΔH3\Delta H_{f}^{\circ}(\text{MgO}) = \Delta H_1 – \Delta H_2 + \Delta H_3
🧪 Enthalpy Calculations
You will have measured ΔH₁ and ΔH₂ experimentally in the lab (likely using calorimetry), and ΔH₃ is known from literature:
- ΔH₃ = –285.8 kJ/mol (combustion of 1 mole of hydrogen gas)
Suppose (example):
- ΔH₁ (Mg + HCl) = –445.6 kJ/mol (measured)
- ΔH₂ (MgO + HCl) = –74.4 kJ/mol (measured)
Then: ΔHf∘(MgO)=(−445.6 kJ/mol)−(−74.4 kJ/mol)+(−285.8 kJ/mol)=−445.6+74.4−285.8=−656.9 kJ/mol\Delta H_f^{\circ}(\text{MgO}) = (-445.6 \text{ kJ/mol}) – (-74.4 \text{ kJ/mol}) + (-285.8 \text{ kJ/mol}) \\ = -445.6 + 74.4 – 285.8 = \boxed{-656.9 \text{ kJ/mol}}
This is close to the accepted value of –601.6 kJ/mol, and any deviation can be discussed as experimental error.
📘 Theoretical Explanation
What is Hess’s Law?
Hess’s Law states that the total enthalpy change of a reaction is independent of the pathway taken. If a chemical equation can be expressed as the sum of two or more other reactions, then the enthalpy change of that reaction is the sum of the enthalpy changes of the constituent reactions.
Mathematically: ΔHnet=∑ΔHsteps\Delta H_{\text{net}} = \sum \Delta H_{\text{steps}}
This is possible because enthalpy is a state function—its change depends only on the initial and final states of the system, not on how it gets from one to the other.
Why Can’t We Measure ΔH_f of MgO Directly?
The reaction: Mg(s) + 12O2(g)→MgO(s)\text{Mg(s) + } \frac{1}{2}O_2(g) \rightarrow \text{MgO(s)}
is highly exothermic and difficult to measure directly because:
- It happens too quickly.
- The heat released may be lost to the environment.
- The reaction may be incomplete or involve side reactions (e.g., formation of Mg(OH)₂).
Instead, we use indirect methods, like calorimetry, and apply Hess’s Law.
Purpose of Each Reaction
- R₁ (Mg + HCl): Easy to carry out in a lab calorimeter. We measure temperature change to find ΔH₁.
- R₂ (MgO + HCl): Allows us to indirectly calculate the energy required to break down MgO, again via temperature change.
- R₃ (H₂ combustion): Already known accurately from literature.
These reactions are strategically chosen so that when summed, the desired target reaction emerges.
How to Perform the Calorimetry
- Weigh a known mass of magnesium or magnesium oxide.
- React with known concentration and volume of HCl.
- Measure the initial and final temperature of the solution.
- Use the formula:
q=mcΔTq = mc\Delta T
Where:
- qq = heat evolved
- mm = mass of solution (assume density of 1.0 g/mL)
- cc = specific heat capacity (typically 4.18 J/g·°C)
- ΔT\Delta T = change in temperature
Convert q to ΔH in kJ/mol by dividing by the number of moles of magnesium or MgO used.
Sources of Experimental Error
- Heat loss to the environment → leads to underestimating ΔH.
- Incomplete reaction → not all Mg or MgO reacts.
- Calorimeter not perfectly insulated.
- Measurement errors in temperature or mass.
These factors explain why your calculated ΔH_f for MgO may differ from the literature value.
Significance of ΔH_f(MgO)
- Thermodynamics: Knowing how much heat is released helps in designing combustion processes.
- Material Science: MgO is used in refractory materials; its heat stability is key.
- Environmental Chemistry: Understanding formation heats is important in modeling atmospheric and geochemical cycles.
Conclusion
By cleverly applying Hess’s Law and combining laboratory measurements with literature values, we can accurately determine the enthalpy of formation of magnesium oxide, even when it is not directly measurable. This process demonstrates the power of indirect reasoning in chemistry and reinforces the importance of energy conservation in chemical reactions.
