\input ../cer.tex

\name{Holden Rohrer}
\course{FVS Chemistry AB 19.3}
\teacher{Kerr} 

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    \omit \tablewidth 5in \vrule width 1pt \htext{Measurement} & \omit \vrule width 0.05pt \htext{Reaction 1 ($Mg + HCl$)} & \omit \vrule width 0.05pt \htext{Reaction 2 ($MgO + HCl$)} \vrule width 1pt \cr \endliner
    Mass of HCl (g) & 100.50 & 100.57 \cr \endliner
    Mass of solid (g) & 0.20 & 1.57 \cr \endliner
    Total mass of reactants, m (g) & 100.70 & 102.14 \cr \thickline
    Initial temperature ({\tinym $^{\circ}C$}) & 22.5 & 22.7 \cr \endliner
    Temperature furthest from initial temperature ({\tinym $^{\circ}C$}) & 31.3 & 30.2 \cr \endliner
    {\tinym $\Delta T$} ({\tinym $^{\circ}C$}) & 8.8 & 7.5 \cr \thickline
    Heat released, {\tinym $q=cm\Delta T$} (J) & 3700 & 3200 \cr \endliner
    Moles of solid reactant (mol) & 0.00823 & 0.0397 \cr \endliner
    Enthalpy of reaction, {\tinym $\Delta H = {{-q}\over{mol}}*{{kJ}\over{1000J}}$} (kJ/mol) & -450 & -81 \cr \thickline
  }
  Combination of $\Delta H_1$, $\Delta H_2$, and $\Delta H_3$ needed (using Hess's Law): $\Delta H_{rxn} = -655{{kJ}\over{mol}}$

  \smallskip
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    \omit \vrule width 1pt \htext{Reaction Equation} & \omit \vrule width 0.05pt \htext{$\Delta H$ (kJ/mol)} \vrule width 1pt \cr \endliner
    Reaction 1: $Mg(s) + 2HCl(aq) \longrightarrow MgCl_2(aq)+H_2(g)$ & -450 \cr \endliner
    Reaction 2: $MgO(s) + 2HCl(aq) \longrightarrow MgCl_2(aq)+H_2O(l)$ & -81 \cr \endliner
    Reaction 3: $H_2(g) + {{1}\over{2}}O_2(g) \longrightarrow H_2O(l)$ & -286 (published value) \cr \thickline
    Magnesium Combustion: $Mg(s)+{{1}\over{2}}O_2(g) \longrightarrow MgO(s)$ & -655 \cr \thickline
  }
  The published value for this reaction is -603 kJ/mol. Percent error of experimental value: 8.62\%
  \smallskip
}

\question{How can you use Hess's Law to determine a reaction's enthalpy when you can't do so using a calorimeter?}
\claim{Hess's Law accurately describes the enthalpy of an unknown reaction where other reactions' enthalpies (such that those reactions can be summed to the unknown reaction) are known.}

\evidence{
\def\enthunit{{{kJ}\over{mol}}}
This experiment measured two chemical reactions, but three were used based off of commonly known values. The first of these is $Mg(s)+2HCl(aq) \longrightarrow MgCl_2(aq) + H_2(g)$. The enthalpy of this reaction was measured and recorded accurately because HCl was in excess, so the only limiting factor was the metal ($Mg$), of which the weight and molar mass was known. $\Delta T$ was also determined, and because a coffee cup calorimeter was used, that was able to be converted into released energy ($q$). The same process was completed for the dissolution of $MgO$ in $HCl$ by the reaction $MgO + 2HCl(aq) \longrightarrow MgCl_2(aq) + H_2O(l)$. Their respective enthalpies of reaction were $-450\enthunit$ and $-81\enthunit$. The third previously known reaction was the combination of gaseous diatomic hydrogen and oxygen into water. This reaction is impossible to conduct with our tools because it requires a bomb calorimeter to contain the gaseous components. Its enthalpy of reaction was $-286\enthunit$.

From these, the reversal of the second reaction provided $H_2O(l)+MgCl_2(aq) \longrightarrow MgO(s)+2HCl(aq)$ at an enthalpy of $81\enthunit$. This allowed the ``cancelling'' of hydrochloric acid, magnesium chloride, hydrogen, and water when summing the chemical equations. After summation, we are left with $Mg(s) + {{1}\over{2}}O_2(g) \longrightarrow MgO(s)$ at a total enthalpy of $-450-(-81)-286=-450+81-286=-655\enthunit$ by Hess's Law. Because this is so similar to the previously published value of $-603 \enthunit$ (an experimental error of $8.62\%$, well within bounds of statistical significance), it can be considered to be an accurate measure of the enthalpy of the reaction (specifically magnesium combustion; however, this generalises).
}

\justification{
Hess's Law's accuracy makes sense because it's logically consistent with enthalpy's property of being a state function. Starting with the assumed 0 enthalpy of elements in their standard form, most bonds release energy, and by conservation of energy, they must have proportionately lower potential energy. This is the energy of formation and is constant between all samples of a substance. In order for energy to be conserved during non-formation or -decomposition chemical reactions, the potential energy difference between products and reactants (enthalpy) must be equal to energy released. This is the foundation of Hess's Law: the known enthalpy amounts allow given compounds' enthalpies of formation to be treated like variables (because enthalpy of formation is an intrinsic property determined only by the identity of the substance and is identical between all samples of the substance) and thus the chemical equations summed like linear equations. This demonstrates the generality of the specific magnesium combustion example shown here.
}

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