2.5 Hess's Law - the Equation
- Page ID
- 32251
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)There is another way to calculate enthalpy changes that occur during chemical reactions that is based on the principal of Hess's Law.
ΔH for a reaction may be calculated using the published ΔHf values and the equation:
| You may not be familiar with the ∑ symbol. It stands for "summation" or "the sum of". To find ΔHo for the reaction, add together all of the heats of formation, ΔHof, for all of the products and subtract from that the sum of the heats of formation of all of the reactants. |
Using this formula is easy. With your Table of Thermochemical Data table handy, locate ΔHf values for all reactants and products in the reaction. The physical state is important, so check that carefully. Also pay close attention to the balancing coefficients in the equation, as you must multiply the ΔHfvalues by these coefficients. Finally, be very careful with + and - values.
Example:
C6H6 (l) + 15/2 O2 (g) → 6 CO2 (g) + 3 H2O (l)
Solution:
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Using the formula ΔH = ∑ΔHproducts - ∑ΔHreactants
C6H6 (l) | + | 15/2 O2 (g) | → | 6 CO2 (g) | + | 3 H2O (l) |
49.0 | + | 15/2 × (0) | | 6 × (-393.5) | + | 3 × (-285.8) |
| | |||||
49.0 | | -3218.4 | ||||
Reactants | | Products |
ΔH = ∑ΔHproducts – ∑ΔHreactants | ||||||
ΔH =-3218.4 – (+49.0) | ||||||
| | ΔH = -3267.4 kJ answer |
Common Sources of Error
While the formula is easy to use, it is also very easy to make some simple mistakes. Students often make mistakes in the following areas, so be extra careful in these areas:
- Forgetting to multiply ΔH values by the appropriate coefficient.
- Using the wrong value of ΔH for water:
ΔHf° for H2O(g) = -241.8 kJ/mol
- Solving for ΔH as "Reactants - Products" instead of "Products – Reactants".
- Accidentally changing the sign for ΔH.