Calculating Biological Chemical Equations
- Page ID
- 50009
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Now we will find out how useful it is, in a Biological context, to understand the amounts of substances which participate in chemical reactions, the quantities of heat given off or absorbed when reactions occur, and the volumes of solutions which react exactly with one another. These seemingly unrelated subjects are discussed together because many of the calculations involving them are almost identical in form. The same is true of the density calculations and of the calculations involving molar mass and the Avogadro constant. In each case one quantity is defined as the ratio of two others.
| Related Quantities | Conversion Factor | Definition | Road Map |
|---|---|---|---|
| Volume ↔ mass | Density, ρ | \(\rho=\dfrac{m}{V}\) | \(V\text{ }\overset{\rho }{\longleftrightarrow}\text{ }m\) |
| Amount of substance ↔ mass | Molar Mass, M | \(M=\dfrac{m}{n}\) | \(n\text{ }\overset{M}{\longleftrightarrow}\text{ }m\) |
| Amount of substance ↔ number of particles | Avogadro constant, NA | \(N_{\text{A}}=\dfrac{N}{n}\) | \(n\text{ }\overset{N_{\text{A}}}{\longleftrightarrow}\text{ }N\) |
| Amount of X consumed or produced ↔ amount of Y consumed or produced | Stoichiometric ratio, S(Y/X) | \(S\text{(Y/X)}=\dfrac{n_{\text{Y}}}{n_{\text{X}}}\) | \(n_{\text{X}}\text{ }\overset{S\text{(Y/X)}}{\longleftrightarrow}\text{ }n_{\text{Y}}\) |
| Amount of X consumed or produced ↔ quantity of heat absorbed during reaction | ΔHm for thermochemical equation | \(\Delta H_{\text{m}}=\dfrac{q}{n_{\text{X}}}\) | \(n_{\text{X}}\text{ }\overset{\Delta H_{m}}{\longleftrightarrow}\text{ }q\) |
| Volume of solution ↔ amount of solute | Concentration of solute, cX | \(c_{\text{X}}=\dfrac{n_{\text{X}}}{V}\) | \(V\text{ }\overset{c_{\text{X}}}{\longleftrightarrow}\text{ }n_{\text{X}}\) |
The first quantity serves as a conversion factor relating the other two. A summary of the relationships and conversion factors we have encountered so far is given in Table \(\PageIndex{1}\).
An incredible variety of problems can he solved using the conversion factors in Table \(\PageIndex{1}\). Sometimes only one factor is needed, but quite often several are applied in sequence. In solving such problems, it is necessary first to think your way through, perhaps by writing down a road map showing the relationships among the quantities given in the problem. Then you can apply conversion factors, making sure that the units cancel, and calculate the result.
The examples in the Biology Track deal with the stoichiometry of carbohydrate metabolism in our bodies, with methods of analyzing carbohydrates (for example, the reaction in blood glucose meters used by diabetics), and with the energy that our bodies produce as a result of carbohydrate metabolism. Stoichiometry also applies to protein synthesis from the foods we eat, and bears directly on devising a good vegetarian diet to supply the essential amino acids in the correct amounts.
Once you have mastered these techniques, you will be able to do a great many useful computations which are related to problems in the biology or biochemical laboratory, in everyday life, and in the general environment. You will find that the same type of calculations, or more complicated problems based on them, will be encountered again and again throughout your study of the sciences.
\[\underbrace{\ce{C6H12O6}}_{\text{glucose}} + \underbrace{ \ce{6 O6}}_{\text{air}} \rightarrow \underbrace{ \ce{6 CO2}}_{\text{carbon dioxide}} + \underbrace{\ce{^H2O}}_{\text{water}} + \text{Energy}\]
There are a great many circumstances in which you may need to use a balanced equation. For example, exercise physiologists concentrate on the VOmax, or maximum volume of oxygen athletes can consume, because that determines how much carbohydrate can be "burned" according to the equation above, which in turn determines the rate of energy production in the body (and the body mass loss). In each instance someone else would probably have determined what reaction takes place, but you would need to use the balanced equation to get the desired information. Insert non-formatted text here
- From ChemPRIME: 3.0: Prelude to Chemical Equations
Contributors and Attributions
Ed Vitz (Kutztown University), John W. Moore (UW-Madison), Justin Shorb (Hope College), Xavier Prat-Resina (University of Minnesota Rochester), Tim Wendorff, and Adam Hahn.