4.5: Open Systems and Actual Free Energy Change
- Page ID
- 88919
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Cells are open systems that are constantly exchanging mass and energy with their environment; they never reach equilibrium. In addition, diverse organisms live under very different atmospheric conditions and maintain different body temperatures (e.g., your cat has a higher body temperature than you do!). Clearly, the conditions under which cells conduct their biochemical reactions are decidedly nonstandard. However, while open systems do not reach equilibrium, they do achieve a steady state in which the rate of input of energy and matter is equal to the rate of output of energy and matter. Think of a biochemical pathway like glycolysis. If a cell’s energy needs are constant, the pathway will reach a steady state. Of course, a cell’s need for energy (as ATP) can change as energy needs change. If it does, then the steady state of ATP production will change to meet the needs of the cell.
Later we will discuss just how energy flows through living things, from sunlight into the chemical energy of nutrient molecules, into energy-rich fuels like ATP, and finally into the performance of all manner of cellular work. For now, let’s characterize open systems by their properties:
- Open systems exchange energy and mass with their surroundings.
- Open systems never reach equilibrium.
- They achieve steady state where the energy input rate = output rate.
- The steady state can change.
- In open systems, endergonic reactions can be energetically favorable (spontaneous) reactions), and exergonic reactions can become energetically unfavorable.
Fortunately, there is an equation to determine free energy changes in open systems. For our chemical reaction \(2A + B <====> 2C + D\), this equation would be the following:
\(\Delta G' = \Delta G^o + \rm RT \ln \dfrac{[C]_{ss}^2 [D]_{ss}}{[A]_{ss}^2 [B]_{ss}}\)
ΔG′ is the actual free energy change for a reaction in an open system; ΔGo is the standard free energy change for the same reaction under standard conditions in a closed system; R is again the gas constant (1.806 cal/mol-deg); and T is the absolute temperature in which the reaction actually occurs. The ss subscripts designate reactant and product concentrations measured under steady-state conditions. You can see here that this equation states a relationship between ΔGo and ΔG′. So to determine the actual free energy of a biochemical reaction in a cell or any living tissue, all you need to know are the ΔGo for the reaction, the steady-state concentrations of reaction components in the cells/tissues, and the absolute T under which the reactions are occurring.
144 The Energetics of Open Systems
Elsewhere, we will use the reactions of the glycolytic pathway to exemplify the properties, as well as the energetics of open and closed systems. At that time, pay careful attention to the application of the terminology of energetics in describing energy flow in closed vs open systems.