10.2: Background
- Page ID
- 379616
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Read section 19.3 of your text before proceeding with this lab. We will look at the spontaneous reaction of zinc metal with copper (II) solutions, for which the net ionic equation is:
\[Zn(s) + Cu^{+2} \rightarrow Cu(s) + Zn^{+2} \]
The Daniel Cell takes advantage of this spontaneous reaction and figure \(\PageIndex{1}\) shows the basic components of an electrochemical cell based on this reaction.
The basic components of a galvanic electrochemical cell.
- Anode, where oxidation occurs (the more active metal, the one with the lower standard state reduction potential)
- Cathode, where reduction occurs (the less active metal, the one with the higher standard reduction potential)
- External circuit (here is is a voltmeter, which has a high resistance and measures the electric potential. This could be a load like a light bulb or motor, in which case work could be done as the current flows through the circuit)
- Salt bridge (these are counter ions that prevent the build up of charge that would stop the current from flowing. They also need to stop the migration of the copper (II) to the zinc strip, then electrons would transfer directly to the copper ion without ever flowing through the external circuit).
In shorthand notation (section 19.3.3) and at standard state conditions the Daniell Cell would be written as:
\[Zn(s)|Zn^{+2}(1M)||Cu^{+2}(1M)|Cu(s)\]
The Nernst Equation (section 19.7) for an electrochemical cell relates the electric potential at any concentration to that at standard state concentrations.
\[E=E° -\frac{RT}{nF} \ln Q\]
Where,
- E= Cell potential at any concentration
- Eo= Cell potential at standard state concentrations (1M)
- R=Ideal gas constant (8.314J/mol-K)
- T=Absolute Temperature (K)
- n=moles electrons transferred in balanced redox reaction
- F=Faraday's constant (96,500J/V-mole e-)
- Q=Reaction Quotient of redox reaction \( \left (\frac{[Zn^{+2}]}{[Cu^{+2}]} \right )\) for the above cell
So for this reaction the Nernst Eq. becomes:
\[E=E° -\frac{RT}{nF} \ln \left (\frac{[Zn^{+2}]}{[Cu^{+2}]} \right )\]
If we know Eocell and the concentration of one species, we can determine the concentration of the other by measuring Ecell. Here we solve for [Zn+2].
\[[Zn^{+2}]=[Cu^{+2}]e^{\frac{nF}{RT}\left ( E_{cell}^{o}-E_{cell} \right )}\]