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Chapter 20: Problem 29

(a) What does the term electromotive force mean? (b) What is the definition of the volt? (c) What does the term cell potential mean?

Short Answer

Expert verified
(a) Electromotive force (EMF) is the energy provided by a power source to move electric charge through a circuit. It is measured in volts (V). (b) The volt (V) is the SI unit of electric potential, potential difference, and EMF. It is defined as the electric potential difference across a conductor when a current of one ampere dissipates one watt of power: \[1 V = \dfrac{1 W}{1 A}\] (c) Cell potential, or cell voltage, is the difference in electric potential between the two electrodes of a galvanic cell. It drives the spontaneous flow of electrons through a connected circuit and depends on the reduction potentials of the half-reactions involved.

Step by step solution

01

(a) Electromotive Force Definition

Electromotive force (EMF) is a measure of the energy provided by a power source, such as a battery or generator, to move electric charge through a circuit. It is the force that pushes the electrons to go through the circuit, and it is not an actual physical force. The unit of electromotive force is the volt (V).
02

(b) Volt Definition

The volt is the unit of electric potential, electric potential difference, and electromotive force in the International System of Units (SI). It is named after Alessandro Volta, an Italian physicist who invented the first chemical battery. One volt (1V) is defined as the electric potential difference across a conductor when a current of one ampere (1A) dissipates one watt (1W) of power. Mathematically, it can be expressed as: \[1 V = \dfrac{1 W}{1 A}\]
03

(c) Cell Potential Definition

Cell potential, also known as cell voltage or cell EMF, refers to the difference in electric potential between the two electrodes of a galvanic (voltaic) cell. It is the driving force behind the spontaneous flow of electrons through a circuit connected to the cell. The cell potential can be positive or negative, depending on the direction of the electron flow. In an electrochemical cell, the cell potential is determined by the reduction potentials of the half-reactions involved in the cell.

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Most popular questions from this chapter

Cytochrome, a complicated molecule that we will represent as \(\mathrm{CyFe}^{2+},\) reacts with the air we breathe to supply energy required to synthesize adenosine triphosphate (ATP). The body uses ATP as an energy source to drive other reactions. (Section 19.7) At pH 7.0 the following reduction potentials pertain to this oxidation of \(\mathrm{CyFe}^{2+}:\) $$ \begin{aligned} \mathrm{O}_{2}(g)+4 \mathrm{H}^{+}(a q)+4 \mathrm{e}^{-} \longrightarrow & 2 \mathrm{H}_{2} \mathrm{O}(l) & & E_{\mathrm{red}}^{\circ}=+0.82 \mathrm{~V} \\\ \mathrm{CyFe}^{3+}(a q)+\mathrm{e}^{-} \longrightarrow \mathrm{CyFe}^{2+}(a q) & & E_{\mathrm{red}}^{\mathrm{o}}=+0.22 \mathrm{~V} \end{aligned} $$ (a) What is \(\Delta G\) for the oxidation of \(\mathrm{CyFe}^{2+}\) by air? (b) If the synthesis of \(1.00 \mathrm{~mol}\) of ATP from adenosine diphosphate (ADP) requires a \(\Delta G\) of \(37.7 \mathrm{~kJ},\) how many moles of ATP are synthesized per mole of \(\mathrm{O}_{2}\) ?

From each of the following pairs of substances, use data in Appendix \(\mathrm{E}\) to choose the one that is the stronger oxidizing agent: (a) \(\mathrm{Cl}_{2}(g)\) or \(\mathrm{Br}_{2}(l)\) (b) \(\mathrm{Zn}^{2+}(a q)\) or \(\mathrm{Cd}^{2+}(a q)\) (c) \(\mathrm{Cl}^{-}(a q)\) or \(\mathrm{ClO}_{3}^{-}(a q)\) (d) \(\mathrm{H}_{2} \mathrm{O}_{2}(a q)\) or \(\mathrm{O}_{3}(g)\)

A voltaic cell utilizes the following reaction: $$\mathrm{Al}(s)+3 \mathrm{Ag}^{+}(a q) \longrightarrow \mathrm{Al}^{3+}(a q)+3 \mathrm{Ag}(s)$$ What is the effect on the cell emf of each of the following changes? (a) Water is added to the anode half-cell, diluting the solution. (b) The size of the aluminum electrode is increased. (c) A solution of \(\mathrm{AgNO}_{3}\) is added to the cathode half-cell, increasing the quantity of \(\mathrm{Ag}^{+}\) but not changing its concentration. (d) \(\mathrm{HCl}\) is added to the \(\mathrm{AgNO}_{3}\) solution, precipitating some of the \(\mathrm{Ag}^{+}\) as \(\mathrm{AgCl}\).

The capacity of batteries such as the typical AA alkaline battery is expressed in units of milliamp-hours (mAh). An AA alkaline battery yields a nominal capacity of \(2850 \mathrm{mAh}\). (a) What quantity of interest to the consumer is being expressed by the units of \(\mathrm{mAh} ?\) (b) The starting voltage of a fresh alkaline battery is \(1.55 \mathrm{~V}\). The voltage decreases during discharge and is \(0.80 \mathrm{~V}\) when the battery has delivered its rated capacity. If we assume that the voltage declines linearly as current is withdrawn, estimate the total maximum electrical work the battery could perform during discharge.

A disproportionation reaction is an oxidation-reduction reaction in which the same substance is oxidized and reduced. Complete and balance the following disproportionation reactions: (a) \(\mathrm{Ni}^{+}(a q) \longrightarrow \mathrm{Ni}^{2+}(a q)+\mathrm{Ni}(s) \quad\) (acidic solution) (b) \(\mathrm{MnO}_{4}^{2-}(a q) \longrightarrow \mathrm{MnO}_{4}^{-}(a q)+\mathrm{MnO}_{2}(s)\) (acidic solution) (c) \(\mathrm{H}_{2} \mathrm{SO}_{3}(a q) \longrightarrow \mathrm{S}(s)+\mathrm{HSO}_{4}^{-}(a q) \quad\) (acidic solution) (d) \(\mathrm{Cl}_{2}(a q) \longrightarrow \mathrm{Cl}^{-}(a q)+\mathrm{ClO}^{-}(a q)\) (basic solution)
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