Worksheet: The Nernst Equation

In this worksheet, we will practice using the Nernst equation to calculate reduction potentials under nonstandard concentrations.

Q1:

A battery is dead when it has no cell potential. Consider a battery with the overall reaction: Cu()+2Ag()2Ag()+Cu()saqsaq+2+. The standard electrode potentials for the half-cells in this battery are given in the table.

Half-equation C u ( ) + 2 e C u ( ) 2 + a q s A g ( ) + e A g ( ) + a q s
Standard electrode potential, 𝐸 (V) + 0 . 3 4 0 + 0 . 7 9 9 6

To 2 significant figures, what is the value of 𝑄 when this battery is dead at 298.15 K?

  • A 3 . 4 × 1 0
  • B 6 . 8 × 1 0
  • C 5 . 9 × 1 0
  • D 4 . 0 × 1 0
  • E 3 . 4 × 1 0

If a particular dead battery is found to have [Cu]2+ = 0.11 M, what is the concentration of silver ions?

  • A 3 . 8 × 1 0 M
  • B 5 . 6 × 1 0 M
  • C 3 . 2 × 1 0 M
  • D 0.22 M
  • E 0.11 M

Q2:

Calculate to 2 significant figures the equilibrium constant at 25C for the following reaction.

H O ( ) H ( ) + O H ( ) 2 + l a q a q

Note that each standard electrode potential is expressed per mole of the half-reaction shown in the table.

Half-Equation 2 H ( ) + 2 e H ( ) + 2 a q g 2 H O ( ) + 2 e H ( ) + 2 O H ( ) 2 2 l g a q
Standard Electrode Potential, 𝐸 (V) 0.000 0 . 8 2 7 7
  • A 1 . 0 × 1 0
  • B 1 . 0 × 1 0
  • C 1 . 0 × 1 0
  • D 1 . 0 × 1 0
  • E 1 . 0 × 1 0

Q3:

Using the standard electrode potentials shown in the table, calculate to 2 significant figures the equilibrium constant at 373 K for the following reaction.

H g ( ) + 4 B r ( ) [ H g B r ] ( ) 2 + 4 2 a q a q a q

Half-Equation H g ( ) + 2 e H g ( ) 2 + a q l [ H g B r ] ( ) + 2 e H g ( ) + 4 B r ( ) 4 2 a q l a q
Standard Electrode Potential, 𝐸 (V) + 0 . 8 5 1 + 0 . 2 1
  • A 7 . 4 × 1 0
  • B 6 . 8 × 1 0
  • C 2 . 1 × 1 0
  • D 1 . 6 × 1 0
  • E 4 . 5 × 1 0

Q4:

Using the standard electrode potentials shown in the table, calculate to 2 significant figures the equilibrium constant at 373 K for the following reaction.

C d S ( ) C d ( ) + S ( ) s a q a q 2 + 2

Half-Equation C d ( ) + 2 e C d ( ) 2 + a q s C d S ( ) + 2 e C d ( ) + S ( ) s s a q 2
Standard Electrode Potential, 𝐸 (V) 0 . 4 0 3 0 1 . 1 7
  • A 5 . 8 × 1 0
  • B 1 . 4 × 1 0
  • C 2 . 8 × 1 0
  • D 3 . 1 × 1 0
  • E 5 . 2 × 1 0

Q5:

Using the standard electrode potentials shown in the table, calculate to 2 significant figures the equilibrium constant at 298.15 K for the following reaction.

A g C l ( ) A g ( ) + C l ( ) s a q a q +

Half-Equation A g ( ) + e A g ( ) + a q s A g C l ( ) + e A g ( ) + C l ( ) s s a q
Standard Electrode Potential, 𝐸 (V) + 0 . 7 9 9 6 + 0 . 2 2 2 3 3
  • A 3 . 8 × 1 0
  • B 3 . 6 × 1 0
  • C 8 . 8 × 1 0
  • D 1 . 7 × 1 0
  • E 1 . 6 × 1 0

Q6:

In the half-cells of an electrochemical cell, 1.00 M aqueous bromide ions are oxidized to 0.110 M bromine and 0.0230 M aluminum ions are reduced to aluminum metal. Using the standard electrode potentials shown in the table, calculate to 3 decimal places the cell potential for the cell at 298.15 K. Note that standard electrode potentials are measured using 1.00 M solutions of the reacting ions.

Half-Equation B r ( ) + 2 e 2 B r ( ) 2 a q a q A l ( ) + 3 e A l ( ) 3 + a q s
Standard Electrode Potential, 𝐸 (V) + 1 . 0 8 7 3 1 . 6 6 2

Q7:

The half-cells of a galvanic cell consist of an aluminum electrode in a 0.0150 M aluminum nitrate solution and a nickel electrode in a 0.250 M nickel(II) nitrate solution. Using the standard electrode potentials shown in the table, calculate to 2 decimal places the cell potential for the galvanic cell at 298.15 K. Note that standard electrode potentials are measured using 1.00 M solutions of the reacting ions.

Half-Equation A l ( ) + 3 e A l ( ) 3 + a q s N i ( ) + 2 e N i ( ) 2 + a q s
Standard Electrode Potential, 𝐸 (V) 1 . 6 6 2 0 . 2 5 7

Q8:

Using the standard electrode potentials shown in the table, calculate to 2 decimal places the cell potential at 298.15 K for the cell with the following overall reaction.

H g ( ) + S ( , 0 . 0 0 1 0 M ) + 2 A g ( , 0 . 0 0 2 5 M ) 2 A g ( ) + H g S ( ) l a q a q s s 2 +

Half-Equation H g S ( ) + 2 e H g ( ) + S ( ) s l a q 2 A g ( ) + e A g ( ) + a q s
Standard Electrode Potential, 𝐸 (V) 0 . 7 0 + 0 . 7 9 9 6

Q9:

Using the standard electrode potential data in the table, calculate the standard cell potential for the following reaction at 298 K.

C o ( ) + F e ( , 1 . 9 4 M ) C o ( , 0 . 1 5 0 M ) + F e ( ) s a q a q s 2 + 2 +

Half-Equation C o ( ) + 2 e C o ( ) 2 + a q s F e ( ) + 2 e F e ( ) 2 + a q s
Standard Electrode Potential, 𝐸 (V) 0 . 2 8 0 . 4 4 7

Q10:

Calculate to 3 significant figures the cell potential for the following reaction at 298 K?

A l ( ) | A l ( , 0 . 1 5 0 M ) C u ( , 0 . 0 2 5 0 M ) | C u ( ) s a q a q s 3 + 2 +

Half-Equation A l ( ) + 3 e A l ( ) 3 + a q s C u ( ) + 2 e C u ( ) 2 + a q s
Standard Electrode Potential, 𝐸 (V) 1 . 6 6 2 + 0 . 3 4 0

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