Question

It is sometimes possible to separate two metal ions through electrolysis. One ion is reduced to the free metal at the cathode, and the other remains in solution. In which of these cases would you expect complete or nearly complete separation: (a) ${\mathrm{Cu}}^{2+}$ and ${\mathrm{K}}^{+};$ (b) ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Ag}}^{+};$ (c) ${\mathrm{Pb}}^{2+}$ and ${\mathrm{Sn}}^{2+}?$ Explain.

Short answer

(a) Nearly complete separation. (b) Partial separation. (c) No separation.

Step-by-step solution

Identifying Reduction Potentials

Start by identifying the reduction potentials of the four types of ions given: ${\mathrm{Cu}}^{2+}$, ${\mathrm{K}}^{+}$, ${\mathrm{Ag}}^{+}$, ${\mathrm{Pb}}^{2+}$, and ${\mathrm{Sn}}^{2+}$. Using standard reduction potential table, the reduction potentials are as follows: ${\mathrm{Cu}}^{2+}$ : +0.34V, ${\mathrm{K}}^{+}$ : -2.93V, ${\mathrm{Ag}}^{+}$ : +0.80V, ${\mathrm{Pb}}^{2+}$ : -0.13V, ${\mathrm{Sn}}^{2+}$ : -0.14V.

Analyzing the Reduction Potentials

Analyze the reduction potentials. The metal ion with the higher reduction potential gets reduced first during electrolysis. Thus, in solution, (a) between ${\mathrm{Cu}}^{2+}$ and ${\mathrm{K}}^{+}$, copper would be reduced first as it has higher reduction potential. (b) Between ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Ag}}^{+}$, silver would get reduced first as it has higher reduction potential and (c) between ${\mathrm{Pb}}^{2+}$ and ${\mathrm{Sn}}^{2+}$, both have nearly same reduction potential and hence they cannot be easily separated.

Responding to the Specific Queries

(a) In the case of ${\mathrm{Cu}}^{2+}$ and ${\mathrm{K}}^{+}$, there can be nearly complete separation as the reduction potential difference is big. (b) In ${\mathrm{Cu}}^{2+}$ and ${\mathrm{Ag}}^{+}$, partial separation is possible with difficulty as reduction potential difference is not too high. (c) In the case of ${\mathrm{Pb}}^{2+}$ and ${\mathrm{Sn}}^{2+}$, there would be almost no separation, as the reduction potential difference is too small.

Key concepts

Reduction Potentials

Let's delve into the fascinating world of reduction potentials, a core concept in electrochemistry! Imagine reduction potentials as a measure of a substance's willingness to gain electrons. In our case, for metal ions during electrolysis, reduction potential indicates how easily a metal ion can be transformed into its metallic form.

When we apply an electric current in electrolysis, metal ions compete to gain electrons. The one with a higher reduction potential calls 'dibs' and gets reduced first. It's like a race where the reduction potential is the speed of the runners. The higher the potential, the faster the ion is reduced to its elemental metal form. Therefore, when separating metal ions via electrolysis, one must be quick to grab electrons (a high reduction potential), while the other should be more leisurely (a low reduction potential) to achieve complete separation.

Standard Reduction Potential Table

Navigating the Table

Imagine a treasure map, but instead of leading to gold, it guides chemists to predict how reactions will go during electrolysis. The standard reduction potential table is exactly that: a chart where each metal ion's propensity to be reduced is listed in volts.

The table includes a list of metal ions with their 'standard reduction potentials.' To put it simply, it's like each metal ion has a score next to its name. When you look up the scores for Cu^2+ and K+, you'll see that Cu^2+ has a higher score, meaning it's more eager to cross the finish line and turn into solid copper during electrolysis.

Electrochemical Series

Order in the Electrochemical Court!

The electrochemical series is essentially the leaderboard in the race of reduction. It ranks substances based on their standard reduction potentials. Think of it as a high school popularity chart but for ions. The ones higher up on the series get the privilege of being reduced first when the time for electrolysis comes.

This series can predict the outcome of reactions, like who wins in a head-to-head electron snatch: Cu^2+ or Ag+. Spoiler: It's Ag+ because it's higher up on the series, also known as the kingpin of the electrochemical hierarchy in this scenario.

Metal Ion Reduction

The Metamorphosis from Ion to Metal

Metal ion reduction is the process where metal ions undergo a striking transformation. Through the gift of electrons, they ditch their ion status and become pure metal. During electrolysis, this is the rags-to-riches story where ions turn into solid metals at the cathode–the negatively charged conductor in the setup.

So, when you put Cu^2+ and K+ ions in the electrolyte and flip the switch, Cu^2+ quickly grabs two electrons to become copper metal because it can't wait to be part of the solid world. On the other hand, K+ would have preferred to linger a bit longer in the solution phase because its reduction potential is way lower. It's somewhat of a wallflower in the electrolysis dance.