Out of $Cu_2Cl_2$ and $CuCl_2$, which is more stable and why?

Out of Cu₂Cl₂ and CuCl₂, which is more stable and why?

NCERT Exemplar · Q27

Cu_2Cl_2

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Concept understanding — Standard Reduction Potential

Cell Representation and the Nernst Equation: From Intuition to Precision

Imagine you have a Daniell cell — a zinc rod in zinc sulphate solution connected by a salt bridge to a copper rod in copper sulphate solution. You know it produces a voltage. But what happens if you dilute the copper sulphate solution? Or if you change the temperature? The voltage changes. The Nernst equation is the tool that tells you exactly how much it changes.

The Intuition First

A battery works because the two half-cells "want" to react — zinc wants to lose electrons, copper ions want to gain them. This "want" is measured as a tendency, or potential. But the strength of that tendency depends on how crowded the ions are.

Think of it like this: If you have a room full of people who all want to leave (like zinc ions wanting to form), the push to get out is stronger when the room is packed. If the room is nearly empty, the push is weaker. Similarly, for copper ions wanting to enter the metal (gain electrons), the pull is stronger when there are many copper ions around, and weaker when there are few.

The Nernst equation quantifies this: the actual cell potential depends on the concentrations (or activities) of the ions involved.

The Precise Statement

For a general cell reaction:

aA + bB \rightarrow cC + dD

The cell potential $E$ under non-standard conditions is given by:

E = E^\circ - \frac{RT}{nF} \ln Q

Where:

$E$ = cell potential under the given conditions (in volts)
$E^\circ$ = standard cell potential (when all reactants/products are at 1 M, 1 atm, 25°C)
$R$ = universal gas constant (8.314 J/mol·K)
$T$ = temperature in Kelvin
$n$ = number of moles of electrons transferred in the balanced half-reactions
$F$ = Faraday constant (96,485 C/mol)
$Q$ = reaction quotient = $\frac{[C]^c [D]^d}{[A]^a [B]^b}$ (using concentrations for dilute solutions)

At 25°C (298 K), the equation simplifies to a very practical form:

E = E^\circ - \frac{0.0591}{n} \log_{10} Q

The 0.0591 comes from $\frac{2.303RT}{F}$ at 298 K. Notice it uses $\log_{10}$ (common log), not natural log.

Cell Representation: How We Write It

In electrochemistry, we represent a cell with a shorthand notation. For the Daniell cell:

\text{Zn(s)} \mid \text{Zn}^{2+}(\text{aq}) \parallel \text{Cu}^{2+}(\text{aq}) \mid \text{Cu(s)}

The single vertical line $\mid$ represents a phase boundary (solid electrode | solution). The double line $\parallel$ represents the salt bridge.

The anode (oxidation) is written on the left, the cathode (reduction) on the right. Electrons flow from left to right in the external circuit.

Applying the Nernst Equation to a Cell Representation

For the Daniell cell, the half-reactions are:

Anode (oxidation): $\text{Zn(s)} \rightarrow \text{Zn}^{2+}(\text{aq}) + 2e^-$
Cathode (reduction): $\text{Cu}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Cu(s)}$

Overall: $\text{Zn(s)} + \text{Cu}^{2+}(\text{aq}) \rightarrow \text{Zn}^{2+}(\text{aq}) + \text{Cu(s)}$

Here $n = 2$ (two electrons transferred). The reaction quotient is:

Q = \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}

So the Nernst equation becomes:

E = E^\circ - \frac{0.0591}{2} \log_{10} \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]}

Note

Solids (Zn, Cu) do not appear in $Q$ because their concentrations are constant (activity = 1).

A Worked Example

Suppose you have a Daniell cell where $[\text{Zn}^{2+}] = 0.1$ M and $[\text{Cu}^{2+}] = 1.0$ M at 25°C. $E^\circ$ for the cell is 1.10 V. …

Why this formula?

Standard Reduction Potential: Why the Formula Holds

Let's build this from first principles — understanding why before memorising what.

1. The Core Idea: A Half-Cell's "Tendency to Gain Electrons"

A standard reduction potential ( $E^\circ$ ) measures how strongly a species wants to gain electrons (be reduced) under standard conditions (1 M concentration, 1 atm pressure, 25°C).

But why can't we measure this directly? Because every reduction must be paired with an oxidation — you can't have electrons flowing without a complete circuit.

2. The Formula: $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

Why subtraction, not addition?

Consider a Daniell cell:

Zn | Zn²⁺ (1 M) || Cu²⁺ (1 M) | Cu

Experimentally, we measure the cell potential as +1.10 V.

Now, we define the standard hydrogen electrode (SHE) as exactly 0.00 V:

2\text{H}^+ + 2e^- \rightarrow \text{H}_2 \quad E^\circ = 0.00 \text{ V}

The reasoning step-by-step:

We can only measure differences — like measuring height difference between two points.
If we connect the SHE to the copper half-cell, we measure +0.34 V (Cu²⁺ is reduced).
If we connect the SHE to the zinc half-cell, we measure −0.76 V (Zn²⁺ is reduced less readily than H⁺).

Now, the cell potential is the difference in their tendencies:

E^\circ_{\text{cell}} = E^\circ_{\text{Cu}} - E^\circ_{\text{Zn}} = (+0.34) - (-0.76) = +1.10 \text{ V}

Key insight: The formula uses subtraction because we're comparing two half-cells against the same reference (SHE). The cathode is where reduction happens (higher $E^\circ$ ), the anode is where oxidation happens (lower $E^\circ$ ).

3. The Nernst Equation: Why $E = E^\circ - \frac{RT}{nF} \ln Q$

This is the thermodynamic derivation — the real "why."

From Gibbs free energy:

\Delta G = \Delta G^\circ + RT \ln Q

For an electrochemical cell:

\Delta G = -nFE \quad \text{and} \quad \Delta G^\circ = -nFE^\circ

Substituting:

-nFE = -nFE^\circ + RT \ln Q

Rearranging:

E = E^\circ - \frac{RT}{nF} \ln Q

Why this makes physical sense:

$RT \ln Q$ represents the entropy penalty of non-standard concentrations
$nF$ converts charge to energy (Faraday's constant × number of electrons)
The minus sign means: as products accumulate ( $Q$ increases), the cell potential drops — the reaction is approaching equilibrium

At equilibrium ( $Q = K$ ), $E = 0$ — the battery is "dead."

--- …

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The stability of copper chlorides depends on the relative ease of reduction of Cu²⁺ vs Cu⁺. $CuCl_2$ is more stable in aqueous solution because Cu⁺ disproportionates into Cu²⁺ and Cu, but $Cu_2Cl_2$ (CuCl) is stabilised in the solid state due to its insolubility and lattice energy.

Concept and Intuition

The question asks you to compare the stability of two copper chlorides: $Cu_2Cl_2$ (copper(I) chloride, also written as CuCl) and $CuCl_2$ (copper(II) chloride). Stability here refers to thermodynamic stability under standard conditions — which compound is less likely to decompose or undergo a spontaneous redox change.

The key lies in the standard reduction potentials of copper. Copper has two common oxidation states: +1 (cuprous) and +2 (cupric). The standard reduction potentials are:

\begin{aligned} \text{Cu}^{2+} + e^- &\rightarrow \text{Cu}^+ \quad E^\circ = +0.153\,\text{V} \\ \text{Cu}^+ + e^- &\rightarrow \text{Cu} \quad E^\circ = +0.521\,\text{V} \end{aligned}

From these, you can calculate the potential for the disproportionation of Cu⁺:

2\text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu}

The cell potential for this reaction is $E^\circ = 0.521 - 0.153 = +0.368\,\text{V}$ . A positive $E^\circ$ means the reaction is spontaneous — Cu⁺ ions in aqueous solution tend to disproportionate into Cu²⁺ and metallic copper. This is why Cu⁺ is generally unstable in water.

However, the story changes when we consider the solid compounds. $Cu_2Cl_2$ is a white solid that is insoluble in water. Its insolubility drastically lowers the concentration of Cu⁺ ions in solution, shifting the equilibrium and preventing disproportionation. In contrast, $CuCl_2$ is soluble and exists as stable Cu²⁺ ions in solution.

Step-by-Step Reasoning

Check the aqueous stability of Cu⁺ vs Cu²⁺ Using the standard reduction potentials, we find that Cu⁺ spontaneously disproportionates in water:

2\text{Cu}^+ \rightarrow \text{Cu}^{2+} + \text{Cu} \quad E^\circ = +0.368\,\text{V}

This means that in solution, Cu⁺ is not stable — it converts to Cu²⁺ and Cu metal. Cu²⁺, on the other hand, has no such tendency; it is the stable oxidation state in water.

Consider the solid state: solubility and lattice energy

$Cu_2Cl_2$ is a covalent solid with low solubility in water (its solubility product $K_{sp}$ is very small). This insolubility means that even if a tiny amount of Cu⁺ enters solution, the equilibrium is heavily shifted toward the solid. The solid itself is stable because the lattice energy and covalent bonding hold the Cu⁺ ions in place, preventing them from disproportionating.

$CuCl_2$ is also stable as a solid, but it dissolves readily to give Cu²⁺ ions. In the solid state, both compounds are stable, but the question likely refers to stability under normal conditions (e.g., in the presence of water or air).
Compare the two compounds directly …

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The Core Concept

The question tests your understanding of standard reduction potentials and how they relate to the stability of different oxidation states of the same element.

For copper:

Cu⁺ (in $Cu_2Cl_2$ ) has copper in the +1 oxidation state.
Cu²⁺ (in $CuCl_2$ ) has copper in the +2 oxidation state.

The key is: a more positive reduction potential means the oxidized form is more stable (easier to reduce, harder to oxidize).

Common Mistake #1: Confusing "Stability" with "Oxidation State"

The error: Students assume the higher oxidation state (+2) is always more stable because "copper commonly shows +2."

Why it's wrong: Stability depends on the specific compound and conditions. For copper in aqueous solution, Cu²⁺ is actually more stable than Cu⁺ because Cu⁺ tends to disproportionate:

2Cu^+ \rightarrow Cu + Cu^{2+}

How to avoid: Always check the reduction potentials:

$E^\circ(Cu^{2+}/Cu^+) = +0.153\ \text{V}$
$E^\circ(Cu^+/Cu) = +0.521\ \text{V}$

The more positive $E^\circ$ for $Cu^+/Cu$ means Cu⁺ is more easily reduced — so it's less stable as an isolated ion.

Common Mistake #2: Ignoring the Disproportionation Reaction

The error: Students forget to check whether an intermediate oxidation state can spontaneously convert to higher and lower states.

Why it's wrong: For Cu⁺, the disproportionation reaction is:

2Cu^+ \rightarrow Cu + Cu^{2+}

The standard cell potential for this reaction is:

E^\circ_{cell} = E^\circ(Cu^{2+}/Cu^+) - E^\circ(Cu^+/Cu) = 0.153 - 0.521 = -0.368\ \text{V}

A common error is stopping here and concluding the reaction is non-spontaneous because this subtraction gives a negative value. That conclusion is wrong — it misidentifies which half-reaction is the cathode and which is the anode for this specific reaction. The correct approach is:

E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}

For $2Cu^+ \rightarrow Cu + Cu^{2+}$ :

Cathode (reduction): $Cu^+ + e^- \rightarrow Cu$ , $E^\circ = +0.521\ \text{V}$
Anode (oxidation): $Cu^+ \rightarrow Cu^{2+} + e^-$ , $E^\circ = -0.153\ \text{V}$

So $E^\circ_{cell} = 0.521 - 0.153 = +0.368\ \text{V}$ — positive, meaning spontaneous.

How to avoid: Always write the half-reactions correctly and compute $E^\circ_{cell}$ carefully. A positive $E^\circ_{cell}$ means the reaction is spontaneous.

Common Mistake #3: Forgetting the Role of the Anion

The error: Students treat $Cu_2Cl_2$ and $CuCl_2$ as if only the copper matters, ignoring chloride's effect.

Why it's wrong: Chloride ions can complex with Cu⁺, stabilizing it. In solid $Cu_2Cl_2$ , Cu⁺ is stabilized by the lattice and by chloride bridging. In solution, Cu⁺ is unstable, but in the solid state, $Cu_2Cl_2$ is quite stable.

How to avoid: Remember that stability depends on the environment:

In aqueous solution: $CuCl_2$ (Cu²⁺) is more stable. …

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Q.Out of $Cu_2Cl_2$ and $CuCl_2$ , which is more stable and why?

Concept understanding — Standard Reduction Potential

Cell Representation and the Nernst Equation: From Intuition to Precision

The Intuition First

The Precise Statement

Cell Representation: How We Write It

Applying the Nernst Equation to a Cell Representation

A Worked Example

Why this formula?

Standard Reduction Potential: Why the Formula Holds

1. The Core Idea: A Half-Cell's "Tendency to Gain Electrons"

2. The Formula: $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

Why subtraction, not addition?

The reasoning step-by-step:

3. The Nernst Equation: Why $E = E^\circ - \frac{RT}{nF} \ln Q$

From Gibbs free energy:

Substituting:

Rearranging:

Why this makes physical sense:

Concept and Intuition

Step-by-Step Reasoning

Method: Using Standard Reduction Potentials to Predict Stability

Step-by-step reasoning

The Core Concept

Common Mistake #1: Confusing "Stability" with "Oxidation State"

Common Mistake #2: Ignoring the Disproportionation Reaction

Common Mistake #3: Forgetting the Role of the Anion

Q.Out of Cu2Cl2Cu_2Cl_2Cu2​Cl2​ and CuCl2CuCl_2CuCl2​, which is more stable and why?

Concept and Intuition

Step-by-Step Reasoning

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Q.Out of $Cu_2Cl_2$ and $CuCl_2$ , which is more stable and why?

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