Question

Zinc metal can be dissolved by acid, which contains \(\mathrm{H}^{+}\) ions. Demonstrate that this is consistent with the fact that this reaction has a spontaneous voltage: $$ \mathrm{Zn}+2 \mathrm{H}^{+} \rightarrow \mathrm{Zn}^{2+}+\mathrm{H}_{2} $$

Short answer

The reaction is spontaneous with a cell potential of 0.76 V.

Step-by-step solution

Identify the Half-Reactions

To determine the spontaneity of the reaction, we first need to identify the oxidation and reduction half-reactions. The reduction half-reaction is \(2 \mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{H}_2\), and the oxidation half-reaction is \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{e}^-\).

Consult Standard Reduction Potentials

Look up the standard reduction potentials for both half-reactions: The standard reduction potential for \(2 \mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{H}_2\) is \(0.00 \text{ V}\). The standard oxidation potential for \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{e}^-\) can be calculated as the negative of its reduction potential, so \(-(-0.76 \text{ V}) = 0.76 \text{ V}\).

Calculate the Cell Potential

Add the potentials of the reduction and oxidation reactions to find the overall cell potential: \(0.76 \text{ V} + 0.00 \text{ V} = 0.76 \text{ V}\).

Determine Spontaneity

A positive cell potential indicates a spontaneous reaction under standard conditions. Since the cell potential for the reaction \(\mathrm{Zn} + 2 \mathrm{H}^+ \rightarrow \mathrm{Zn}^{2+} + \mathrm{H}_2\) is \(0.76 \text{ V}\), the reaction is spontaneous.

Key concepts

Half-Reactions

In a redox reaction like the one between zinc and acid with hydrogen ions, we break the reaction into two half-reactions. This separation allows us to clearly see the movement of electrons.
The half-reactions are as follows:

• Reduction half-reaction: This involves the gain of electrons, usually by the species in a lower oxidation state. For our example: \(2 \mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{H}_2\). Here, the hydrogen ions gain electrons to form hydrogen gas.
• Oxidation half-reaction: This involves the loss of electrons, usually by the species in a higher oxidation state. For our example: \(\mathrm{Zn} \rightarrow \mathrm{Zn}^{2+} + 2\mathrm{e}^-\). Here, zinc loses electrons to form zinc ions.

Breaking the reaction into these parts makes understanding the electron flow easier and is crucial for the next steps in analyzing the reaction.

Standard Reduction Potentials

Standard reduction potentials give us the ability to predict the direction of electron flow in a redox reaction. They are measured under standard conditions, usually at \(25^\circ\text{C}\), 1 atm pressure, and 1 M concentrations.
In electrochemical cells, each half-reaction has an associated standard reduction potential, usually denoted as \(E^\circ\).

• The standard reduction potential for the reduction half-reaction (\(2 \mathrm{H}^+ + 2\mathrm{e}^- \rightarrow \mathrm{H}_2\)) is \(0.00 \text{ V}\).
• The oxidation potential for the zinc reaction is calculated as the negative of its reduction potential. Thus, \(-(-0.76 \text{ V}) = 0.76 \text{ V}\).

These standard potentials help us determine if the reaction will proceed spontaneously.

Cell Potential

The cell potential (also known as electromotive force or \(EMF\)) is the force that drives electrons through the circuit in an electrochemical cell. Calculating the cell potential involves adding up the standard reduction potentials of the cathode and anode half-reactions. This value tells us how much voltage the cell can provide.
In our case of zinc and acid:

• The reduction potential of hydrogen ions is \(0.00 \text{ V}\).
• The oxidation potential for zinc is \(0.76 \text{ V}\).

By adding these values, the overall cell potential is \(0.76 \text{ V}\). A positive cell potential signifies that the reaction is favorable or spontaneous under standard conditions. This is crucial in determining whether the reaction would naturally proceed or require external energy.

Spontaneity

Spontaneity in redox reactions is determined by the sign of the cell potential. A positive cell potential indicates that the reaction is spontaneous, while a negative potential signifies a non-spontaneous reaction.
For the reaction \(\mathrm{Zn} + 2 \mathrm{H}^+ \rightarrow \mathrm{Zn}^{2+} + \mathrm{H}_2\), we calculated a cell potential of \(0.76 \text{ V}\).

• Since this value is positive, it means the reaction can occur without the need for additional energy input.
• A spontaneous reaction under standard conditions also implies a thermodynamically favorable process where products are more energetically stable than reactants.

Understanding spontaneity helps us predict reaction behavior and decide if additional measures are needed to make a reaction proceed.