Problem 75 - Chemistry Matter and Change

Question

Predict Suppose that scientists had chosen the \(\mathrm{Cu}^{2+} |\) Cu half-cell as a standard instead of the \(\mathrm{H}^{+} | \mathrm{H}_{2}\) half-cell? What would the potential of the hydrogen electrode be if the copper electrode were the standard? How would the relationships among the standard reduction potentials change?

Step-by-Step Solution

Answer

If copper were the standard, hydrogen electrode potential would be -0.34 V, and all standard reduction potentials decrease by 0.34 V.

Step 1: Understand Standard Reduction Potentials

Each half-cell has a standard reduction potential, which is measured under standard conditions (1M concentration, 1 atm pressure, and 25°C). These potentials are determined relative to the standard hydrogen electrode (SHE), which is assigned a value of 0 V.

Step 2: Reassign Copper Reduction Potential

The reduction half-reaction for the copper electrode is \( ext{Cu}^{2+} + 2e^- \rightarrow ext{Cu}\), which has a standard potential of +0.34 V when measured against SHE. If the copper electrode becomes the standard with an assigned potential of 0 V, then the potential of the hydrogen electrode must shift accordingly.

Step 3: Calculate the New Hydrogen Electrode Potential

To find the potential for the hydrogen electrode under the new standard, subtract the standard reduction potential of copper (0.34 V) from the hydrogen electrode potential when measured against the copper standard. Hence, the new potential for the hydrogen electrode is \(0 - (0.34) = -0.34\) V.

Step 4: Analyze Impact on Other Reduction Potentials

With the copper standard set as 0 V instead of hydrogen, all standard reduction potentials in the table shift by -0.34 V. This involves subtracting 0.34 V from each potential as they were originally measured against the hydrogen electrode.

Key Concepts

Electrochemistry

Electrochemistry is a field of chemistry that studies the relationship between electricity and chemical reactions. It involves the movement of electrons between electrodes and solutions, which can generate or use electrical energy. This might sound complex, but at its core, it is about how electrical energy affects chemical species and vice versa.

• An electrochemical cell is the main unit where these reactions occur. It consists of two electrodes (one positive and one negative) submerged in electrolyte solutions.
• These processes occur in devices called galvanic cells when energy is produced spontaneously, or electrolytic cells when energy is consumed.
• Key to these reactions are half-reactions, where oxidation and reduction occur separately at the two electrodes.

In electrochemistry, the most crucial concept is the notion of potential difference, or voltage, between electrodes, which drives electron flow and thus current in the cell.

Standard Hydrogen Electrode

The Standard Hydrogen Electrode (SHE) is a reference electrode used in electrochemistry to measure electrode potentials. It provides a standard against which other electrodes' potentials can be compared.

• The SHE involves a half-cell reaction where hydrogen gas is bubbled over a platinum electrode submerged in a 1 M acid solution.
• By convention, the SHE is assigned a potential of 0 volts at all temperatures.
• This reference point allows for the determination of other substances' ability to either gain or lose electrons when in contact with ions in solution.

Using the SHE, scientists can determine the tendency of a substance to be reduced (gain electrons) or oxidized (lose electrons). This is integral in establishing a series called the electrochemical series, a list of standard reduction potentials.

Copper Reduction Potential

Copper's reduction potential is an essential concept in electrochemistry because it illustrates the ability of copper ions to gain electrons and form metallic copper. This specific half-reaction is written as \(\mathrm{Cu}^{2+} + 2e^- \rightarrow \mathrm{Cu}\) with a standard reduction potential of +0.34 V against the Standard Hydrogen Electrode.

• Reduction potential serves as a measure of the readiness of a chemical species to acquire electrons.
• The positive value of +0.34 V indicates that copper ions have a strong tendency to gain electrons compared to hydrogen in the standard state.
• When the copper reduction potential is used as a standard at 0 V, other potentials shift accordingly, altering the way we measure other chemical species' abilities to undergo reduction or oxidation.

This understanding underscores how varying the standard can shift perceived electron-flow characteristics in electrochemical series, affecting interpretations of how different metals will react.