The production of H2 gas by the electrolysis of water...

The production of $\mathrm{H}_{2}$ gas by the electrolysis of water typically requires about $400 \mathrm{~kJ}$ of energy per mole. (a) Use the relationship between work and cell potential (Section 21.4 to calculate the minimum work needed to form $1.0 \mathrm{~mol}$ of $\mathrm{H}_{2}$ gas at a cell potential of $1.24 \mathrm{~V}$ (b) What is the energy efficiency of the cell operation? (c) Find the cost of producing 500 . mol of $\mathrm{H}_{2}$ if electricity is 50.06 per kilowatt-hour ( 1 watt-second $=1$ joule).

The production of $\mathrm{H}_{2}$ gas by the electrolysis of water typically requires about $400 \mathrm{~kJ}$ of energy per mole. (a) Use the relationship between work and cell potential (Section
21.4 to calculate the minimum work needed to form $1.0 \mathrm{~mol}$ of
$\mathrm{H}_{2}$ gas at a cell potential of $1.24 \mathrm{~V}$
(b) What is the energy efficiency of the cell operation?
(c) Find the cost of producing 500 . mol of $\mathrm{H}_{2}$ if electricity is 50.06 per kilowatt-hour ( 1 watt-second $=1$ joule).

Key Concepts

Cost Analysis of Energy Consumption

Cost analysis in the context of electrochemical processes involves converting the energy requirements from joules or watt?seconds to a more usable unit like kilowatt-hours, and then applying the cost per unit of energy to determine the overall expense. This process ensures that economic evaluations of energy-demanding processes consider both the energy consumption and the monetary cost associated with the electricity used.

Energy Efficiency in Electrochemical Processes

Energy efficiency in electrochemical cells refers to the comparison of the theoretical minimum energy required for a reaction, as calculated from thermodynamic principles, to the actual energy input used in the process. It is typically expressed as a percentage, indicating how effectively the input electrical energy is converted into chemical energy, while losses due to resistance, overpotential, and other inefficiencies are taken into account.

Electrolysis of Water

Electrolysis is the process of using electrical energy to drive a non-spontaneous chemical reaction, such as splitting water into hydrogen and oxygen. This technique is fundamental in chemistry and energy production, allowing for the production of hydrogen gas by applying a specific cell potential to overcome the reaction’s thermodynamic barriers.

Cell Potential and Electrical Work

In electrochemistry, the relationship between cell potential and the work done by an electrochemical cell is described by the equation W = -nFE, where W is the work, n is the number of moles of electrons transferred, F is Faraday’s constant, and E is the cell potential. This concept links the electrical energy provided to the chemical energy stored in the products, establishing the minimum energy required for an electrochemical reaction.

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