Sodium hypochlorite is produced by the electrolysis of cold...

Sodium hypochlorite is produced by the electrolysis of cold sodium chloride solution. How long must a cell operate to produce $1.500 \times 10^{3} \mathrm{~L}$ of $5.00 \%$ NaClO by mass if the cell current is $2.00 \times 10^{3} \mathrm{~A} ?$ Assume that the density of the solution is $1.00 \mathrm{~g} / \mathrm{cm}^{3}$.

Key Concepts

Electrolysis

Electrolysis is the process of driving a non-spontaneous chemical reaction using an electric current. In industrial and laboratory settings, it is employed to decompose compounds or produce new substances. Understanding electrolysis involves recognizing how electrical energy can induce redox reactions and how the efficiency of the process depends on the applied current and cell design.

Faraday's Laws of Electrolysis

Faraday's laws provide the quantitative framework for electrolysis by establishing that the amount of chemical change is directly proportional to the quantity of electricity passed through the electrolyte. This concept is central to calculating how much substance is formed or consumed when a known current is applied over a certain period, and it introduces the use of Faraday's constant in relating moles of electrons to electrical charge.

Current, Charge, and Time Relationship

The relationship between current, charge, and time—expressed as Q = I × t—is fundamental in electrochemistry. This equation allows one to determine the total electrical charge passed through a system when the current is known and helps in calculating the duration of electrolysis required to produce a specific amount of product.

Electrochemical Stoichiometry

Electrochemical stoichiometry involves analyzing the redox reactions at the electrodes to correlate the number of electrons transferred to the number of moles of substances produced or consumed. It enables the conversion of electrical charge (in coulombs) into a quantitative measure of chemical yield by using the stoichiometric coefficients from the balanced reaction.

Concentration and Density Conversions

Concentration and density concepts are used to convert between volume, mass, and composition in solutions. When a solution’s concentration is expressed as a percent by mass and its density is known, these conversions are critical for determining the total mass of the solution and the amount of active species it contains, facilitating the calculation of yields in electrochemical processes.

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