WEB Calcium metal can be obtained by the direct electrolysis...

WEB Calcium metal can be obtained by the direct electrolysis of molten $\mathrm{CaCl}_2$, at a voltage of 3.2 V . (a) How many joules of electrical energy are required to obtain 12.0 lb of calcium? (b) What is the cost of the electrical energy obtained in (a) if electrical energy is sold at the rate of nine cents per kilowatt hour?

WEB Calcium metal can be obtained by the direct electrolysis of molten $\mathrm{CaCl}_2$, at a voltage of 3.2 V .
(a) How many joules of electrical energy are required to obtain 12.0 lb of calcium?
(b) What is the cost of the electrical energy obtained in (a) if electrical energy is sold at the rate of nine cents per kilowatt hour?

Key Concepts

Unit Conversions

Unit conversions are crucial when solving real-world problems that involve different measurement systems. In such problems, mass units (e.g., pounds to kilograms or grams) and energy units (e.g., joules to kilowatt-hours) often need to be converted to ensure consistency in calculations.

Energy Calculation Using Voltage (E = V × Q)

The energy required in an electrolytic process is determined by the product of the applied voltage and the total charge passed through the system. This relationship (E = V × Q) allows one to compute the electrical energy in joules needed to produce a specified amount of a substance.

Cost Calculation for Electrical Energy

Cost calculation involves determining the total electrical energy consumed (commonly expressed in kilowatt-hours) and then applying the given rate to estimate the monetary cost. This step bridges the gap between theoretical energy consumption and practical economic considerations.

Electrolysis

Electrolysis is a process in which electrical energy is used to drive a chemical reaction that would not occur spontaneously. In the context of metal production, molten salts are electrolyzed to reduce metal ions to pure metal at the cathode, while the corresponding anions are oxidized at the anode.

Faraday's Law of Electrolysis

Faraday's Law quantifies the relationship between the amount of electric charge passed through the electrolyte and the amount of substance transformed at the electrodes. It is essential for calculating the moles of electrons transferred, which is directly related to the mass of the metal produced during the electrolysis process.

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