13. Fundamentals of Electrochemistry

Basic Concepts

13. Fundamentals of Electrochemistry

Basic Concepts

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Multiple Choice

A metal forms the salt MCl ₃. Electrolysis of the molten salt with a current of 0.700 A for 6.63 h produced 3.00 g of the metal. What is the molar mass of the metal?

8.6610 g/mol

103.9323 g/mol

51.9662 g/mol

5.77 g/mol

25.98 g/mol

Verified step by step guidance

First, calculate the total charge passed through the molten salt during electrolysis using the formula: \( Q = I \times t \), where \( Q \) is the charge in coulombs, \( I \) is the current in amperes, and \( t \) is the time in seconds. Convert the time from hours to seconds by multiplying by 3600.

Next, use Faraday's laws of electrolysis to determine the number of moles of electrons transferred. The relationship is given by \( n = \frac{Q}{F} \), where \( n \) is the number of moles of electrons and \( F \) is Faraday's constant (approximately 96485 C/mol).

Since the metal forms the salt \( \text{MCl}_3 \), it implies that each metal ion \( \text{M}^{3+} \) requires 3 moles of electrons to be reduced to the metal \( \text{M} \). Therefore, calculate the moles of the metal produced by dividing the moles of electrons by 3.

Determine the molar mass of the metal by using the formula: \( \text{Molar mass} = \frac{\text{mass of metal}}{\text{moles of metal}} \). Use the given mass of the metal (3.00 g) and the moles of metal calculated in the previous step.

Finally, compare the calculated molar mass with the given options to identify the correct answer.