The current of 9.65 A flowing for 10 min deposits 3.0 g of a metal. The equivalent weight of the met — Electrochemistry Chemistry Question

💡 Solution & Explanation

Step 1 - State Faraday's First Law of Electrolysis According to Faraday's First Law of Electrolysis, the mass ($W$) of a substance deposited at an electrode during electrolysis is directly proportional to the quantity of electricity ($Q$) passed through the electrolyte: $$W = Z \cdot Q$$ Since the quantity of electricity is the product of current ($I$ in amperes) and time ($t$ in seconds), we write: $$Q = I \cdot t$$ The electrochemical equivalent ($Z$) of a substance is related to its equivalent weight ($E$) by: $$Z = \frac{E}{F}$$ where $F$ is Faraday's constant ($96500\text{ C/mol}$). Combining these relationships gives the mathematical formula: $$W = \frac{E \cdot I \cdot t}{96500}$$ Step 2 - Identify the Given Parameters and Convert Units We are given the following values: * Mass of metal deposited ($W$) = $3.0\text{ g}$ * Current ($I$) = $9.65\text{ A}$ * Time ($t$) = $10\text{ min}$ To use Faraday's formula, the time must be converted from minutes to seconds: $$t = 10\text{ min} \times 60\text{ s/min} = 600\text{ s}$$ Step 3 - Substitute Values and Calculate the Equivalent Weight Using the rearranged formula to solve for the equivalent weight ($E$): $$E = \frac{W \cdot 96500}{I \cdot t}$$ Substituting the values into the formula: $$E = \frac{3.0\text{ g} \times 96500\text{ C/mol}}{9.65\text{ A} \times 600\text{ s}}$$ Let us simplify the calculation by dividing $96500$ by $9.65$: $$\frac{96500}{9.65} = 10000$$ Substitute this back into the equation: $$E = \frac{3.0 \times 10000}{600}$$ $$E = \frac{30000}{600} = \boxed{50}$$ Step 4 - Analyze the Options * **Option (A)** represents $10$, which is incorrect. * **Option (B)** represents $30$, which is incorrect. * **Option (C)** represents $50$, which matches our calculated value of the equivalent weight of the metal. * **Option (D)** represents $96.5$, which is incorrect. Therefore, the correct choice is **Option (C)**.