A galvanic cell consisting of standard concentrations: Zn|Zn2+||Ag+|Ag, is connected to a small light bulb for 50 minutes. During that time the average current drawn by the bulb is... A galvanic cell consisting of standard concentrations: Zn|Zn2+||Ag+|Ag, is connected to a small light bulb for 50 minutes. During that time the average current drawn by the bulb is 0.2 Amp. During this time how many grams of zinc became dissolved at the anode? (Atomic weight of Zinc = 65.4 g/mol)
Understand the Problem
The question is asking for the amount of zinc that dissolved at the anode of a galvanic cell given the current drawn by a light bulb over a specific duration. We need to use the concept of electrochemistry to calculate this using Faraday's laws of electrolysis.
Answer
The mass of zinc that became dissolved at the anode is approximately \( 0.405 \, \text{g} \).
Answer for screen readers
The mass of zinc that became dissolved at the anode is approximately ( 0.405 , \text{g} ).
Steps to Solve
- Calculate Total Charge (Q)
To find the total charge that passed through the galvanic cell, use the formula:
$$ Q = I \times t $$
where:
- ( I = 0.2 , \text{A} ) (current)
- ( t = 50 , \text{min} = 50 \times 60 , \text{s} = 3000 , \text{s} )
So,
$$ Q = 0.2 , \text{A} \times 3000 , \text{s} = 600 , \text{C} $$
- Calculate Moles of Zinc Dissolved (n)
Using Faraday's first law of electrolysis:
$$ n = \frac{Q}{F} $$
where ( F = 96500 , \text{C/mol} ) (Faraday’s constant).
Therefore,
$$ n = \frac{600 , \text{C}}{96500 , \text{C/mol}} \approx 0.0062 , \text{mol} $$
- Calculate Mass of Zinc Dissolved (m)
Use the formula:
$$ m = n \times \text{molar mass} $$
where the molar mass of Zinc is ( 65.4 , \text{g/mol} ).
Thus,
$$ m = 0.0062 , \text{mol} \times 65.4 , \text{g/mol} \approx 0.405 , \text{g} $$
The mass of zinc that became dissolved at the anode is approximately ( 0.405 , \text{g} ).
More Information
This calculation uses Faraday's laws of electrolysis, which relate the amount of substance transformed at an electrode to the electric charge passed through the circuit. The formula for total charge (( Q )) allows us to connect current, time, and charge, leading to the determination of moles of zinc dissolved.
Tips
- Forgetting to convert time from minutes to seconds, which could lead to an incorrect value for total charge.
- Not using the correct value for Faraday's constant, which is approximately ( 96500 , \text{C/mol} ).
- Miscalculating the amount of zinc by incorrectly interpreting the mole relationship.
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