A current of 4.10 A is passed through a Ni(NO3)2 solution for 1.30 h. How much nickel is plated out of the solution?
Understand the Problem
The question asks how much nickel is plated from a Ni(NO3)2 solution when a current of 4.10 A is passed through it for 1.30 hours. This involves using Faraday's laws of electrolysis to calculate the mass of nickel deposited based on the current and time given.
Answer
The mass of nickel plated is approximately \( 11.68 \, \text{g} \).
Answer for screen readers
The mass of nickel plated out of the solution is approximately ( 11.68 , \text{g} ).
Steps to Solve
- Convert Time to Seconds
First, convert the time from hours to seconds since the current is measured in amperes (A), which is in coulombs per second.
[ 1.30 , \text{h} = 1.30 \times 3600 , \text{s} = 4680 , \text{s} ]
- Calculate Total Charge (Coulombs)
Using the formula for charge ( Q ), which is the product of current ( I ) and time ( t ):
[ Q = I \times t = 4.10 , \text{A} \times 4680 , \text{s} = 19188 , \text{C} ]
- Determine Moles of Nickel Deposited
Using Faraday's law, the number of moles ( n ) of nickel plated can be calculated using the equation for the charge:
[ n = \frac{Q}{F} ]
Where ( F ) (Faraday's constant) is approximately ( 96485 , \text{C/mol} ):
[ n = \frac{19188 , \text{C}}{96485 , \text{C/mol}} \approx 0.199 , \text{mol} ]
- Calculate Mass of Nickel Plated
Using the molar mass of nickel (approximately ( 58.69 , \text{g/mol} )), we can find the mass ( m ):
[ m = n \times \text{molar mass} = 0.199 , \text{mol} \times 58.69 , \text{g/mol} \approx 11.68 , \text{g} ]
The mass of nickel plated out of the solution is approximately ( 11.68 , \text{g} ).
More Information
This calculation uses Faraday's laws of electrolysis, which relate the amount of substance deposited at an electrode to the charge passed through the electrolyte. Nickel is commonly used in electroplating due to its resistance to corrosion and attractive finish.
Tips
- Not converting time correctly: Ensure time is converted to seconds for accurate calculations.
- Misusing Faraday's constant: Remember to use the correct value for ( F ) and check unit consistency.
- Forgetting molar mass: Ensure to use the correct molar mass specific to nickel for mass calculations.
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