To calculate the amount of silver deposited on the copper spoon during electroplating, we can use Faraday's laws of electrolysis. The formula for the mass of the substance deposited is given by:
\[ m = \frac{Q \cdot M}{n \cdot F} \]
where:
- \( m \) = mass of the substance deposited (in grams)
- \( Q \) = total electric charge (in coulombs)
- \( M \) = molar mass of the substance (in grams/mole)
- \( n \) = valency of the substance (for silver, \( n = 1 \))
- \( F \) = Faraday's constant (in coulombs/mole), \( F = 96500 \) C/mol
Step 1: Calculate the total charge \( Q \)
First, we need to calculate the total charge \( Q \) that has passed through the circuit:
\[ Q = I \cdot t \]
where:
- \( I = 0.5 \) amperes (the current)
- \( t = 18 \) minutes = \( 18 \times 60 = 1080 \) seconds (the time in seconds)
Now, substituting the values:
\[ Q = 0.5 , \text{A} \cdot 1080 , \text{s} = 540 , \text{C} \]
Step 2: Calculate the mass of silver deposited
Now we can substitute \( Q \), \( M \) (where \( M = 108 \) g/mol for silver), \( n = 1 \), and \( F = 96500 \) C/mol into the mass formula:
\[ m = \frac{540 , \text{C} \cdot 108 , \text{g/mol}}{1 \cdot 96500 , \text{C/mol}} \]
Calculating it step by step:
- Calculate the numerator:
\[ 540 , \text{C} \cdot 108 , \text{g/mol} = 58320 , \text{g} \cdot \text{C} \]
- Now divide by Faraday's constant:
\[ m = \frac{58320 , \text{g} \cdot \text{C}}{96500 , \text{C/mol}} = 0.604 , \text{g} \]
Thus, the amount of silver deposited on the copper spoon is approximately
\[ \boxed{0.604 , \text{g}} \]