To calculate the mass of pure silver deposited on a metal object made into the cathode in an electroplating cell when a current is passed through it, follow these steps:
1. Determine the total charge passed through the cell:
- The current [tex]\( I \)[/tex] is 0.800 A (amperes).
- The time [tex]\( t \)[/tex] is 73.0 seconds.
- The total charge [tex]\( Q \)[/tex] passed through the cell is given by the formula:
[tex]\[ Q = I \times t \][/tex]
- Substituting the values, we get:
[tex]\[ Q = 0.800 \, \text{A} \times 73.0 \, \text{s} \][/tex]
- This gives:
[tex]\[ Q = 58.4 \, \text{C} \][/tex]
2. Calculate the moles of electrons transferred:
- Faraday's constant [tex]\( F \)[/tex] is [tex]\( 96485 \, \text{C/mol} \)[/tex].
- The moles of electrons [tex]\( n \)[/tex] can be calculated using the formula:
[tex]\[ n = \frac{Q}{F} \][/tex]
- Substituting the values, we get:
[tex]\[ n = \frac{58.4 \, \text{C}}{96485 \, \text{C/mol}} \][/tex]
- This gives:
[tex]\[ n = 0.000605 \, \text{mol} \][/tex]
3. Determine the moles of silver deposited:
- In the electroplating process, each mole of electrons reduces an equivalent mole of [tex]\( Ag^+ \)[/tex] ions to form silver metal.
- Therefore, the moles of silver deposited will be the same as the moles of electrons:
[tex]\[ \text{Moles of silver} = 0.000605 \, \text{mol} \][/tex]
4. Calculate the mass of silver deposited:
- The molar mass of silver [tex]\( Ag \)[/tex] is [tex]\( 107.8682 \, \text{g/mol} \)[/tex].
- The mass of silver [tex]\( m \)[/tex] can be calculated using the formula:
[tex]\[ m = \text{moles} \times \text{molar mass} \][/tex]
- Substituting the values, we get:
[tex]\[ m = 0.000605 \, \text{mol} \times 107.8682 \, \text{g/mol} \][/tex]
- This gives:
[tex]\[ m = 0.06529 \, \text{g} \][/tex]
Thus, the mass of pure silver deposited on the metal object is [tex]\( 0.065 \, \text{g} \)[/tex].
