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Answer :
To find out how many grams of nickel metal are plated out when a current is passed through an aqueous [tex]\( NiCl_2 \)[/tex] solution, we can follow these steps:
1. Determine the Total Charge:
- The current ([tex]\( I \)[/tex]) is 15.0 amperes.
- The time ([tex]\( t \)[/tex]) is 60.0 minutes, which we convert to seconds:
[tex]\[ 60.0 \, \text{minutes} \times 60 \, \text{seconds/minute} = 3600 \, \text{seconds} \][/tex]
- The total charge ([tex]\( Q \)[/tex]) passed is calculated using the formula:
[tex]\[ Q = I \times t \][/tex]
[tex]\[ Q = 15.0 \, \text{A} \times 3600 \, \text{s} = 54000 \, \text{Coulombs} \][/tex]
2. Calculate the Moles of Electrons:
- Using Faraday's constant ([tex]\( F \)[/tex]), which is approximately 96485 C/mol, we can calculate the moles of electrons ([tex]\( n \)[/tex]):
[tex]\[ n = \frac{Q}{F} \][/tex]
[tex]\[ n = \frac{54000 \, \text{C}}{96485 \, \text{C/mol}} \approx 0.5597 \, \text{moles of electrons} \][/tex]
3. Determine the Moles of Nickel:
- The electrochemical reaction for plating nickel is: [tex]\( Ni^{2+} + 2e^- \rightarrow Ni \)[/tex]. This means 2 moles of electrons are needed to plate 1 mole of nickel.
- The moles of nickel are:
[tex]\[ \text{Moles of nickel} = \frac{\text{Moles of electrons}}{2} \][/tex]
[tex]\[ \text{Moles of nickel} = \frac{0.5597}{2} \approx 0.2798 \, \text{moles of nickel} \][/tex]
4. Calculate the Mass of Nickel:
- The molar mass of nickel is approximately 58.69 g/mol.
- The mass of nickel plated is:
[tex]\[ \text{Mass of nickel} = \text{Moles of nickel} \times \text{Molar mass of nickel} \][/tex]
[tex]\[ \text{Mass of nickel} = 0.2798 \, \text{moles} \times 58.69 \, \text{g/mol} \approx 16.4 \, \text{grams} \][/tex]
Therefore, about 16.4 grams of nickel metal are plated out, corresponding to answer choice B.
1. Determine the Total Charge:
- The current ([tex]\( I \)[/tex]) is 15.0 amperes.
- The time ([tex]\( t \)[/tex]) is 60.0 minutes, which we convert to seconds:
[tex]\[ 60.0 \, \text{minutes} \times 60 \, \text{seconds/minute} = 3600 \, \text{seconds} \][/tex]
- The total charge ([tex]\( Q \)[/tex]) passed is calculated using the formula:
[tex]\[ Q = I \times t \][/tex]
[tex]\[ Q = 15.0 \, \text{A} \times 3600 \, \text{s} = 54000 \, \text{Coulombs} \][/tex]
2. Calculate the Moles of Electrons:
- Using Faraday's constant ([tex]\( F \)[/tex]), which is approximately 96485 C/mol, we can calculate the moles of electrons ([tex]\( n \)[/tex]):
[tex]\[ n = \frac{Q}{F} \][/tex]
[tex]\[ n = \frac{54000 \, \text{C}}{96485 \, \text{C/mol}} \approx 0.5597 \, \text{moles of electrons} \][/tex]
3. Determine the Moles of Nickel:
- The electrochemical reaction for plating nickel is: [tex]\( Ni^{2+} + 2e^- \rightarrow Ni \)[/tex]. This means 2 moles of electrons are needed to plate 1 mole of nickel.
- The moles of nickel are:
[tex]\[ \text{Moles of nickel} = \frac{\text{Moles of electrons}}{2} \][/tex]
[tex]\[ \text{Moles of nickel} = \frac{0.5597}{2} \approx 0.2798 \, \text{moles of nickel} \][/tex]
4. Calculate the Mass of Nickel:
- The molar mass of nickel is approximately 58.69 g/mol.
- The mass of nickel plated is:
[tex]\[ \text{Mass of nickel} = \text{Moles of nickel} \times \text{Molar mass of nickel} \][/tex]
[tex]\[ \text{Mass of nickel} = 0.2798 \, \text{moles} \times 58.69 \, \text{g/mol} \approx 16.4 \, \text{grams} \][/tex]
Therefore, about 16.4 grams of nickel metal are plated out, corresponding to answer choice B.
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