A total charge of 96.5 kC is passed through an electrolytic cell. What mass of silver metal will be produced from a silver nitrate solution?
Answer in units of g
96,500 C will deposit 1 gram equivalent weight of any metal. For Ag that is 107.9 grams.
a Coulomb ≈ 6.24x10^18 electrons
find the number of moles in 96.5 kC (by multiplying)
this equals the moles of Ag produced
mass = moles * molar mass
To calculate the mass of silver metal produced from a silver nitrate solution, we need to use Faraday's laws of electrolysis and the molar mass of silver.
Step 1: Determine the number of moles of electrons transferred.
We can use Faraday's constant (F), which is equal to 96,485 C/mol of electrons, to convert the total charge (Q) to moles of electrons (n).
Q = 96.5 kC = 96,500 C
n = Q / F
n = 96,500 C / 96,485 C/mol
n ≈ 1 mol
Step 2: Balance the chemical equation.
The balanced chemical equation for the electrolysis of silver nitrate (AgNO3) is:
2 AgNO3 (aq) → 2 Ag (s) + O2 (g) + 2 NO2 (g)
Step 3: Determine the stoichiometry.
From the balanced equation, we can see that 2 moles of silver (Ag) are produced for every 2 moles of AgNO3 consumed. Therefore, 1 mole of electrons is required to produce 1 mole of Ag.
Step 4: Calculate the molar mass of silver.
The molar mass of silver (Ag) is approximately 107.87 g/mol.
Step 5: Calculate the mass of silver produced.
The mass of silver produced is equal to the molar mass of silver multiplied by the number of moles of silver.
Mass = n × molar mass
Mass = 1 mol × 107.87 g/mol
Mass ≈ 107.87 g
Therefore, approximately 107.87 grams of silver metal will be produced from the silver nitrate solution.
To find the mass of silver metal produced from the silver nitrate solution, we need to use Faraday's law of electrolysis and the molar mass of silver.
1. Convert the total charge passed through the electrolytic cell from kilocoulombs to coulombs:
96.5 kC = 96.5 × 1000 C = 96,500 C
2. Determine the number of moles of electrons transferred. In electrolysis, one mole of electrons corresponds to one Faraday (F), which is equal to 96,500 C:
Moles of electrons = 96,500 C / 96,500 C = 1 F
3. Find the molar mass of silver (Ag) from the periodic table:
Molar mass of Ag = 107.87 g/mol
4. Use Faraday's law of electrolysis, which states that the amount of substance (in moles) deposited or liberated from an electrolyte is directly proportional to the quantity of electricity (in coulombs) passed through the electrolyte. The relationship is given by:
Moles of substance = (Quantity of electricity in coulombs) / (Faraday's constant)
Quantity of electricity in coulombs = 96,500 C
Faraday's constant = 96,500 C/mol
Moles of silver = 96,500 C / 96,500 C/mol = 1 mol
5. Finally, calculate the mass of silver using the molar mass:
Mass of silver = Moles of silver × Molar mass of silver
= 1 mol × 107.87 g/mol
= 107.87 g
Therefore, a total of 96.5 kC charge passed through the electrolytic cell will produce 107.87 grams of silver metal from the silver nitrate solution.