Gaurav
Last Activity: 11 Years ago
To determine how long the current flowed and the masses of copper and zinc deposited in cells A and C, we can use Faraday's laws of electrolysis. These laws relate the amount of substance deposited during electrolysis to the quantity of electricity passed through the cells. Let's break this problem down step by step.
Understanding Faraday's Laws
Faraday's first law states that the mass of a substance deposited at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the cell. Mathematically, this can be expressed as:
m = (Q × M) / (F × z)
Where:
- m = mass of the substance deposited (in grams)
- Q = total electric charge (in coulombs)
- M = molar mass of the substance (in g/mol)
- F = Faraday's constant (approximately 96500 C/mol)
- z = number of moles of electrons exchanged per mole of substance deposited
Calculating the Charge for Silver Deposition
In cell B, we have silver (Ag) being deposited from AgNO3. The molar mass of silver is approximately 108 g/mol, and it has a valency of +1, meaning one mole of electrons is needed to deposit one mole of silver (z = 1).
The mass of silver deposited is 1.45 g. We can rearrange Faraday's equation to find the charge (Q) used:
Q = (m × F × z) / M
Plugging in the values for silver:
Q = (1.45 g × 96500 C/mol × 1) / 108 g/mol
Calculating this gives us:
Q ≈ 1282.1 C
Finding the Current Flow Duration
We know that the current (I) is 1.5 A (amperes), which is equal to 1.5 C/s. To find the time (t) the current flowed, we use the relationship:
Q = I × t
Rearranging gives us:
t = Q / I
Substituting the values we have:
t = 1282.1 C / 1.5 C/s
Calculating this results in:
t ≈ 854.73 seconds
Determining Masses of Copper and Zinc Deposited
Next, we need to calculate how much copper and zinc were deposited in cells A and C, respectively. For copper (Cu) from CuSO4, the molar mass is approximately 63.5 g/mol, and it has a valency of +2 (z = 2). For zinc (Zn) from ZnSO4, the molar mass is approximately 65.4 g/mol, and it also has a valency of +2 (z = 2).
Mass of Copper Deposited
Using the total charge Q that we already calculated, we can find the mass of copper deposited:
m_Cu = (Q × M_Cu) / (F × z_Cu)
Substituting the values:
m_Cu = (1282.1 C × 63.5 g/mol) / (96500 C/mol × 2)
Calculating this gives:
m_Cu ≈ 0.413 g
Mass of Zinc Deposited
Now for zinc, we can use the same formula:
m_Zn = (Q × M_Zn) / (F × z_Zn)
Substituting the values:
m_Zn = (1282.1 C × 65.4 g/mol) / (96500 C/mol × 2)
Calculating this gives:
m_Zn ≈ 0.426 g
Summary of Results
To summarize, the current flowed for approximately 854.73 seconds, with around 0.413 grams of copper and 0.426 grams of zinc deposited during this process. Understanding these calculations provides a clear insight into the relationships between current, charge, and mass in electrolytic processes.
