Calculating the Mass of Ag Deposited at the Cathode

To calculate the mass of Ag deposited at the cathode, we need to use Faraday's law of electrolysis, which states that the amount of a substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

Step 1: Calculate the Quantity of Electricity Passed Through the Electrolyte

To calculate the quantity of electricity passed through the electrolyte, we need to use the formula:

Quantity of electricity (Q) = Current (I) x Time (t)

In this case, the current is 2 amperes, and the time is 15 minutes, which is equivalent to 900 seconds. Therefore:

Q = 2 A x 900 s = 1800 C

Step 2: Calculate the Amount of Ag Deposited at the Cathode

To calculate the amount of Ag deposited at the cathode, we need to use the formula:

Amount of Ag = (Q x M) / (n x F)

Where:

Q = Quantity of electricity passed through the electrolyte (in coulombs)
M = Atomic mass of Ag (107.87 g/mol)
n = Number of electrons transferred per Ag ion (in this case, it is 1)
F = Faraday's constant (96485 C/mol)

Substituting the values:

Amount of Ag = (1800 C x 107.87 g/mol) / (1 x 96485 C/mol)
Amount of Ag = 1.992 g

Therefore, the mass of Ag deposited at the cathode is 1.992 grams.

Explanation

During electrolysis, the Ag+ ions in the AgNO3 solution are reduced at the cathode to form Ag atoms, which deposit on the electrode. The amount of Ag deposited is directly proportional to the quantity of electricity passed through the solution. Faraday's law of electrolysis relates the quantity of electricity passed to the amount of substance produced at the electrode. By using the formula, we can calculate the amount of Ag deposited at the cathode when a current of 2 amperes is passed through the AgNO3 solution for 15 minutes.