Solution:

Electrolysis of CuCl2 solution using an inert electrode results in the deposition of Cu at the cathode and the evolution of Cl2 gas at the anode.

Finding the Amount of Cu Deposited

The balanced chemical equation for the electrolysis of CuCl2 is as follows:

CuCl2 (aq) → Cu (s) + Cl2 (g)

From the equation, it can be seen that for every mole of Cl2 gas evolved, one mole of Cu is deposited.

The volume of Cl2 gas evolved is given as 11.2 mL at STP. We can use the ideal gas law to convert this volume into moles:

PV = nRT

where P = 1 atm, V = 11.2 mL = 0.0112 L, n = ?, R = 0.08206 L atm mol-1 K-1, and T = 273 K.

Solving for n, we get:

n = PV/RT = (1 atm)(0.0112 L)/(0.08206 L atm mol-1 K-1)(273 K) = 0.000475 mol

Therefore, 0.000475 mol of Cu is deposited at the cathode.

Finding the Current Passed

The amount of charge (Q) passed through the solution can be calculated using Faraday's laws of electrolysis:

Q = nF

where n is the number of moles of electrons transferred during the electrolysis and F is the Faraday constant (96,485 C mol-1).

In the case of CuCl2, each mole of Cu requires two moles of electrons to be deposited at the cathode, so n = 2(0.000475) = 0.00095 mol.

Substituting into the equation for Q, we get:

Q = nF = (0.00095 mol)(96,485 C mol-1) = 91.6 C

The time taken for the electrolysis is given as 965 seconds, so the current (I) passed through the solution can be calculated using the equation:

I = Q/t

where t is the time taken for the electrolysis in seconds.

Substituting the given values, we get:

I = Q/t = (91.6 C)/(965 s) = 0.095 A

Finding the Current Efficiency

The current efficiency (CE) of the electrolysis is the ratio of the actual amount of metal deposited to the theoretical amount of metal that should have been deposited based on the amount of charge passed through the solution.

CE = (actual amount of metal deposited/theoretical amount of metal deposited) x 100%

The theoretical amount of Cu that should have been deposited can be calculated using the equation:

m = nM

where m is the mass of Cu deposited, n is the number of moles of Cu deposited, and M is the molar mass of Cu (63.55 g/mol).

Substituting the given values, we get:

m = nM = (0.000475 mol)(63.55 g/mol) = 0.0302 g

Therefore, the theoretical amount of Cu that should have been deposited is 0.0302 g.

The actual amount of Cu deposited is given as the same value, so the CE can be calculated as follows:

CE = (actual amount of metal deposited/theoretical amount of metal deposited)