What volume of a chlorine gas (measured at stp ) would be liberated by a current of 2.2mp following for the period of 1.8 hours through an aqueous solution of silver chloride

To determine the volume of chlorine gas liberated by a current of 2.2 mA over a period of 1.8 hours through an aqueous solution of silver chloride, we can use Faraday's laws of electrolysis. Let's break this down step by step.

Understanding the Electrolysis Process

During electrolysis, when a direct current passes through an electrolyte, chemical reactions occur at the electrodes. In the case of silver chloride (AgCl), the electrolysis will produce chlorine gas (Cl₂) at the anode. The relevant half-reaction at the anode can be represented as:

• 2Cl^- → Cl₂ + 2e^-

Calculating the Charge Passed

First, we need to calculate the total charge (Q) that has passed through the solution. The formula for charge is:

Q = I × t

Where:

• I = current in amperes (A)
• t = time in seconds (s)

Given that the current is 2.2 mA, we convert this to amperes:

I = 2.2 mA = 2.2 × 10^-3 A

Next, we convert the time from hours to seconds:

t = 1.8 hours × 3600 seconds/hour = 6480 seconds

Now, we can calculate the total charge:

Q = 2.2 × 10^-3 A × 6480 s = 14.256 C

Determining Moles of Chlorine Gas Produced

According to Faraday's laws, 1 mole of electrons (approximately 96500 C) is required to produce 1 mole of chlorine gas. Since the half-reaction shows that 2 moles of electrons are needed to produce 1 mole of Cl₂, we can find the moles of Cl₂ produced using the formula:

n(Cl₂) = Q / (2 × F)

Where:

• F = Faraday's constant ≈ 96500 C/mol

Substituting the values:

n(Cl₂) = 14.256 C / (2 × 96500 C/mol) ≈ 0.0000740 mol

Calculating the Volume of Chlorine Gas at STP

At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. Therefore, we can find the volume of chlorine gas produced:

V = n × 22.4 L/mol

Substituting the number of moles:

V = 0.0000740 mol × 22.4 L/mol ≈ 0.00166 L

To convert this to milliliters:

V ≈ 1.66 mL

Final Result

In summary, the volume of chlorine gas liberated by a current of 2.2 mA over a period of 1.8 hours through an aqueous solution of silver chloride is approximately 1.66 mL at STP. This calculation illustrates the relationship between electric current, time, and the amount of gas produced during electrolysis, showcasing the principles of electrochemistry in action.