The density of copper is 8.94gm/L.Find the charge needed to plate an area of 10*10 cm2 to a thickness of 1/100 cm using CUSO4 soln as electrolyte.

To determine the charge needed to plate copper onto a surface, we can use Faraday's laws of electrolysis. The process involves calculating the mass of copper required for plating, and then converting that mass into charge using the relationship between charge, moles of electrons, and the Faraday constant. Let’s break this down step by step.

Step 1: Calculate the Volume of Copper to be Plated

First, we need to find the volume of copper that corresponds to the desired thickness. The area to be plated is given as 10 cm x 10 cm, which equals 100 cm². The thickness of the copper layer is 1/100 cm, or 0.01 cm.

The volume (V) of copper can be calculated using the formula:

V = Area × Thickness

Substituting the values:

V = 100 cm² × 0.01 cm = 1 cm³

Step 2: Calculate the Mass of Copper

Next, we need to find the mass of copper that corresponds to this volume. We know the density of copper is 8.94 g/cm³. The mass (m) can be calculated using the formula:

m = Density × Volume

Substituting the values:

m = 8.94 g/cm³ × 1 cm³ = 8.94 g

Step 3: Convert Mass to Moles

To find out how many moles of copper we have, we use the molar mass of copper, which is approximately 63.55 g/mol. The number of moles (n) can be calculated as follows:

n = m / Molar Mass

Substituting the values:

n = 8.94 g / 63.55 g/mol ≈ 0.140 mol

Step 4: Calculate the Charge Required

In electrolysis, copper ions (Cu²⁺) gain two electrons (2e⁻) to become solid copper. Therefore, for every mole of copper deposited, 2 moles of electrons are required. The total moles of electrons (n_e) needed can be calculated as:

n_e = 2 × n

Substituting the values:

n_e = 2 × 0.140 mol = 0.280 mol

Now, we can find the total charge (Q) using Faraday's constant, which is approximately 96485 C/mol. The charge can be calculated using:

Q = n_e × Faraday's Constant

Substituting the values:

Q = 0.280 mol × 96485 C/mol ≈ 27000 C

Final Result

The total charge required to plate an area of 10 cm x 10 cm to a thickness of 1/100 cm using a CuSO₄ solution as the electrolyte is approximately 27000 Coulombs.