Answered

IDNLearn.com: Your trusted platform for finding reliable answers. Find accurate and detailed answers to your questions from our experienced and dedicated community members.

A rod measuring 13.870000 x 3.640000 x 5.980000 cm was plated by means of a current of 84.780000 milliamps for 3.670000 hours. What is the thickness in millimeters of the silver deposit on the rod, given that the density of silver is 10.650000 g / cm3

Sagot :

Oladayoademosuidn

Answer:

0.024 mm

Explanation:

The quantity of charge deposited Q = It where I = current = 84.780000 mA = 0.084780000 A and t = time = 3.670000 hours = 3.670000 × 3600 s = 132120000 s.

Also Q = nF where n = number of moles of electrons silver deposited and F = Faraday's constant = 96500 C/mol

So, It = nF

n = It/F = 0.084780000 A × 132120000 s/96500 C/mol = 1120.1134 C/96500 C/mol = 0.012 mol

So, we have 0.012 mol of electrons

Our chemical equation is

Ag⁺ + e⁻ → Ag

Since 1 mol of electrons deposits 1 mol of silver atoms, then, 0.012 mol of electrons deposits 0.012 mol of silver atoms.

Since number of moles of silver atoms, n' = m/M where m = mass of silver atoms deposited and M = molar mass of silver = 107.868 g/mol

So, m = n'M

since n' = 0.012 mol,

m = 0.012 mol × 107.868 g/mol = 1.294 g

Since density of silver ρ = m/V where m = mass of silver deposited = 1.294 g and V = volume of silver deposited

V = m/ρ

Since, ρ = 10.650000 g/cm³

V = 1.294 g/10.650000 g/cm3 =

V = 0.122 cm³

Since the dimensions of the measuring rod are 13.870000 x 3.640000 x 5.980000 cm which represent its length, l, width, w and height, h respectively, the volume of silver deposited V = Ah' where A = area of the rod, lw and h' = thickness of silver deposited

So, V = Ah

V = lwh'

h' = V/lw

= 0.122 cm³/13.870000 cm x 3.640000 cm

= 0.122 cm³/50.4868 cm²

= 0.0024 cm

= 0.024 mm

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Your questions find clarity at IDNLearn.com. Thanks for stopping by, and come back for more dependable solutions.