Question

Part A:

How many coulombs are required to plate a layer of chromium metal 0.24 mm thick on an auto bumper with a total area of 0.29 m2 from a solution containing CrO2−4? The density of chromium metal is 7.20 g/cm3. Express your answer using two significant figures. Q = ______ C

Part B:

What current flow is required for this electroplating if the bumper is to be plated in 16.8 s ? Express your answer using two significant figures.

Answer 1

A) Thickness, h = 0.24 mm = 0.24 x 10^-3 m

Total area, A = 0.29 m²

Volume = A X h = 0.29 m² x 0.24 x 10^-3 m = 0.0696 x 10^-3 m³ (1 m³ = 10⁶ cm³) = 0.0696 x 10^-3 x 10⁶ cm³ = 69.6 cm³

Density = 7.20 g/cm³ = mass/volume

Mass of chromium metal = Volume x density = 7.20 g/cm³ x 69.6 cm³ = 501.12 g

Molar mass of chromium = 52 g/mol

No. of moles of chromium = Mass of chromium/molar mass = 501.12 g/52 g/mol = 9.64 moles

chromate ion : CrO₄^-2(charge of chromium = x + 2 x-4 = -2 ==> x-8 = -2 , x = -2+8 = +6), Cr⁺⁶ this shows that it require 6 electrons to reduce it to Cr metal

Number of electrons per 1 mole of Chromium = 6

then number of electrons for 9.64 moles = 9.64 x 6 = 57.84 mole of electrons.

1 mole of electron contain Avogadro number of electrons i.e 6.023 x 10²³ electrons

57.84 mole of electrons -----------> 57.84 x 6.023 x 10²³ = 348.37 x 10²³ electrons = 3.484 x 10²⁵ electrons

6.24 x 10¹⁸ electrons == 1 coulomb (1C)

3.484 x 10²⁵ electrons == C coulombs   

C = 3.484 X 10²⁵ electrons x 1 C / 6.24 x 10¹⁸ = 0.55834 x 10⁷ C = 5.58 X 10⁶ C = 5.6 X 10⁶ C (2 significant numbers)

B) current flow in amperes, i = Number of coulombs per time = coulomb/sec = q/t

time = 16.8 secs

i = q/t = 5.6 X 10⁶ C /16.8 s = 0.3333 x 10⁶ amps = 330000 amps (2 significant numbers)