Question #202873

**Calculate the oxidation number of chromium in an unknown salt if the electrolysis of the salt yields 9.71g of chromium at the cathode after a current of 10A is passed through a cell for 1.5 hours.the relative atomic mass of chromium is 52.**

Expert's answer

**Solution:**

Current, I = 10 A

Time, t = 1.5 hrs = 90 min = 5400 s

Quantity of electricity, Q = I × t = (10 A) × (5400 s) = 54000 C

Mass of chromium (Cr), m = 9.71 g

Molar mass of chromium (Cr), M = 52 g/mol

Faraday's 1^{st} law can be used.

Faraday's 1^{st} law can be expressed as:

m = (Q × M) / (Z × F)

where:

m = mass of material (g)

M = molar mass of material (g/mol)

Q = quantity of electricity (C)

Z = number of electrons

F = Faraday constant, 96485 (C mol^{-1})

Thus:

Z = (Q × M) / (m × F)

Z = (54000 C × 52 g/mol) / (9.71 g × 96485 C mol^{-1}) = 2.997 = 3

Z = 3

Therefore, the oxidation number of chromium in an unknown salt is +3.

**Answer: The oxidation number of chromium (Cr) in an unknown salt is +3.**

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