Calculate the relative atomic mass of a divalent metal M if 0.66 g of it is deposited by passing a current of…

Question

Calculate the relative atomic mass of a divalent metal M if 0.66 g of it is deposited by passing a current of 1.35 A for 1500 s.

ScanSolve AI Tutor · Accepted Answer

This problem requires applying Faraday's First Law of Electrolysis.

Given:

Mass of metal M deposited ( $m$ ) = 0.66 g
Current ( $I$ ) = 1.35 A
Time ( $t$ ) = 1500 s
Metal M is divalent, meaning its valency ( $z$ ) = 2.
Faraday's constant ( $F$ ) = 96500 C/mol (This is a standard constant you should know for electrolysis problems).

Calculate the total quantity of electricity (charge, $Q$ ) passed.
The formula for charge is $Q = I \times t$ .
$Q = 1.35 \text{ A} \times 1500 \text{ s}$ $Q = 2025 \text{ C}$
Use Faraday's First Law to calculate the Relative Atomic Mass (RAM) of M.
Faraday's First Law states that the mass deposited ( $m$ ) is given by:
$m = \frac{\text{RAM} \times Q}{z \times F}$
We need to find RAM (which is the molar mass, $M$ ). Rearrange the formula:
$\text{RAM} = \frac{m \times z \times F}{Q}$
Substitute the known values:
$\text{RAM} = \frac{0.66 \text{ g} \times 2 \times 96500 \text{ C/mol}}{2025 \text{ C}}$ $\text{RAM} = \frac{127380}{2025} \text{ g/mol}$ $\text{RAM} \approx 62.9037 \text{ g/mol}$
Rounding to three significant figures:
$\text{RAM} \approx 62.9 \text{ g/mol}$
The relative atomic mass (RAM) of M is $\text{62.9}$ .

Calculate the relative atomic mass of a divalent metal M if 0.66 g of it is deposited by passing a current of 1.35 A for 1500 s.