Question

If the total electricity required to deposit 1 mole of a metal M is equal to that of 10.7 amperes of current for 10 hours. The equivalent weight of the metal is (atomic weight = M u)

• A. M
• B. M/2
• C. M/3
• D. M/4

Hint:

Total charge $Q = I \times t$ (ensure $t$ is in seconds).
Charge required to deposit 1 mole of M$^{n+}$ is $nF$ coulombs.
Faraday's constant $F \approx 96500$ C/mol of electrons.
Equivalent weight $E = \text{Atomic Weight} / \text{Valency } (n)$.
From $Q=nF$, determine $n$. Then find $E$.

Answer 1

The Correct Option is D

The total charge ($Q$) passed is given by $Q = I \times t$, where $I$ is current in amperes and $t$ is time in seconds. Given current $I = 10.7 \text{ amperes}$. Time $t = 10 \text{ hours} = 10 \times 60 \times 60 \text{ seconds} = 10 \times 3600 \text{ s} = 36000 \text{ s}$. Total charge $Q = 10.7 \text{ A} \times 36000 \text{ s} = 385200 \text{ Coulombs (C)}$. According to Faraday's laws of electrolysis, the amount of substance deposited is proportional to the quantity of electricity passed. To deposit 1 mole of a metal M from its ion M$^{n+}$, the charge required is $n \times F$, where $n$ is the valency (charge number) of the metal ion and $F$ is Faraday's constant ($F \approx 96485 \text{ C/mol}$, often approximated as $96500 \text{ C/mol}$). The problem states that the electricity $Q = 385200 \text{ C}$ is required to deposit 1 mole of metal M. So, $Q = nF$. $385200 \text{ C} = n \times F$. Let's use $F \approx 96500 \text{ C/mol}$. $n = \frac{Q}{F} = \frac{385200}{96500}$. $n = \frac{3852}{965}$. $3852 / 965 \approx 3.9917... \approx 4$. So, the valency of the metal ion $n \approx 4$. The equivalent weight ($E$) of an element is its atomic weight ($A_w$) divided by its valency ($n$). $E = \frac{A_w}{n}$. The problem states the atomic weight is M u (let's use $A_w = M_{atomic}$ to avoid confusion with the metal symbol M). So, Equivalent weight $E = \frac{M_{atomic}}{n}$. Since $n \approx 4$, the equivalent weight $E = \frac{M_{atomic}}{4}$. If the atomic weight is denoted by the symbol M itself (as in the options), then $E = \text{M}/4$. This matches option (d). Let's check if the value $10.7$ A is related to silver (atomic weight $\approx 107.8$, often rounded to 108). Equivalent weight of silver is $107.8/1 = 107.8$. Not directly relevant here except if it's a hint for $F$. $10.7 \text{ A} \times 10 \text{ h} = 107 \text{ Ah}$. $1 \text{ Ah} = 3600 \text{ C}$. $Q = 107 \times 3600 = 385200 \text{ C}$. This is exactly $4 \times 96300$. If $F=96300$, then $n=4$. If $F=96485$, $n=385200/96485 = 3.992$. If $F=96500$, $n=385200/96500 = 3.9917$. All these point to $n=4$ being the integer valency. \[ \boxed{\text{M/4}} \]