JAMB 2024 Physics · Question 52

Find the amount of current required to deposit 0.02kg of metal in a given electrolysis for 120 seconds…

Question

Find the amount of current required to deposit 0.02kg of metal in a given electrolysis for 120 seconds. [electro chemical equivalent of the metal = 1.3 x 10 $^{-7}$ kgC $^{-1}$ ]

A.7.8 x 10 $^{-4}$ A
B.7.8 x 10 $^{-2}$ A
C.1.3 x 10 $^3$ A
D.1.3 x 10 $^5$ A

Answer: C. 1.3 x 10 $^3$ A

Explanation written with AI and checked against the answer key

Analysis

To solve this problem, we need to use Faraday’s First Law of Electrolysis, which relates the mass of a substance deposited during electrolysis to the quantity of electricity (charge) passed through the electrolyte.

Concept

Faraday's law states that the mass ( $m$ ) of a substance deposited is given by the formula:

m = zIt

Where:

$m$ = mass of the metal deposited (in kg)
$z$ = electrochemical equivalent of the metal (in kg/C)
$I$ = current (in Amperes, A)
$t$ = time (in seconds, s)

Solution

Step 1: Identify the given values

Mass ( $m$ ) = $0.02\text{ kg} = 2 \times 10^{-2}\text{ kg}$
Electrochemical equivalent ( $z$ ) = $1.3 \times 10^{-7}\text{ kg/C}$
Time ( $t$ ) = $120\text{ s}$

Step 2: Rearrange the formula to solve for current ( $I$ )

I = \frac{m}{z \times t}

Step 3: Substitute the values into the equation

I = \frac{2 \times 10^{-2}}{(1.3 \times 10^{-7}) \times 120}

Step 4: Perform the calculation First, multiply the denominator:

1.3 \times 10^{-7} \times 120 = 156 \times 10^{-7} = 1.56 \times 10^{-5}

Now, divide the numerator by the denominator:

I = \frac{2 \times 10^{-2}}{1.56 \times 10^{-5}}

I = \left(\frac{2}{1.56}\right) \times 10^{-2 - (-5)}

I \approx 1.282 \times 10^3\text{ A}

Rounding to two significant figures as presented in the options, we get approximately $1.3 \times 10^3\text{ A}$ .

Conclusion

Comparing our result to the given options, we find that it matches option C.

Exam Tip

When dealing with scientific notation in JAMB Physics, always convert your units to standard SI units first (e.g., grams to kilograms, minutes to seconds). Also, keep an eye on the powers of 10; a common mistake is miscalculating the exponent during division. Remember: when dividing, subtract the exponents ( $10^a / 10^b = 10^{a-b}$ ).

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