During electrolysis, 2.0 g of a metal is deposited using a current of 0.4A in 6 hours. The mass of the same metal which can be deposited using a current of 1.5A in 2 hour is?
charge = current * time
2.0 g /(0.4 A * 6 h) = m / (1.5 A * 2 h)
To solve this problem, we can use Faraday's Law of Electrolysis, which states that the amount of substance deposited during electrolysis is directly proportional to the electric charge passed through the electrolyte.
The formula to calculate the amount of substance deposited is:
Mass = (Current × Time) / Faraday's Constant
First, let's calculate the amount of substance deposited using the given values:
Current = 0.4A
Time = 6 hours
We need to determine the amount of substance in grams, so we should convert the given current and time to SI units:
Current = 0.4A
Time = 6 hours = 6 × 3600 seconds = 21,600 seconds
Now, let's calculate the amount of substance deposited:
Mass = (0.4A × 21,600 seconds) / Faraday's Constant
Faraday's Constant is a known constant equal to 96,485 C/mol.
Since we need to find the mass in grams, we also need to convert Faraday's Constant to C/g:
Faraday's Constant = 96,485 C/mol × (1 mol/Atomic Mass)
Given that the atomic mass of the metal is not provided, we cannot directly calculate the mass of the metal deposited. We need the atomic mass to convert Faraday's Constant to C/g.
However, we can determine the ratio between the currents and times in order to calculate the mass of the metal deposited using different current and time values.
Let's define the ratio as:
Ratio = (Current 2 / Current 1) × (Time 2 / Time 1)
Now, we can use this ratio to calculate the unknown mass. Let's consider the second scenario:
Current 1 = 0.4A
Time 1 = 6 hours
Current 2 = 1.5A
Time 2 = 2 hours
Ratio = (1.5A / 0.4A) × (2 hours / 6 hours)
Simplifying the ratio:
Ratio = 3.75
(Current 2 / Current 1) = 3.75
(Time 2 / Time 1) = (2 / 6) = 0.3333
Now, using the given mass from the first scenario (2.0 g), we can calculate the mass using the second scenario:
Mass 2 = Mass 1 × Ratio = 2.0 g × 3.75 = 7.50 g
Therefore, the mass of the metal that can be deposited using a current of 1.5A in 2 hours is 7.50 grams.