1. A current of 3.0A deposited 2.0g of a metal in 20 minutes. (a) calculate the mass of the metal deposited by 1 faraday. (b) determine the atomic mas of the metals given that it is trivalent. [1 faraday =96500c]
2. A quantity of 3.35g of a certain group III element was deposited by the passage of 10 amperes flowing for 1 hour. calculate the atomic mass of the element. [1 faraday = 96500c]
1a. coulombs = A x seconds = 3 x 20 min x (60 s/min) = 3600 C
2g x (96,500/3600) = ?
1b. 96,500 C will deposit ?grams/3 or 53.61 so
?g/3 = 53.61. Solve for x.
2 is worked similarly.
To solve these questions, we can use the relationship between current, time, and the amount of metal deposited. We'll need to use the formula:
Amount of metal deposited = (Current x Time x Atomic mass) / (Charge of 1 faraday)
Let's solve each question step by step.
1. (a) Calculate the mass of the metal deposited by 1 faraday.
We're given:
Current = 3.0A
Time = 20 minutes = 20 x 60 seconds = 1200 seconds
Mass of the metal = 2.0g
Charge of 1 faraday = 96500C
We can plug in the values into the formula:
Amount of metal deposited = (Current x Time x Atomic mass) / (Charge of 1 faraday)
Rearranging the formula to solve for the Atomic mass:
Atomic mass = (Amount of metal deposited x Charge of 1 faraday) / (Current x Time)
Plugging in the values:
Atomic mass = (2.0g x 96500C) / (3.0A x 1200s)
Canceling units and calculating:
Atomic mass = 64.1667 g/mol
Therefore, the mass of the metal deposited by 1 faraday is approximately 64.17g.
1. (b) Determine the atomic mass of the metal given that it is trivalent.
Since the metal is trivalent, it means that each atom of the metal contributes 3 units of charge. Therefore, the atomic mass will be 1/3rd of the mass calculated in part (a).
Atomic mass = (1/3) x 64.17g
Atomic mass = 21.39 g/mol
Therefore, the atomic mass of the metal, given that it is trivalent, is approximately 21.39 g/mol.
2. Calculate the atomic mass of the element.
We're given:
Current = 10A
Time = 1 hour = 1 x 60 minutes = 60 x 60 seconds = 3600 seconds
Mass of the metal = 3.35g
Charge of 1 faraday = 96500C
Following the same steps as in question 1:
Atomic mass = (Amount of metal deposited x Charge of 1 faraday) / (Current x Time)
Plugging in the values:
Atomic mass = (3.35g x 96500C) / (10A x 3600s)
Canceling units and calculating:
Atomic mass = 88.4028 g/mol
Therefore, the atomic mass of the element is approximately 88.40 g/mol.