A total charge of 97.4 kC passes through an electrolytic cell. Determine the quantity of substance produced in each of the following cases.
(a) the mass (in grams) of silver metal from a silver nitrate solution
?g
(b) the volume (in liters at 273 K and 1.00 atm) of chlorine gas from a brine solution (concentrated aqueous sodium chloride solution)
? L
if sum1 can tell me what equations to use i can probly do them on my own. thx!
96,485 coulombs will produce 1 equivalent weight of material.
You have 97,400 coulomgs which is
97,400/96,485 = ?? coulombs,
1 equivalent weight of Ag is the molar mass/1
1 equivalent weight of chlorine gas is 70.9 g/2. Find grams, convert to moles, and use PV = nRT to find volume.
so for the 1 equivalent weight of Ag i just divide molar mass 107.87 by 1.009 and get 106.8?? is the 1 equivalent weight in material in grams?
I wouldn't do that.
If 1 C will deposit 107.87 g, then 1.009 C should deposit less? Looks to me that it would deposit more.
i thought you were saying to divide by the 1 equivalent?
To determine the quantity of substance produced in each case, we need to use the concept of Faraday's law of electrolysis. Faraday's law states that the amount of substance produced or consumed in an electrolytic cell is directly proportional to the quantity of electric charge passed through the cell.
The formula to calculate the quantity of substance produced is as follows:
Quantity of Substance = (Charge Passed / Faraday's Constant) × Molar Mass
Now, let's solve each case separately:
(a) To find the mass of silver metal produced from a silver nitrate solution, we need to know the molar mass of silver. The molar mass of silver is 107.87 g/mol, and the Faraday's constant is approximately 96,500 C/mol.
Using the formula, we have:
Charge Passed = 97.4 kC = 97,400 C
Molar Mass of Silver (Ag) = 107.87 g/mol
Quantity of Substance (Ag) = (97,400 C / 96,500 C/mol) × 107.87 g/mol
= 108.89 g
Therefore, the mass of silver metal produced is approximately 108.89 grams.
(b) To find the volume of chlorine gas produced from a brine solution, we need to know the molar mass of chlorine. The molar mass of chlorine is 35.45 g/mol, and the Faraday's constant is the same as in the previous case, 96,500 C/mol.
Using the formula, we have:
Charge Passed = 97.4 kC = 97,400 C
Molar Mass of Chlorine (Cl₂) = 2 × 35.45 g/mol = 70.9 g/mol
Quantity of Substance (Cl₂) = (97,400 C / 96,500 C/mol) × 70.9 g/mol
= 71.58 g
To convert the mass of chlorine gas to volume at 273 K and 1.00 atm, we can use the ideal gas law, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
At 273 K and 1.00 atm, the pressure and temperature are known. The gas constant, R, is 0.0821 L·atm/(K·mol). Rearranging the ideal gas law equation gives us:
V = (nRT) / P
Using the values:
n = 71.58 g / 70.9 g/mol = 1.009 mol
R = 0.0821 L·atm/(K·mol)
P = 1.00 atm
T = 273 K
V = (1.009 mol × 0.0821 L·atm/(K·mol) × 273 K) / 1.00 atm
= 22.74 L
Therefore, the volume of chlorine gas produced is approximately 22.74 liters at 273 K and 1.00 atm.