(1) The same quantity of electricity is passed through 2voltameters connected in series, one copper voltmeter with copper electrode in a copper(ii) tetraoxosulphate(vi) solution. The other platinum electrode in a dilute solution of tetraoxosulphate (vi) acid. 500cm³ of dry hydrogen gas measured at 20°C and 720mmHg are collected in one voltmeter. What mass of copper will be deposited on the cathode of the other? (Cu=64,H=1,Faraday's constant 96500Cmol-1,molar volume =22.4dm³..
(2) A metal of RAM 27 was deposited by electrolysis. If 0.176g of the metal was deposited on the cathode when a current of 0.15A flows for 7/2 hours, what's the charge on the cathode of this metal? (Faraday's constant =96500Cmol-1)...
Solution to the questions above
M2=1.26g
(1) To find the mass of copper deposited on the cathode, we can use Faraday's laws of electrolysis.
1. Calculate the number of moles of hydrogen gas collected:
Moles of H2 = (Volume of H2) / (Molar volume)
= (500 cm³) / (22.4 dm³)
= 22.32 dm³
2. Calculate the charge passed through the copper voltmeter:
Charge = (Moles of H2) * (2 Faraday's constants)
= (22.32 dm³) * (2 * 96500 C mol⁻¹)
3. Use Faraday's law to find the mass of copper deposited:
Mass of Copper = (Charge) / (Number of Faraday's constants) * (Atomic mass of copper)
= (Charge) / (96500 C mol⁻¹) * (64 g mol⁻¹)
(2) To find the charge on the cathode, we can use Faraday's laws of electrolysis.
1. Calculate the number of moles of the deposited metal:
Moles of metal = (Mass of metal) / (RAM of metal)
= 0.176 g / 27 g mol⁻¹
2. Calculate the charge passed through the cathode:
Charge = (Moles of metal) * (Faraday's constant)
= (0.176 g / 27 g mol⁻¹) * 96500 C mol⁻¹
Note: Make sure to convert the given time of 7/2 hours to hours or seconds if necessary.
Please let me know if you need any further assistance.
To solve these problems, we need to understand the principles of electrolysis and use the concept of Faraday's laws.
(1) In electrolysis, the amount of substance deposited or produced is directly proportional to the electric charge passed through the electrolyte. This can be determined using Faraday's laws. In this case, we are given the volume of hydrogen gas collected in one voltmeter as 500cm³.
To find the mass of copper deposited on the cathode, we need to follow these steps:
Step 1: Calculate the number of moles of hydrogen gas collected.
We can use the ideal gas law equation: PV = nRT
P = 720mmHg = 720/760 atm (converting to atm)
V = 500cm³ = 500/1000 = 0.5 dm³ (converting to dm³)
T = 20°C + 273.15 = 293.15K (converting to Kelvin)
R = 0.0821 atm·dm³/mol·K (gas constant)
Given the molar volume (22.4 dm³) is at standard temperature and pressure (STP), we can set up a proportion:
(0.5 dm³) / (22.4 dm³) = n / 1 mol
Solving for n (number of moles):
n = 0.5 dm³ * (1 mol / 22.4 dm³)
n ≈ 0.0223 mol
Step 2: Determine the number of electrons involved in the reduction of one mole of hydrogen ions.
In this case, we can look at the balanced equation:
2H⁺(aq) + 2e⁻ → H₂(g)
From the equation, we see that 2 moles of electrons are involved in the reduction of 2 moles of hydrogen ions.
Step 3: Calculate the number of electrons passed through the circuit.
Since 1 mole of hydrogen gas corresponds to 2 moles of electrons, the number of electrons passed through the circuit is:
electrons = 2 * n (moles of hydrogen gas)
electrons = 2 * 0.0223 mol
Step 4: Use Faraday's constant to determine the charge passed through the circuit.
Faraday's constant tells us that 1 mole of electrons corresponds to 96500 Coulombs of charge.
So, the total charge passed through the circuit can be calculated as:
charge (Coulombs) = electrons * Faraday's constant
charge (Coulombs) = (2 * 0.0223 mol) * 96500 C/mol
Step 5: Calculate the mass of copper deposited on the cathode.
According to Faraday's second law, the mass of a substance deposited or released during electrolysis is directly proportional to the amount of charge passed through the circuit.
The molar mass of copper (Cu) is 64 g/mol.
So, we can set up a proportion:
charge (Coulombs) / 96500 C/mol = mass of copper (g) / 64 g/mol
Solving for mass of copper (g):
mass of copper (g) = (charge (Coulombs) * 64 g/mol) / 96500 C/mol
Now, you can substitute the calculated values into the equation to obtain the mass of copper deposited on the cathode.
(2) Similarly, in this problem, we need to apply Faraday's laws.
Step 1: Convert the given mass of the metal (0.176g) to moles.
To do this, we divide the mass by the molar mass of the metal (RAM - Relative Atomic Mass).
moles of metal = mass of metal (g) / molar mass of metal (g/mol)
Step 2: Calculate the number of electrons passed through the circuit.
Since 1 mole of electrons corresponds to 96500 Coulombs of charge, we can use Faraday's constant.
electrons = moles of metal * 96500 C/mol
Step 3: Calculate the charge passed through the circuit.
The charge can be obtained by multiplying the number of electrons by Faraday's constant.
charge (Coulombs) = electrons * Faraday's constant
Now, you can substitute the known values into the equation to find the charge on the cathode.
Remember to use the correct units and follow the steps carefully to obtain accurate results.