In the electrolysis of aqueous NaCl, how many grams of Cl2 are generated by a current of 3.25 amperes flowing for 500 minutes?
an ampere is a Coulomb per second
there are 6.242E18 electrons in a Coulomb
moles of electrons = (6.242E18 * 3.25 * 500 * 60) / 6.02E23
it takes two electrons to generate a Cl2 molecule
find the moles of electrons
... divide by two to find the moles of Cl2
multiply by the molar mass of Cl2 to find the grams
To determine the number of grams of Cl2 generated in the electrolysis of aqueous NaCl, we need to follow these steps:
Step 1: Calculate the total charge (Q) in Coulombs.
The charge (Q) can be calculated using the equation:
Q = I × t
Where:
Q = charge in coulombs (C)
I = current in amperes (A)
t = time in seconds (s)
Given:
I = 3.25 amperes
t = 500 minutes
To convert minutes to seconds, multiply the number of minutes by 60:
t = 500 minutes × 60 seconds/minute = 30000 seconds
Now we can calculate Q:
Q = 3.25 amperes × 30000 seconds = 97500 Coulombs
Step 2: Calculate the moles of electrons (n) transferred.
In the electrolysis of 1 mole of any ion, the number of moles of electrons transferred (n) is equal to the magnitude of its charge in coulombs (Q). Since each mole of Cl2 requires 2 moles of electrons, we divide the charge (Q) by the Faraday constant (F) to find the moles of electrons:
n = Q / F
Where:
n = moles of electrons transferred (mol)
Q = charge in coulombs (C)
F = Faraday constant = 96500 C/mol
Substituting the given values:
n = 97500 C / 96500 C/mol ≈ 1.01 mol
Step 3: Calculate the mass of Cl2 generated.
Since we know that 2 moles of electrons are required to produce 1 mole of Cl2, and the molar mass of Cl2 is approximately 71 g/mol, we can now calculate the mass of Cl2 produced:
mass of Cl2 = moles of electrons × (1 mol Cl2 / 2 mol electrons) × molar mass of Cl2
mass of Cl2 = 1.01 mol × (1 mol Cl2 / 2 mol electrons) × 71 g/mol ≈ 35.92 g
Therefore, approximately 35.92 grams of Cl2 are generated by a current of 3.25 amperes flowing for 500 minutes in the electrolysis of aqueous NaCl.
To solve this problem, we need to use Faraday's laws of electrolysis. According to Faraday's law of electrolysis, the amount of substance produced (in moles) is directly proportional to the amount of electric charge passed through the electrolyte.
The formula to calculate the amount of substance produced during electrolysis is:
moles = (current × time) / (96,485 coulombs/mol)
Where:
- current is the electric current in amperes (A)
- time is the time in seconds (s)
- 96,485 is the Faraday constant (coulombs per mole)
First, we need to convert the time from minutes to seconds:
500 minutes × 60 seconds/minute = 30,000 seconds
Now, we can calculate the moles of Cl2 produced:
moles = (3.25 A × 30,000 s) / 96,485 C/mol
moles = 0.9997 mol
The balanced equation for the electrolysis of aqueous NaCl is:
2 NaCl (aq) + 2 H2O (l) → Cl2 (g) + H2 (g) + 2 NaOH (aq)
From the balanced equation, we can see that for every 1 mole of Cl2 produced, we have 2 moles of NaCl.
Therefore, the moles of NaCl consumed are also 0.9997 mol.
Now, we can calculate the molar mass of Cl2:
molar mass of Cl2 = 35.453 g/mol
Finally, we can calculate the mass of Cl2 produced:
mass of Cl2 = moles of Cl2 × molar mass of Cl2
mass of Cl2 = 0.9997 mol × 35.453 g/mol
mass of Cl2 ≈ 35.437 g
Therefore, approximately 35.437 grams of Cl2 are generated by a current of 3.25 amperes flowing for 500 minutes.