Assuming 100% efficiency, how many kilowatt hours (kW⋅h) of electrical energy are required to produce 1.00 kg of chlorine gas by the following reaction: NaCl(aq) + H₂O(l) → NaOH(aq) + 1/2 Cl₂(g) + 1/2 H₂(g) E° = -1.36 V
To determine the amount of electrical energy required to produce 1.00 kg of chlorine gas, we need to calculate the total charge transferred during the reaction.
First, we need to determine the number of moles of chlorine gas produced. Since the molar mass of chlorine is 35.45 g/mol, the number of moles can be calculated as follows:
1.00 kg of chlorine gas = 1000 g of chlorine gas
Number of moles = Mass / Molar mass
Number of moles = 1000 g / 35.45 g/mol ≈ 28.21 mol
Next, we can use Faraday's Law to calculate the total charge transferred during the reaction. Faraday's Law states that the charge (Q) transferred during an electrochemical reaction is directly proportional to the number of moles of electrons (n) transferred:
Q = n * F
Where:
Q = charge transferred (in coulombs, C)
n = number of moles of electrons
F = Faraday's constant = 96485 C/mol (coulombs per mole)
Looking at the balanced equation, we can see that 1 mole of chlorine gas involves the transfer of 2 moles of electrons. Therefore, the number of moles of electrons transferred is equal to 2 times the number of moles of chlorine gas:
n = 2 * 28.21 mol = 56.42 mol
Now, we can calculate the total charge transferred:
Q = n * F = 56.42 mol * 96485 C/mol ≈ 5,449,829.7 C (coulombs)
Finally, to calculate the electrical energy in kilowatt-hours (kW⋅h), we can use the formula:
Energy (kW⋅h) = (Q * V) / (3600 * 1000)
Where:
Q = charge transferred (in coulombs)
V = voltage (in volts)
Here, the standard reduction potential of the reaction (E°) is given as -1.36 V. Since the reaction is an oxidation, we consider the positive value of the reduction potential:
V = -1.36 V
Plugging in the values:
Energy (kW⋅h) = (5,449,829.7 C * -1.36 V) / (3600 * 1000)
Energy (kW⋅h) ≈ -9.89 kW⋅h
Note: The negative sign in the result indicates that energy is consumed during the reaction, as expected in an electrolysis process.
Therefore, assuming 100% efficiency, approximately 9.89 kilowatt-hours (kW⋅h) of electrical energy are required to produce 1.00 kg of chlorine gas by the given reaction.