To determine the amount of current needed in the first reaction to produce enough intermediate for 100 grams of pure hydrogen peroxide (H2O2) per hour, we need to break down the problem into manageable steps. We will analyze the reactions involved, calculate the moles of H2O2 required, and then use Faraday's laws of electrolysis to find the necessary current.
Understanding the Reactions
The first reaction involves the electrolytic decomposition of ammonium hydrogen sulfate (NH4HSO4) to produce ammonium persulfate ((NH4)2S2O8). The overall reaction can be simplified as follows:
- 2 NH4HSO4 → H2 + (NH4)2S2O8
In the second reaction, ammonium persulfate reacts with water to produce ammonium hydrogen sulfate and hydrogen peroxide:
- (NH4)2S2O8 + 2 H2O → 2 NH4HSO4 + H2O2
Calculating Moles of H2O2
To find out how much current is needed, we first need to calculate the number of moles of H2O2 required to yield 100 grams. The molar mass of H2O2 is approximately 34 grams per mole.
Using the formula:
Number of moles = mass (g) / molar mass (g/mol)
We can calculate:
Number of moles of H2O2 = 100 g / 34 g/mol ≈ 2.94 moles
Relating Moles to Electrons
From the second reaction, we see that 1 mole of (NH4)2S2O8 produces 1 mole of H2O2. Therefore, to produce 2.94 moles of H2O2, we need 2.94 moles of (NH4)2S2O8. The first reaction produces (NH4)2S2O8 from NH4HSO4, and we need to know how many moles of electrons are involved in this process.
In the electrolytic reaction, the formation of 1 mole of (NH4)2S2O8 from 2 moles of NH4HSO4 involves the transfer of 2 moles of electrons (since each sulfate ion requires 2 electrons for its formation). Therefore, to produce 2.94 moles of (NH4)2S2O8, we need:
Electrons required = 2.94 moles × 2 = 5.88 moles of electrons
Using Faraday's Law
Faraday's law states that the amount of substance produced at an electrode during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte. The charge (Q) can be calculated using:
Q = n × F
Where:
- n = number of moles of electrons
- F = Faraday's constant (approximately 96485 C/mol)
Substituting the values:
Q = 5.88 moles × 96485 C/mol ≈ 566,000 C
Calculating Current
Current (I) can be calculated using the formula:
I = Q / t
Where t is the time in seconds. Since we want to produce this amount of H2O2 per hour, we convert hours to seconds:
t = 1 hour = 3600 seconds
Now we can calculate the current:
I = 566,000 C / 3600 s ≈ 157.22 A
Adjusting for Current Efficiency
Since the current efficiency is given as 50%, we need to adjust our current calculation accordingly. The actual current required will be double the calculated value:
Actual Current = 157.22 A / 0.50 = 314.44 A
Therefore, to produce 100 grams of pure H2O2 per hour, you would need to use approximately 314.44 Amperes of current in the first electrolytic reaction, assuming a current efficiency of 50%.
