What volume of hydrogen gas at standard temperature and pressure can be collected from the electrolysis of water using a current of 100mA for a period of 3 hours?
I know that the answer is 0.125 L but I don't know how to approach the problem.
I multiplied 100*10^-3 by 3600 to get 10800 C and then converted that into moles which came out to be .06
Where am I wrong and how should I approach the problem? Please help.
3 hours * 3600 seconds/hour = 10800 seconds
10800 seconds * 0.1 amps = 1080 Coulombs
H2O --> 2H+ + O--
1 mol electrons = 96,500 Coulombs
so
1080 C * 1/96500 = .0112 mol electrons
looking at equation, we need 2 mol electrons for every mol of H2
so we get
.0056 mol of H2
.0056 * 22.4 L/mol at STP = .125 Liter
by the way
http://www.quora.com/How-much-water-can-you-split-into-hydrogen-and-oxygen-using-electrolysis-with-one-kilowatt-hour-of-electricity
To solve this problem, you need to follow the steps correctly. Let's go through the solution step by step:
Step 1: Determine the number of electrons transferred in the electrolysis process.
Since hydrogen gas is produced through the electrolysis of water, we need to consider the balanced equation for this reaction:
2H₂O(l) → 2H₂(g) + O₂(g)
From the equation, we can see that for every 2 moles of water decomposed, 1 mole of oxygen gas and 2 moles of hydrogen gas are produced. The electrolysis of water consists of the transfer of 4 electrons, which are used to produce 1 mole of hydrogen gas.
Step 2: Calculate the total charge.
You correctly calculated the total charge by multiplying the current (100mA) by the time (3 hours). However, you made a mistake in converting the charge to moles.
Correct calculation:
Total charge = current × time
= 100mA × 3 hours
= 0.1A × 3 × 3600s [since 1 hour = 3600 seconds]
= 1080 C
Step 3: Convert charge to moles of electrons.
To convert charge to moles of electrons, you need to use Faraday's constant, which represents the amount of charge carried by one mole of electrons. Its value is approximately 96,485 C/mol.
Total moles of electrons = Total charge (C) / Faraday's constant (C/mol)
= 1080 C / 96485 C/mol
≈ 0.0112 mol
Step 4: Convert moles of electrons to moles of hydrogen gas.
Since 4 moles of electrons produce 1 mole of hydrogen gas (according to the balanced equation from step 1), we can set up a ratio:
Moles of hydrogen gas = Total moles of electrons (mol) / 4
= 0.0112 mol / 4
= 0.0028 mol
Step 5: Convert moles of hydrogen gas to volume at standard temperature and pressure (STP).
At STP, 1 mole of any ideal gas occupies 22.4 liters. Therefore, we can set up another ratio:
Volume of hydrogen gas (liters) = Moles of hydrogen gas (mol) × 22.4 L/mol
= 0.0028 mol × 22.4 L/mol
= 0.06272 L
≈ 0.063 L (rounded to three decimal places)
So, the correct answer is approximately 0.063 L, not 0.125 L as you mentioned. It seems you made a mistake in one of the conversion steps.