First, let's determine the amount of oxygen generated during the electrolysis in terms of moles. We are given a volume of
100‌ml which is equivalent to
0.1L.
At standard temperature and pressure (STP), 1 mole of any ideal gas occupies
22.4L. Therefore, the number of moles of oxygen gas
(O2) can be calculated as:
In the electrolysis of water, the reaction at the anode (for oxygen) is:
2H2O(l)⟶O2(g)+4H+(aq)+4e−According to the balanced chemical equation,
1‌mol of
O2 requires
4‌mol of electrons. Therefore, the amount of charge needed to produce
0.004464‌mol of
O2 can be calculated using Faraday's first law of electrolysis, which states that the amount of substance liberated at an electrode is directly proportional to the quantity of electricity passed through the electrolyte. This gives us:
Q=n×F×zWhere:
n is the number of moles of
O2,
F is the Faraday constant
(96500C/‌mol of electrons), and
z is the number of moles of electrons per mole of
O2 (which is 4).
Let's calculate the total charge
(Q) :
Q=0.004464‌mol×96500C/‌mol×4=1721.792C To find the current in amperes, we use the relation between the charge
(Q), current
(I), and time
(t) :
I=‌We are given that the time duration is 2 hours, so converting this to seconds gives us:
t=2‌ hours ‌×3600‌ seconds ‌/‌ hour ‌=7200‌ seconds ‌Now we can calculate the required electric current
(I) :
I=‌≈0.2391AThis value aligns very closely with Option
D, which is
0.2393A. Hence, the correct answer is:
Option D:
0.2393A