In the electrolysis of water, 3490 hour will it take to produce 165.0 L of H2 at 1.0 atm and 273 K using an electrolytic cell through which the current is 113.0 mA.
The ideal gas law states that the pressure of gas is directly proportional to the volume and temperature of the gas.
It is expressed as
PV = nRT
where,
P = Pressure
V = Volume in liters
n = number of moles of gas
R = Ideal gas constant
T = Temperature in kelvin
Here,
P = 1.0 atm
V = 165.0 L
R = 0.0821 atm. L/mol.K (Ideal gas constant)
T = 273 K
n = ?
Now put the value in above expression, we get
PV = nRT
1.0 atm × 165.0 L = n × 0.0821 atm. L/mol.K × 273 K
165.0 atm. L = n × 22.4 atm. L/mol
[tex]n = \frac{165.0\ \text{atm. L}}{22.4\ \text{atm. L/mol}}[/tex]
n = 7.36 mol
The reaction is
2H⁺ + 2e⁻ → H₂
1 mol of electrons is produced from 96500 C
So,
[tex]96500 \frac{C}{\text{mol} \times e} \times 2e \times 7.36\ \text{mol}[/tex]
= 1,420,480 C
Convert milliampere to C/s
1mA = 0.001 C/s
113.0 mA = 113.0 × 0.001
= 0.113 c/s
The relation between current, charge and time is expressed as:
[tex]I = \frac{Q}{t}[/tex]
where,
I = Current
Q = Charge in Coulomb
t = time
Now put the value in above formula we get
[tex]I = \frac{Q}{t}[/tex]
[tex]= \frac{1,420,480\ C}{0.113\ C/s}[/tex]
= 12,570,619.469 s
= 3490 hour
Thus from the above conclusion we can say that In the electrolysis of water, 3490 hour will it take to produce 165.0 L of H2 at 1.0 atm and 273 K using an electrolytic cell through which the current is 113.0 mA.
Learn more about the Ideal Gas Law here: https://brainly.com/question/25290815
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