A student designs an ammeter (a device that measures electrical current) that is based on the electrolysis of water into hydrogen and oxygen gases. When electrical current of unknown magnitude is run through the device for 1.00 min , 15.4 mL of water-saturated H2(g) is collected. The temperature and pressure of the system are 25 ∘C and 715 torr.
To calculate the electrical current, we need to use Faraday's law of electrolysis, which states that the amount of substance produced or consumed is directly proportional to the amount of electrical charge passed through it.
Step 1: Calculate the number of moles of H2 gas produced.
We can use the ideal gas law to calculate the number of moles of H2 gas.
PV = nRT
Where:
P = pressure = 715 torr (convert to atm by dividing by 760 torr/atm)
V = volume = 15.4 mL = 0.0154 L
n = number of moles of H2 gas
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature = 25 °C = 298 K
Substituting the values into the equation:
(715/760) * 0.0154 = n * 0.0821 * 298
Now solve for n:
n ≈ 1.42 * 10^-3 moles
Step 2: Calculate the number of coulombs of charge passed.
Since water is composed of two moles of H atoms for every mole of H2 gas produced, we need to divide the number of moles by 2 to get the number of moles of H atoms.
nH = (1.42 * 10^-3) / 2 ≈ 7.11 * 10^-4 moles
According to Faraday's law, one mole of electrons (6.022 x 10^23) carries one Faraday of charge (96485 coulombs). So, we can multiply the number of moles of H atoms by Avogadro's number and the Faraday constant to get the total charge passed in coulombs.
Q = nH * (6.022 x 10^23) * (96485 C/mol)
Now substitute the value of nH and calculate Q:
Q ≈ (7.11 x 10^-4) * (6.022 x 10^23) * (96485)
Q ≈ 4.11 x 10^20 coulombs
Step 3: Calculate the electrical current.
The electrical current (I) is the total charge passed (Q) divided by the time (t).
I = Q / t
Given that the time is 1.00 min or 60 seconds, substitute the values and calculate I:
I = (4.11 x 10^20) / (60)
I ≈ 6.85 x 10^18 amperes (A)
Therefore, the electrical current passing through the device is approximately 6.85 x 10^18 A.
To begin, we need to find the amount of hydrogen gas produced during the electrolysis of water. The balanced equation for the electrolysis of water is:
2H₂O(l) → 2H₂(g) + O₂(g)
From the equation, we see that for every 2 molecules of water, we obtain 2 molecules of hydrogen gas (H₂).
To find the number of moles of H₂ gas produced, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atm (convert torr to atm by dividing by 760)
V = volume in liters (convert mL to liters by dividing by 1000)
n = number of moles
R = ideal gas constant (0.0821 L·atm / mol·K)
T = temperature in Kelvin (convert Celsius to Kelvin by adding 273.15)
Given information:
Volume of H₂ gas (V) = 15.4 mL = 15.4 / 1000 L = 0.0154 L
Temperature (T) = 25°C = 25 + 273.15 = 298.15 K (Kelvin)
Pressure (P) = 715 torr / 760 = 0.9408 atm
Now we can rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
Plugging in the given values:
n = (0.9408 atm) * (0.0154 L) / (0.0821 L·atm/mol·K * 298.15 K)
Calculating this will give you the moles of hydrogen gas produced.
Finally, to find the electrical current (in amperes) used during the electrolysis, we can use Faraday's law of electrolysis:
Q = n * F
Where:
Q = charge in Coulombs
n = number of moles of electrons transferred (equal to the number of moles of hydrogen produced)
F = Faraday's constant (96485 C/mol)
Rearranging the equation:
I = Q / t
Where:
I = current (in amperes)
Q = charge (in Coulombs)
t = time (in seconds)
Plugging in the known values (n, F, and time), you will be able to calculate the electrical current used in the device.
Use PV=nRT to find n, the moles of hydrogen gas.
V= 1.68x10^-2 L
P= 715 torr-VP of water at 25C (about 25 torr; look it up in Wikipedia)
T= 298.2K
R = Applicable value for the above units.