What volume of H2(g), stored at 26°C at a pressure of 141 atm, would be needed to run an electric motor drawing a current of 8.4 A for 4.8 h?
To find the volume of H2 gas needed, we need to calculate the number of moles of H2 gas required.
First, let's calculate the number of coulombs (C) of charge consumed by the electric motor:
Charge (C) = Current (A) × Time (s) = 8.4 A × (4.8 h × 3600 s/h)
Now, let's calculate the number of moles of electrons consumed:
Moles of electrons = Charge (C) / Faraday's constant
The Faraday's constant is 96,485 C/mol.
Next, we need to calculate the number of moles of H2 gas produced during the electrolysis of water (2H2O → 2H2 + O2):
Using the stoichiometry, the ratio is 2 moles of H2 per mole of electrons.
So, Moles of H2 gas = Moles of electrons / 2
To find the volume of H2 gas, we will use the Ideal Gas Law equation: PV = nRT
R is the ideal gas constant with a value of 0.0821 L.atm/mol.K.
Rearranging the equation to solve for volume:
V = (n × R × T) / P
Where:
V = Volume of H2 gas (in liters)
n = Moles of H2 gas
R = Ideal gas constant
T = Temperature (in Kelvin)
P = Pressure (in atm)
Now, let's put in the values and solve for volume:
Temperature (in Kelvin) = 26°C + 273.15
n = Moles of H2 gas (calculated earlier)
P = 141 atm (given)
Substituting these values, we can calculate the volume of H2 gas.