By definition, the same current liberates masses of different substances that are proportional to the equivalent masses.
Therefore, we must determine the equivalent masse of copper, oxygen and hydrogen, so we have 31.8 g of copper, 8 g of oxygen and 1.008 g of hydrogen.
We must find first the number of eq in 0.504 g of hydrogen:
n = 0.504g/1.008(g/eq) = 0.5 eq
Now that we know the number of eq of hydrogen, we can easily calculate the mass of copper and the mass of oxygen liberated by the same current. So, we just multiplicate each equivalent mass by 0.5 eq:
Mass of copper = 31.8*0.5 = 15.9 g
Mass of oxygen = 8*0.5 = 4 g
You answer is: 15 g liberated copper and 4 g liberated oxygen.
The Faraday law of electrilysis states that for a charge Q that passed through a solution the mass of the substance liberated is
m = (Q/F)*(M/z)
where F =96485 C/mol is the Faraday constant
M is the molecular mass of substance and
z is the valence of the substance ions in solution
Thus for liberated hydrogen (z=1, M=1 g/mol) the total charge Q is
Q = m*F*z/M =0.504*96485*1/1 =46628.44 C
For Cu(2+) (z =2, M=63.5 g/mol) the liberated mass is
m=(Q/F)*(M/z) = (46628.44/96485)*(63.5/2) =15.343 g
For oxygen O(2-) (z=2, M=16 g/mol) the liberated mass is
m = (Q/F)*(M/z) =(46628/96485)*(16/2) =3.867 g
`1.008 gm` hydrogen is liberated by the passage of `96500 C ` electric charge.
`0.504 gm` hydrogen is liberated by the passage of `(96500*0.504)/1.008 C= 48250 C` electric charge.
For `Cu^(2+)` solution:
`2*96500 C ` electric charge deposists `63.5 gm` copper from `Cu^(2+)` solution
Hence, `48250 C` electric charge deposists `(63.5*48250)/(2*96500) =15.875` `gm` copper from `Cu^(2+)` solution
`2*96500 C` electric charge liberates 16 gm copper from `Cu^(2+) ` solution
Hence, `48250 C` electric charge liberates `(16*48250)/(2*96500) ` =`4 gm` oxygen from `Cu^(2+)` solution
Therefore, 15.875 gm copper and 4 gm oxygen from `Cu^(2+) ` solution are liberated by the same current that liberates 0.504 g hydrogen in 2 hours.