Respuesta :
Answer: The mass of gallium produced by the electrolysis is 0.0354 grams.
Explanation:
The equation for the deposition of Ga(s) from Ga(III) solution follows:
[tex]Ga^{3+}(aq.)+3e^-\rightarrow Ga(s)[/tex]
- To calculate the total charge, we use the equation:
[tex]C=I\times t[/tex]
where,
C = charge
I = current = 0.490 A
t = time required (in seconds) = [tex]50\times 60=300s[/tex] (Conversion factor: 1 min = 60 s)
Putting values in above equation, we get:
[tex]C=0.490\times 300=147C[/tex]
- To calculate the moles of electrons, we use the equation:
[tex]\text{Moles of electrons}=\frac{C}{F}[/tex]
where,
C = charge = 147 C
F = Faradays constant = 96500
[tex]\text{Moles of electrons}=\frac{147}{96500}=1.52\times 10^{-3}mol[/tex]
- Now, to calculate the moles of gallium, we use the equation:
[tex]\text{Moles of Gallium}=\frac{\text{Moles of electrons}}{n}[/tex]
where,
n = number of electrons transferred = 3
Putting values in above equation, we get:
[tex]\text{Moles of Gallium}=\frac{1.52\times 10^{-3}}{3}=5.077\times 10^{-4}mol[/tex]
- To calculate the mass of gallium, we use the equation:
[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}[/tex]
Moles of Gallium = [tex]5.077\times 10^{-4}mol[/tex]
Molar mass of Gallium = 69.72 g/mol
Putting values in above equation, we get:
[tex]5.077\times 10^{-4}mol=\frac{\text{Mass of Gallium}}{69.72g/mol}\\\\\text{Mass of Gallium}=0.0354g[/tex]
Hence, the mass of gallium produced by the electrolysis is 0.0354 grams.
