Respuesta :
2.4 × 10⁴ days the battery produce a current of 0.85 microamps.
How to find number of mole ?
To find number of moles use this expression:
Number of moles = [tex]\frac{\text{Given Mass}}{\text{Molar mass}}[/tex]
= [tex]\frac{0.75\ g}{65\ \text{g/mol}}[/tex]
= 1.15 × 10⁻² moles
It is given that battery run until 80% of the zinc is consumed.
80 % of Zn = 80% × 1.15 × 10⁻² moles
= 9.2 × 10⁻³ moles
Oxidation: Zn(s) + 2OH⁻ (aq) → ZnO (s) + H₂O (l) + 2e⁻
Reduction: Ag₂O (s) + H₂O (l) + 2e⁻ → 2Ag (s) + 2OH⁻ (aq)
From the above equation we can see that there is transfer of 2 electrons
Charge = moles of e⁻ × number of e⁻ transferred × Faraday's constant
= 9.2 × 10⁻³ moles × 2 × 9.65 × 10⁴
= 1.8 × 10² C
Now,
Current = [tex]\frac{\text{Charge in C}}{\text{time in sec}}[/tex]
Here,
Current = 0.85 microamperes
= 0.85 × 10⁻⁶ A
Charge = 1.8 × 10² C
Put the value in above formula we get
Current = [tex]\frac{\text{Charge in C}}{\text{time in sec}}[/tex]
Time taken = [tex]\frac{\text{charge}}{\text{current}}[/tex]
= [tex]\frac{1.82 \times 10^2\ C}{0.85 \times 10^{-6}\ A}[/tex]
= 2.1 × 10⁸ sec
= 2.4 × 10⁴ days
Thus from the above conclusion we can say that 2.4 × 10⁴ days the battery produce a current of 0.85 microamps.
Learn more about the Mole here: https://brainly.com/question/24322641
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