What mass of zinc will be deposited from A solution of zinc 2 chloride when a current of 3A Is passed through the zinc (ii) chloride Solution during electrolysis of 50 minutes(Zn=65 , 1Faraday=96500C)
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Convert time to seconds.
The given time is $50 \text{ minutes}$.
$$t = 50 \text{ min} \times 60 \text{ s/min}$$
$$t = 3000 \text{ s}$$
Step 2: Calculate the total charge (Q) passed.
The given current is $I = 3 \text{ A}$.
$$Q = I \times t$$
$$Q = 3 \text{ A} \times 3000 \text{ s}$$
$$Q = 9000 \text{ C}$$
Step 3: Write the half-reaction for zinc deposition.
Zinc(II) ions ($Zn^{2+}$) gain electrons to form solid zinc.
$$Zn^{2+}(aq) + 2e^- \to Zn(s)$$
This reaction shows that $2 \text{ moles of electrons}$ are required to deposit $1 \text{ mole of Zn}$.
Step 4: Calculate the moles of electrons transferred.
Faraday's constant is $F = 96500 \text{ C/mol e}^-$.
$$\text{Moles of electrons} = \frac{\text{Charge (Q)}}{\text{Faraday's constant (F)}}$$
$$\text{Moles of electrons} = \frac{9000 \text{ C}}{96500 \text{ C/mol e}^-}$$
$$\text{Moles of electrons} \approx 0.093264 \text{ mol e}^-$$
Step 5: Calculate the moles of zinc deposited.
From the half-reaction, $1 \text{ mole of Zn}$ requires $2 \text{ moles of electrons}$.
$$\text{Moles of Zn} = \frac{\text{Moles of electrons}}{2}$$
$$\text{Moles of Zn} = \frac{0.093264 \text{ mol}}{2}$$
$$\text{Moles of Zn} \approx 0.046632 \text{ mol}$$
Step 6: Calculate the mass of zinc deposited.
The molar mass of Zn is $65 \text{ g/mol}$.
$$\text{Mass of Zn} = \text{Moles of Zn} \times \text{Molar mass of Zn}$$
$$\text{Mass of Zn} = 0.046632 \text{ mol} \times 65 \text{ g/mol}$$
$$\text{Mass of Zn} \approx 3.031 \text{ g}$$
The mass of zinc deposited is approximately $\boxed{\text{3.031 g}}$.
3 done, 2 left today. You're making progress.