To calculate the current for the reduction of Sn$^{4+}$ to Sn$^{1+}$ and the power delivered by the battery, we can use the following formulas.

1. Current from the reduction reaction

The reduction of Sn$^{4+}$ to Sn$^{1+}$ involves a transfer of 3 electrons:

$\text{Sn}^{4+} + 3e^- \rightarrow \text{Sn}^{1+}$

To find the current, we can use Faraday's law of electrolysis:

$I = \frac{nF}{t}$

Where:

• $I$ = current (A)
• $n$ = number of moles of electrons transferred
• $F$ = Faraday's constant ($96485 \, \text{C/mol}$)
• $t$ = time (in seconds)

Given:

• Reduction rate = 5.846 mmol/h = $5.846 \times 10^{-3} \, \text{mol/h}$
• Convert to moles of electrons: $n = 5.846 \times 10^{-3} \, \text{mol/h} \times 3 = 1.754 \times 10^{-2} \, \text{mol/h}$
• Convert hours to seconds: $t = 1 \, \text{h} = 3600 \, \text{s}$

Substituting values into the equation:

$I = \frac{1.754 \times 10^{-2} \, \text{mol}}{3600 \, \text{s}} \times 96485 \, \text{C/mol}$

Calculating this:

$I \approx \frac{1.754 \times 10^{-2} \times 96485}{3600} \approx 0.468 \, \text{A}$

2. Power delivered by the battery

The power $P$ delivered by the battery can be calculated using the formula:

$P = \frac{V^2}{R}$

Where:

• $V$ = voltage (V)
• $R$ = resistance (Ω)

Given:

• $V = 2.80 \, \text{V}$
• $R = 200 \, \Omega$

Substituting the values:

$P = \frac{(2.80)^2}{200}$

Calculating this:

$P = \frac{7.84}{200} = 0.0392 \, \text{W} \, \text{or} \, 39.2 \, \text{mW}$

Summary of Results

• The current passing through the solution is approximately 0.468 A.
• The power delivered by the battery is approximately 39.2 mW.

Would you like more details on these calculations or have any specific questions? Here are some related questions you might consider:

1. What other reactions could occur during the reduction of Sn$^{4+}$?
2. How does temperature affect the electrochemical processes?
3. What is the significance of Faraday's law in electrochemistry?
4. How do changes in resistance affect the current in a circuit?
5. What are some practical applications of Sn$^{4+}$ reduction in industry?

Tip: Understanding the relationship between voltage, current, and resistance (Ohm's Law) can help you analyze various electrical circuits effectively.