Question

how many minutes will it take to plate the spoon with 10.3 g cr? cr³⁺ + 3e⁻ → cr e°_cell = -0.73 v i = 9.30 a t = ? min

Explanation:

Step1: Calculate moles of Cr

Molar mass of Cr is 52.00 g/mol. Moles of Cr, $n = \frac{mass}{molar\ mass} = \frac{10.3\ g}{52.00\ g/mol} \approx 0.1981\ mol$.

Step2: Determine moles of electrons

From the reaction $Cr^{3+} + 3e^-
ightarrow Cr$, 3 moles of electrons are needed per mole of Cr. So moles of electrons, $n_{e^-} = 3 \times 0.1981\ mol = 0.5943\ mol$.

Step3: Calculate charge (Q)

Using Faraday's constant, $F = 96485\ C/mol$. Charge $Q = n_{e^-} \times F = 0.5943\ mol \times 96485\ C/mol \approx 57340\ C$.

Step4: Relate charge to current and time

Current $I = \frac{Q}{t}$, so $t = \frac{Q}{I}$. Substituting values: $t = \frac{57340\ C}{9.30\ A} \approx 6165\ s$.

Step5: Convert seconds to minutes

$t (min) = \frac{6165\ s}{60\ s/min} \approx 102.75\ min$.

Answer:

103 (rounded to a reasonable number of significant figures)