Question

a current of 6.00 a is applied to the chromium(iii) nitrate solution for 75.0 minutes. what mass of chromium is plated onto the part?
cr³⁺ + 3e⁻ → cr
mass = ? g cr

Explanation:

Step1: Calculate the total charge (Q)

The formula for charge is \( Q = I \times t \), where \( I \) is current in amperes (A) and \( t \) is time in seconds (s). First, convert time from minutes to seconds: \( 75.0 \, \text{min} \times 60 \, \text{s/min} = 4500 \, \text{s} \). Then, \( Q = 6.00 \, \text{A} \times 4500 \, \text{s} = 27000 \, \text{C} \).

Step2: Determine moles of electrons

Faraday's constant \( F = 96485 \, \text{C/mol e}^- \). Moles of electrons \( n_{e^-} = \frac{Q}{F} = \frac{27000 \, \text{C}}{96485 \, \text{C/mol e}^-} \approx 0.2798 \, \text{mol e}^- \).

Step3: Relate moles of electrons to moles of Cr

From the reaction \( \text{Cr}^{3+} + 3\text{e}^-
ightarrow \text{Cr} \), 3 moles of \( \text{e}^- \) produce 1 mole of Cr. So moles of Cr \( n_{\text{Cr}} = \frac{n_{e^-}}{3} = \frac{0.2798 \, \text{mol e}^-}{3} \approx 0.09327 \, \text{mol} \).

Step4: Calculate mass of Cr

Molar mass of Cr is \( 52.00 \, \text{g/mol} \). Mass \( m = n_{\text{Cr}} \times \text{molar mass} = 0.09327 \, \text{mol} \times 52.00 \, \text{g/mol} \approx 4.85 \, \text{g} \).

Answer:

\( 4.85 \)