In an electrochemical cell, dichromate ions in aqueous acidic medium are reduced to Cr³⁺. The current (in amperes) that flows through the cell for 48.25 minutes to produce 1 mole of Cr³⁺ is ______.

Use: 1 Faraday = 96500 C mol−1

The correct answer is 100.

To find the current flowing through the cell, we can follow these step-by-step calculations:

Step 1: Write down the balanced reduction half-reaction for dichromate ions
In an acidic medium, dichromate ions (${\mathrm{Cr}}_2{O}_7^{2-}$) are reduced to chromium(III) ions (${\mathrm{Cr}}^{3+}$). The balanced half-reaction is:
${\mathrm{Cr}}_2{O}_7^{2-}+14H^{+}+6e^{-}\to 2{\mathrm{Cr}}^{3+}+7H_{2}O$
From the stoichiometry of the reaction, 6 moles of electrons are required to produce 2 moles of ${\mathrm{Cr}}^{3+}$ ions.

Step 2: Determine the moles of electrons required to produce 1 mole of ${\mathrm{Cr}}^{3+}$
To produce 1 mole of ${\mathrm{Cr}}^{3+}$ ions, the number of moles of electrons (n) required is:
$n=\frac{6\text{moles of electrons}}{2\text{moles of}{\mathrm{Cr}}^{3+}}=3\text{moles of electrons}$

Step 3: Calculate the total charge (Q) in coulombs
Using Faraday's constant ($F=96500{\text{C mol}}^{-1}$), the total charge Q required is:
$Q=n\times F$
$Q=3\text{mol}\times 96500{\text{C mol}}^{-1}=289500\text{C}$

Step 4: Convert the time (t) into seconds
The given time is 48.25 minutes:
$t=48.25\text{minutes}=48.25\times 60\text{seconds}=2895\text{seconds}$

Step 5: Calculate the current (I) in amperes
Using the relationship between charge, current, and time ($Q=I\times t$), we can solve for current:
$I=\frac{Q}{t}$
$I=\frac{289500\text{C}}{2895\text{s}}=100\text{A}$
Thus, the current that flows through the cell is 100 amperes.