A chemist wants to produce Cl₂(g) from molten NaCl. How many grams could be produced if he uses a steady current of 2 amp for 2.5 minutes?

0.110 g

The correct answer is option 3. 0.110 g.

To determine the amount of Cl$_2$(g) produced from molten NaCl using electrolysis, we can use Faraday's laws of electrolysis.

Faraday's first law states that the amount of substance produced or consumed during electrolysis is directly proportional to the quantity of electricity passed through the electrolyte.

The equation to calculate the amount of substance produced is:

\(\text{Amount of substance (in moles)} = \frac{{\text{Current (in amperes)} \times \text{Time (in seconds)}}}{{\text{Faraday's constant}}}\)

Given:

Current (\(I\)) = 2 A

Time (\(t\)) = 2.5 minutes = \(2.5 \times 60\) seconds = 150 seconds

Faraday's constant (\(F\)) = 96500 C/mol (charge of one mole of electrons)

Substituting the values into the equation:

\(\text{Amount of substance (in moles)} = \frac{{2 \, \text{A} \times 150 \, \text{s}}}{{96500 \, \text{C/mol}}}\)

Calculating the expression:

\(\text{Amount of substance (in moles)} \approx 0.003105 \, \text{mol}\)

The balanced equation for the electrolysis of molten NaCl is:

\(2\text{NaCl}(\text{l}) \rightarrow 2\text{Na}(\text{l}) + \text{Cl}_2(\text{g})\)

From the balanced equation, we can see that 1 mole of Cl$_2$(g) is produced for every 2 moles of NaCl consumed.

Therefore, the amount of Cl$_2$(g) produced is half of the amount of substance calculated:

\(\text{Amount of Cl}_2(\text{g}) \, (\text{in moles}) \approx \frac{0.003105 \, \text{{mol}}}{2} \approx 0.0015525 \, \text{mol}\)

To calculate the mass of Cl$_2$(g), we need to multiply the amount of Cl$_2$(g) by its molar mass.

The molar mass of Cl$_2$ is approximately 70.906 g/mol.

\(\text{Mass of Cl}_2(\text{g}) = \text{Amount of Cl}_2(\text{g}) \times \text{Molar mass of Cl}_2(\text{g})\)

\(\text{Mass of Cl}_2(\text{g}) \approx 0.0015525 \, \text{mol} \times 70.906 \, \text{g/mol} \approx 0.110 \, \text{g}\)

Therefore, the chemist could produce approximately (c) 0.110 g of Cl$_2$(g) by using a steady current of 2 A for 2.5 minutes.