Calculation of Alum Quantity:
To calculate the quantity of alum required, we can use the following formula:

Quantity of Alum = Alum Dose * Quantity of Water

Given that the alum dose required is 12 ppm (parts per million) and the quantity of water to be treated is 13 million liters per day, we can substitute these values into the formula:

Quantity of Alum = 12 ppm * 13 million liters

Converting 13 million liters to kilograms (1 liter of water weighs 1 kg), we get:

Quantity of Alum = 12 ppm * 13 million kg

Calculation of Carbon Dioxide:
The production of alum involves the reaction of aluminum sulfate with sodium hydroxide, which produces aluminum hydroxide and sodium sulfate. This reaction also releases carbon dioxide gas.

The balanced chemical equation for the reaction is:

Al2(SO4)3 + 6NaOH -> 2Al(OH)3 + 3Na2SO4 + 3CO2

From the balanced equation, we can see that for every 2 moles of aluminum sulfate, 3 moles of carbon dioxide are produced.

To calculate the amount of carbon dioxide released, we need to determine the number of moles of aluminum sulfate used. We can use the molar mass of aluminum sulfate to convert the mass of alum used to moles:

Number of moles of Alum = Mass of Alum / Molar mass of Alum

Given that the mass of alum used is 156 kg and the molar mass of aluminum sulfate is 342.15 g/mol, we can calculate the number of moles of alum:

Number of moles of Alum = 156,000 g / 342.15 g/mol

Finally, we can use the mole ratio from the balanced equation to calculate the amount of carbon dioxide released:

Amount of Carbon Dioxide = (Number of moles of Alum / 2 moles) * (3 moles of CO2 / 2 moles of Alum)

Substituting the calculated values, we get:

Amount of Carbon Dioxide = (156,000 g / 342.15 g/mol) * (3 mol CO2 / 2 mol Alum)

Converting grams to kilograms and moles to kilograms, we get:

Amount of Carbon Dioxide = (156 kg / 342.15 kg/mol) * (3 kg CO2 / 2 kg Alum)

Simplifying the expression, we find:

Amount of Carbon Dioxide = 0.68 kg

Thus, the amount of carbon dioxide released in this process is 0.68 kg, which is approximately 0.68 kg. Therefore, the correct answer is (A) 0.68 kg.