## Tuesday, September 30, 2014

### Ionization Constant for Acid Problems, 3

Category: Chemical Engineering Math

"Published in Newark, California, USA"

In a salt manufacturing firm in California, there's a spill of 10 gallons of 50% caustic soda solution from the gate valve of 10,000 gallon tank that contains 50% caustic soda solution. Before the disposal of the spill, the state law requires to neutralize the hazardous waste first by adding citric acid and then wipe-off the neutralized spill. How many bags of citric acid will be needed for neutralization process? One bag of citric acid weighs 50 pounds. Is it safe to dispose the blankets used to wipe-off the neutralized spill? What is the pH of the neutralized spill? The pH range required for the disposal of industrial waste in California is 2.0 to 12.5. Outside of the range is considered as a corrosive. (density of 50% caustic soda solution = 1.515 g/mL; density of citric acid = 1.66 g/mL; molecular weight of sodium hydroxide = 40 g/mole;  and molecular weight of citric acid = 192 g/mole)

Solution:

Since the spill is a strong base, then the state law of California requires to neutralize it with a weak acid. We cannot use any strong acid because they are hazardous and corrosive, too. Same thing with a strong acid. We need to neutralize it with a weak base. That's the law for the safety of everyone and the environment as well.

The weight of 50% caustic soda solution which is also 50% of sodium hydroxide solution is

The weight of pure sodium hydroxide in 50% caustic soda solution is

The number of moles of sodium hydroxide in 50% caustic soda solution is

If citric acid is added to the spill that contains 50% caustic soda solution, then the chemical reaction is

The weight of citric acid used to neutralize sodium hydroxide is

Therefore, the number of bags of citric acid used is

or

Since the product which is trisodium citrate is soluble in water, then it is completely ionized as follows

The number of moles of trisodium citrate is

Hence, the number of moles of citrate ion is

Citrate ion is slightly soluble in water as follows

From Table of Ionization Constant of Acids and Bases, citric acid is ionized in three steps as follows

In this neutralization process, we will use the ionization constant at the third equation.

Consider again the solubility of citrate ion in water

Since one of the product has hydroxide ion, then we need to get the conjugate of ionization constant at the third equation as follows

The total volume of a neutralized spill is

The concentration of citrate ion in molarity is

The ionization constant of citrate ion is

where x is the amount of citrate ion that is converted into hydrogen citrate ion and hydroxide ion.

Since the value of Kb is less than 1 x 10-3, then we can neglect x at the denominator as follows

Hence, the concentration of  hydroxide ion is

Therefore, the pH of a neutralized spill is

Since the pH of a neutralized spill is less than 12.5, then it is safe to dispose the blankets used to wipe-off the neutralized spill. Trisodium citrate is a basic salt because pH is greater than 7 and it is a product of strong base (sodium hydroxide) and weak acid (citric acid).

## Monday, September 29, 2014

### Empirical and Molecular Formula Problems, 6

Category: Chemical Engineering Math

"Published in Daly City, California, USA"

The compound ascorbic acid (vitamin C) is a carbon-hydrogen-oxygen compound. This water-soluble vitamin cannot be stored in the body and thus must continuously be supplied by the diet. Combustion analysis of a 3.08 g ascorbic acid sample yields 6.17 g of CO2 and 2.52 g of H2O. What is the empirical formula for ascorbic acid?

Solution:

Since the molecule of ascorbic acid consists of carbon, hydrogen, and oxygen atoms, then we need to get the weight of each atoms first as follows:

Weight of carbon in a sample is

Weight of hydrogen in a sample is

Weight of oxygen in a sample is

Next, we need to get the number of moles of each atoms in a sample as follows:

Moles of carbon in a sample is

Moles of hydrogen in a sample is

Moles of oxygen in a sample is

From the number of moles of each component, we need to divide all of them by their least number of moles which is oxygen in order to get the number of atoms in a sample.

Number of carbon in a sample is

Number of hydrogen in a sample is

Number of oxygen in a sample is

Therefore, the empirical formula of ascorbic acid (vitamin C) is