"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
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).