Question

You arrive at a crime scene and are told the body of the victim is in the 10 m deep pool. You walk over to what you are told is a 12 m in diameter, cylindrical pool. From the outside of the pool, you can see that the body looks badly burnt. Your partner says, “It looks like our victim had been burned alive and tried to put out the fire by jumping in the pool. The victim likely drowned to death.” Something does not sit right with you though. If there was a fire, where did it start? There are no signs of combustion anywhere. You aren’t so sure and ask the crime scene investigator to run a sample of the pool water before letting anybody try to pull the body out. The CSI comes back to you and tells you that normal pool water pH is roughly around 7.2, but the pool pH is actually highly basic at a level of 13 with a concentration of hydroxide ions at 1.0 x 10-1 mol/L. It becomes obvious to you that the body wasn’t burned before going in to the pool , but AFTER and there was no fire needed! You order the body to be removed from the pool, but the CSI interjects, “It would be too dangerous with a pH that high. I suggest you get some vinegar from the store and pour it in to the pool before hand to drop the pH to 7. Draining the pool would take far too long and we need to examine the body as soon as possible.” She asks one of your constables to go to the store to purchase 5 – 4L jugs of vinegar (pH = 2) to pour in the pool, as she states it is enough to bring the pH to a safe level of 7. It sounds like it could be enough vinegar based on your knowledge of acids and bases, but you want to double-check her estimate before sending your constable to the store. Verify whether or not she is correct using calculations. A diagram may help you with your calculations. Hint 1: 1m3 = 1000L Hint 2: Vcylinder = πr2h

Answer 1

Given, diameter of pool is 2r = 12 m
r = 6 m
depth, h = 10 m
Volume of water, V = pi*r^2*h = 1130.9733 m^3

now, molar concentration of hydroxyl ions in the pool is c = 10^-1 mol/L
c = 0.1 mol / L
1 L = 1000 cm^3 = 10^-3 m^3
c = 0.1 mol / 10^-3 m^3 = 100 mol / m^3
so total number of hydroxyl ions is n = Vc = 113097.335529
so to bring pH to 7, we need same number of H+ ions

let volume of required vinegar be x m^3
then concentration of H+ ions in pH = 2 acid is y

then
2 = -log(y)
y = 10^(-2) = 0.01 mol/L
y = 10 mol/m^3
so,
xy = 113097.335529
x = 113097.33552/10 = 11309.73355 m^3

Volume of a jug of vinegar = 4 L
so number of jugs required = 2827.433388
hence, So, 5 4L jugs of pH 2 vinegar wont do the trick, we need about 2800 such jugs of vinegar