Under certain water conditions, the free chlorine (hypochlorous acid, HOCl) in a swimming pool decomposes according to the law of uninhibited decay. After shocking a pool, the pool boy, Geoff, tested the water and found the amount of free chlorine to be 2.3 parts per million (ppm). Twenty-four hours later, Geoff tested the water again and found the amount of free chlorine to be 1.9 ppm. What will be the reading after 4 days (that is, 96 hours)? When the chlorine level reaches 1.0 ppm, Geoff must shock the pool again. How long can Geoff go before he must shock the pool again?

After 4 days the chlorine level reaches 1 ppm.

Explanation:

The formula  N(t) = N₀ e⁽⁻kt⁾  models this decay process well, where

t     = time measured in 24-hour days, so t =0, 1, 2, 3, ...

N₀   = initial measurement of HOCl at time t=0, just after first shocking the pool (given as 2.3 ppm)

N(t) = measurement of HOCl at time any time t  (N at t=1 is given as 1.9 ppm)

e = exponential function

k = rate of decay constant

First, we have to find k from the measurements at t= 0 and t=1

N(1) = N(0) e⁽⁻k(1))  so  1.9 = 2.3 e⁻k  and  e⁻k = 1.9/2.3 = 0.826

Taking the logarithm of both sides:  -k = ln (0.826) = - 0.191  

so k = + 0.191

After 4 days,

N(4) = 2.3e⁻(0.191ₓ4) = 1.07 ≈ 1 ppm

After 4 days Geoff must shock the pool again.

hydrocarbons are organic compounds that contain only hydrogens and carbons. they can be saturated (those which contain only carbon-carbon single bonds) or unsaturated (those which contain carbon-carbon double or triple bonds) in nature. hydrocarbons can undergo several reactions like substitution, elimination etc.  

on substituting one or more hydrogen atoms in hydrocarbon it results in the formation of haloalkane. as the halogen atoms are large compared to the carbon and hydrogen atoms, due to which the molecular weight increases and the bond become polar because of presence electronegative halogen atom and results in the increase in boiling point of the haloalkane.

thus, the correct option is (b) that is the boiling point of the new compound increases on substituting a hydrogen atom with a halogen in a hydrocarbon.