Question

You have three wells. Well 1 has sewage contamination and has elevated levels of chloride at 800mg/Liter and arsenic at 4mg/Liter. There is an uncontaminated background well (Well 2) with Chloride levels at 100mg/Liter and arsenic at 0.1mg/Liter. Well 3 is located down gradient of the contaminated area with a Chloride level of 300mg/liter. What would be the mixing fraction for Well 3? Note the component with contamination with the letter "p"

Answer 1

Since all the three wells are down the gradient ,water in each well would get contaminated with chloride

and arsenic , so as to have the same concentrations in terms mole fractions of the respective impurities.

hence we need to calculate the mole fractions of chloride and arsenic separately in well 1.

............................................................No. of mMols...........................mole fraction

Chloride ..............( 800 / 35.5 ) = 22.5352 mMols...............................( 22.5 / 22.5886 ) = 0.9976

Arsenic................( 4.00 / 74.92 ) = 0.0534 mMols ...............................(0.0534 / 22.5886) = 0. 0024

Now, in well 3 -

mMols of chloride is = ( 300 /35.5 ) = 8.4507

Let the number of mMols of arsenic be = x mMols

So,mol fraction of chloride = { 8.4507 / ( 8.4507 + x ) } = same as in tank well1

...........................................................................................= 0.9976

hence , x = 0.0203

Substituting the value of x we get the answer .

p_chloride   = 0 & p _arsenic   = 2.3964 x 10^-3