Question

How much water must be added to 12 grams of a 90% iodine solution to produce a 25% iodine solution?

Answer 1

You would have to add 31.2 g of water.

Explanation:

Iodine dissolves in water only to 0.03 % concentration, so this is a purely hypothetical question.

90 % iodine means `"90 g iodine"/"100 g solution"`

So in 12 g of 90 % solution:

`"Mass of iodine" = 12 color(red)(cancel(color(black)("g soln"))) × "90 g iodine"/(100 color(red)(cancel(color(black)("g soln")))) = "10.8 g iodine"`

We add `x " g"` of water to `"12 g"` of 90 % iodine to get `12+x " g"` of 25 % iodine.

`10.8/(12+x) = 25/100`

`10.8×100=25(12+x)`

`1080=300+25x`

`25x = 1080-300 = 780`

`x = 780/25`

`x = 31.2`

We have to add 31.2 g of water.

Check:

`10.8/(12+31.2) = 25/100`

`10.8/43.2 = 25/100`

`1/4=1/4`

It checks!