A chemist tries to invent a tasteful solution. He added a tablespoon of pepper and a spoonful of salt into 400 ml of water. The concentration of solution is 50%. Now he adds thrice the amount of salt and pepper. What is the increase in concentration?
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Let the amount of a tablespoon pepper and a spoon salt be x g.
Using the formula of percentage by mass= M a s s o f s o l u t i o n M a s s o f s o l u t e × 1 0 0 % = M a s s o f s o l u t e + M a s s o f s o l v e n t M a s s o f s o l u t e × 1 0 0 % ,
We have
x + 4 0 0 x × 1 0 0 % = 5 0 %
x + 4 0 0 x = 2 1
2 x = x + 4 0 0
x = 4 0 0
Hence, the mass of solute (a tablespoon pepper and a spoon salt)= 4 0 0 g
The concentration later= 4 0 0 × ( 3 + 1 ) + 4 0 0 4 0 0 × ( 3 + 1 ) × 1 0 0 % = 2 0 0 0 1 6 0 0 × 1 0 0 % = 8 0 %
So, the change in concentration (percentage by mass)= 8 0 % − 5 0 % = 3 0 %
Note: Unless it is stated in the question, all the solute added cannot be extracted.
So, the concentration later= 4 0 0 × ( 3 + 1 ) + 4 0 0 4 0 0 × ( 3 + 1 ) × 1 0 0 % = 2 0 0 0 1 6 0 0 × 1 0 0 % = 8 0 % ,
instead of the concentration later= 4 0 0 × 3 + 4 0 0 4 0 0 × 3 × 1 0 0 % = 1 6 0 0 1 2 0 0 × 1 0 0 % = 7 5 % .