Question

Two solutions of salt water contain 0.06% and 0.26% salt respectively. A lab technician wants to make 1 liter of solution which contains 0.11% salt. How much of

each solution should she use?
Amount of 0.06% solution= milliliters
Amount of 0.26% solution=
milliliters

Answer 1

The volume for the 0.26% is 250 ml and the volume for the 0.06% is 750 ml.

Explanation:

In the solution the techinician wants to create there's a total of:

salt = 1*0.11/100 = 0.0011

So the sum of the salt from the other two solutions must be equal to that, since the quantity of salt in each is given by:

salt1 = volume1*0.06/100 = volume1*0.0006

salt2 = volume2*0.26/100 = volume2*0.0026

The sum of the from the two solutions must be equal to the final one:

salt = salt1 + salt2

0.0011 = 0.0006*volume1 + 0.0026*volume2

while the volume of the solutions must be equal to 1 liter:

volume1 + volume2 = 1

If we isolate volume1 on the second equation and replace that on the first one we have:

volume1 = 1 - volume2

0.0006*(1 - volume2) + 0.0026*volume2 = 0.0011

0.0006 - 0.0006*volume2 + 0.0026*volume2 = 0.0011

0.002*volume2 = 0.0011-0.0006

0.002*volume2 = 0.0005

volume2 = 0.0005/0.002 = 0.25 liters = 250 ml

volume1 = 1 - 0.25 = 0.75 liters = 750 ml

The volume for the 0.26% is 250 ml and the volume for the 0.06% is 750 ml.