SOLUTION: When salt and water are combined they form a saline solution, How much water must be added to a 150 mL of an 80% saline solution to produce a 30% saline solution?

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Question 1190166: When salt and water are combined they form a saline solution, How much water must be added to a 150 mL of an 80% saline solution to produce a 30% saline solution?
Found 3 solutions by ikleyn, Alan3354, greenestamps:
Answer by ikleyn(52794)   (Show Source): You can put this solution on YOUR website!
.

Saline solution  MAY  NOT  have a concentration higher than ~ 26%   -   it becomes  saturated  and does not dissolve more salt.

so the problem as stated  SCARES  readers who are familiar with Science.


About saline water, read and learn from this Wikipedia article

https://en.wikipedia.org/wiki/Saline_water#:~:text=Salt%20concentration%20in%20slightly%20saline,ppm%20(1%E2%80%933.5%25).


Below is a cut from this article,  to learn for all who wish it . . .

It starts from the definition what  " saline water "  is 

        +-------------------------------------------------------------------+
        |     Saline water (or salt water) is water that contains a high    |
        |     concentration of dissolved salts (mainly sodium chloride).    |
        +-------------------------------------------------------------------+


    The salt concentration is usually expressed in parts per thousand (permille, ‰) and parts per million (ppm). 
    The United States Geological Survey classifies saline water in three salinity categories. 
    Salt concentration in slightly saline water is around 1,000 to 3,000 ppm (0.1  -  0.3%), 
    in moderately saline water 3,000 to 10,000 ppm (0.3  -  1%) 
    and in highly saline water 10,000 to 35,000 ppm (1  -  3.5%). 
    Seawater has a salinity of roughly 35,000 ppm, equivalent to 35 grams of salt per one liter (or kilogram) of water. 
    The saturation level is only nominally dependent on the temperature of the water.[1]
    At 20 °C one liter of water can dissolve about 357 grams of salt, a concentration of 26.3% w/w. 
    At boiling (100 °C) the amount that can be dissolved in one liter of water increases to about 391 grams, 
    a concentration of 28.1% w/w.


To say that saline water has concentration of 80% is the same as to say that water boils at 90 °C at normal conditions . . .

Or to say that the right angle is 100°.



Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Does the 26% limit apply to all salts?
Or just to NaCl?
---------------------
KI, potassium iodide, is a salt that that can have much higher solubility in water, especially at temperatures above 70 degs C. Apx 6 times that of NaCl.
But, the term "saline" means it's NaCl, not KI, so we're back to square 1.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


The fact that a saline solution can have a concentration of no more than 26% is not universal knowledge. This is a math website, not a physics/chemistry website. The intent of the question is clearly to give the student practice in learning how to solve mixture problems. Ignore the fact that the given situation is physically impossible and help the student learn.

(1) Using formal algebra....

x = mL of water to be added

Adding water adds no salt to the mixture, so the 30% of the (150+x) mL of the final mixture that is salt is still only the 80% of the 150mL of the original solution. So






ANSWER (algebraically): 250mL

(2) If a formal algebraic solution is not required....

You are starting with a solution that is 80% salt, adding water (0% salt), stopping when the solution reaches 30%.

Look at the three percentages 80, 30, and 0 on a number line and observe/calculate that 30 is 5/8 of the way from 80 to 0.
That means 5/8 of the final mixture is what you are adding (water); and that makes the 150mL you started with 3/8 of the final mixture.
A simple proportion then shows the amount of water to be added is 250mL.

ANSWER (informally): 250mL
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