Chemical mixture problem.. please help?

Question

A chemist has one soluton that is 25% salt and 75% water and another solution that is only 5% salt. How many milliliters of each should the chemist use to make 1600ml of a solution that is 15% salt?

Can anyone please help me figure out the above? Or go over the steps with me to figuring it out? Thanks a bunch in advance! =)

Answer 1

Suppose that we must take x ml from the first solution and y ml from the second solution. Then clearly x and y must satisfy :

x + y = 1600

There must be 15% * 1600 ml= 240 ml salt in the result.

Then x and y must also satisfy

25% * x + 5% * y = 240, or
x/4 + y/20 = 240, or
5x + y = 4800.

From these 2 equations we will have x = 800 and y = 800.

Answer 2

I Guess you dont need to look up NACL and figure atomic weight or nothing this is really simple I think

if you want 15% from two solutions one 25 and one 5 well you say 15 is the avg of the two ie its the mid point 10 lower than 25 and ten higer than 5 so there is no work here you just notice symatry and take equal amounts of each to achieve the balance
so since the amount you want is 1600ml you divide by two and take that from both 800

If you notice the symatry on this you save alot of work

Answer 3

ok

Theres no point just giving you the answer you should understand the concept of this question. I believe it is very important to have an idea of what the answer should roughly be before you do the sums that way if you make a mistake in your numbers you will know because your answer wont look right.

The question is asking at what ratio are the two solutions to be mixed to acheive a concentration of 15% the volume is just to confuse you so we can look at that last.

Here is another way to understand this problem
If you mixed 1ltr of 100% salt solution and another 1ltr at 0% solution your final solution would be 50% salt solution
It just so happens that if you mixed 1ltr of 25% with 1ltr of 5% you get a final solution of 15%.

Whats happening; the starting solutions contain a disolved amount of salt, 25% having 250gr / ltr and 5% having 50gr / ltr so if you combine a litre of these two solutions you produce a final solution of 2ltr containing a total of 300gr or 150gr / ltr which is 15%

(if for example the final solution had to be 10% the ratio would be 3 parts of 5% solution to 1part 25% solution in other words to make a litre of 10% soltion from these two solutions you would have 750ml of 5% and 250ml of 25%)

Now working to the volumes, remeber we have already looked at how to acheive the final concentration so now we need to work out the volumes, in this case its a ratio of 1:1 therefore half of the 1600ml solution will be the 25% solution and the other half will be the 5% solution as half of 1600ml is 800ml of each solution.

Hope this helps you understand the problem

Answer 4

Let the chemist take 'x' ml from 25% salt solution and
'y' ml from 5% salt solution.
From given conditions:

Final volume = x+y =1600.....(1)

Since the resulting salt solution is 15%
amount of salt required in solution=15*1600/100 =240 ml

25% of x ml = 25*x/100 = x/4 = 0.25*x
5% of y ml = 5 *y/100 = y/20 =0.05*y

Hence, 0.25x+0.05y = 240......(2)

We get two simultaneous equations
Solving equations (1) & (2) we get:
x=800
y=800

Thus equal amounts of 800 ml has to be taken from both the given solutions.

Answer 5

OK, say you have Xml of the 25% solution and Yml of the 5% solution
so, X + Y = 1600ml
and
0.25X +0.05Y = 0.15(1600)

two equations two variables
plug one in the other

and X=Y=800

Answer 6

let him mix x ml of th first and y of the second to get x+y of the reqd. soln.
equation 1 x+y=1600
the secondequation
0.25x+0.05y=0.15*1600
multiplying by100
25x+5y=1600*15
dividing by 5
5x+y=4800
x+y=1600
subtracting4x=3200
x=800
sub y=800
so 800 ml of 25% salt mix. ismixed with
800 ml of 5% salt mix to get 1600 ml of 15% salt mix

Answer 7

0ml of sol A + 1600ml of sol B -> 5%
1600ml of sol A + 0ml of sol B -> 25%


15%-5%/(25%-5%) * 1600ml = 800ml
You need 800ml of sol A
and 1600ml-800ml=800ml of sol B

Answer 8

let x = the 25% salt solution
then 1-x = 5% salt solution

0.25x + (1-x)(0.05) = 0.15
0.25x + 0.05 -0.05x = 0.15
0.20x = 0.15 - 0.05 = 0.10
0.20x = 0.10
0.20x/0.20 = 0.10/0.20
x = 50%
1-x = 50%

so 800ml 25% soln and 800ml 5% soln