Respuesta :
Answer:
(a)[tex]2000\text{ ml}[/tex] (b)[tex]40\text{ ml and }60\text{ ml}[/tex] (c)NO
Step-by-step explanation:
GIVEN: Solution A is an [tex]\$80\%[/tex] acid solution. Solution B is a [tex]\$30\%[/tex] acid solution.
TO FIND: (a) Find the amount of Solution A (in mL) that must be added to [tex]500 \text{ml}[/tex] of Solution B in order to produce a [tex]70\%[/tex] acid solution. (b) Find the amount of Solution A and Solution B (in mL) that can be combined in order to form a [tex]100 \text{ml}[/tex] solution that is [tex]50\%[/tex] acid. (c) Does there exist a combination of Solution A and Solution B that is [tex]90\%[/tex] acid.
SOLUTION:
(a)
Let total amount of solution A added be [tex]x[/tex]
Total amount of mixture [tex]=500+x\text{ ml}[/tex]
As resulting solution is [tex]70\%[/tex] acid solution.
Amount of acid in final solution is sum of acid in both solutions
[tex]\frac{70}{100}(500+x)=\frac{80}{100}x+\frac{30}{100}\times500[/tex]
[tex]35000+70x=80x+15000[/tex]
[tex]x=2000\text{ ml}[/tex]
(b)
Let amount of Solution A be [tex]x\text{ ml}[/tex]
Amount of solution B [tex]=100-x\text{ ml}[/tex]
As resulting solution is [tex]50\%[/tex] acidic solution
Amount of acid in final solution is sum of acid in both solutions
[tex]\frac{50}{100}\times100=\frac{80}{100}x+\frac{30}{100}(100-x)[/tex]
[tex]5000=80x+3000-30x[/tex]
[tex]50x=2000[/tex]
[tex]x=40\text{ ml}[/tex]
Amount of solution B [tex]=100-40=60\text{ ml}[/tex]
(c)
No as concentration of final solution can not be greater than one with higher concentration.
