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Rajan needs 1 liter of 15% hydrochloric acid solution for an experiment. He checks his storage cabinet, but he only has a 5-liter bottle of 5% hydrochloric acid solution and a 1-liter bottle of 45% hydrochloric acid solution. How many liters of the 5% hydrochloric acid and the 45% hydrochloric acid solutions should Rajan combine to make 1 liter of a solution that is 15% hydrochloric acid?

Respuesta :

InesWalston

Answer:

  1. 0.75 liters of 5% hydrochloric acid solution
  2. 0.25 liters of 45% hydrochloric acid solution.

Step-by-step explanation:

Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.

As Rajan need total of 1 liter of solution, so

[tex]x+y=1[/tex]

i.e [tex]x=1-y[/tex] --------------------1

As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so

[tex]0.05x+0.45y=1\times 0.15[/tex]

i.e [tex]5x+45y=15[/tex] -------------2

Putting value of x from equation 1 in equation 2,

[tex]\Rightarrow 5(1-y)+45y=15[/tex]

[tex]\Rightarrow 5-5y+45y=15[/tex]

[tex]\Rightarrow 5+40y=15[/tex]

[tex]\Rightarrow 40y=15-5=10[/tex]

[tex]\Rightarrow y=0.25[/tex]

Putting the value of y in equation 1,

[tex]x=1-0.25=0.75[/tex]

Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters  of 45% hydrochloric acid solution.

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