A scientist has 40 liters of a 50% acidic solution. She adds a 20% acidic solution to create a mixture that has been diluted to
have 30% acidity. The graph models the percent of acidity in the final mixture.
20 40 60 80
How many liters of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture?

A:0.5
B:30
C:80
D:37

Question

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Respuesta :

frika frika · Answer 1 · 2019-10-11T13:21:46+02:00

Answer:

C. 80 liters

Step-by-step explanation:

A scientist has 40 liters of a 50% acidic solution. So, there are

[tex]40\cdot 0.50=20\ liters[/tex]

of acid in this solution.

She adds x liters of 20% acidic solution to create a new mixture. In x liters of 20% acidic solution there are

[tex]x\cdot 0.20=0.2x\ liters[/tex] of acid.

The total volume of the mixture is (40 + x) liters. This mixture has 30% acidity, so there are

[tex](40+x)\cdot 0.30=0.3(40+x)\ liters[/tex] of acid.

The amount of acid is the same, thus,

[tex]20+0.2x=0.3(40+x)\\ \\200+2x=3(40+x)\ [\text{Multiplied by 10}]\\ \\200+2x=120+3x\\ \\2x-3x=120-200\\ \\-x=-80\\ \\x=80[/tex]

kobenhavn kobenhavn · Answer 2 · 2019-10-22T12:28:15+02:00

Answer: C) 80 L

Step-by-step explanation:

According to the dilution law,

[tex]C_1V_1+C_2V_2=C_3V_3[/tex]

where,

[tex]C_1[/tex] = concentration of acid solution = 50 %

[tex]V_1[/tex] = volume of acid solution = 40 L

[tex]C_2[/tex] = concentration of another acid solution= 20%

[tex]V_2[/tex] = volume of another acid solution= x L

[tex]C_3[/tex] = concentration of resulting acid solution = 30 %

[tex]V_1[/tex] = volume of resulting acid solution = (40+x) L

Putting the values in the equation:

[tex]50\times 40+20\times x=30\times (40+x)[/tex]

[tex]x=80L[/tex]

Thus 80 L of the 20% acidic solution should be added to create the needed 30% acidity in the final mixture.