Question

you need to prepare 200 ml of a 10% v/v ethanol solution using a 30% v/v ethanol solution and a 5% v/v ethanol solution. how many milliliters of the 30% solution should be used?
o 25 ml
o 40 ml
o 171 ml
o 150 ml

Explanation:

Step1: Let the volume of 30% solution be $x$ mL.

Then the volume of 5% solution is $(200 - x)$ mL.

Step2: Set up equation based on ethanol - content.

The ethanol - content in the 30% solution is $0.3x$, the ethanol - content in the 5% solution is $0.05(200 - x)$, and the ethanol - content in the final 10% solution is $0.1\times200$. So, $0.3x+0.05(200 - x)=0.1\times200$.

Step3: Expand and simplify the equation.

$0.3x + 10-0.05x=20$. Combine like - terms: $0.3x-0.05x=20 - 10$, which gives $0.25x=10$.

Step4: Solve for $x$.

$x=\frac{10}{0.25}=40$ mL.

Answer:

40 mL