What volume of water must be added to 30ml of alcohol to obtain a 40%(by volume)by mass of salt solution?
1 Answer
The question is not clear. It seems to want to know 40% my volume or 40% by mass.
Let's look at the approach to answering both. The phrase "percent by volume" such as "40% by volume" or "40% (v/v)" indicates "40 ml per 100 ml" of the total volume. Thus "X% (v/v)" means "X ml per 100 ml"
A percent by mass would be "X% (w/w)", that is, weight per weight, which is X grams per 100 grams.
That is the principal point to understand. The rest is setting up the correct equation.
Let's assume you want 40% alcohol by volume. So that is 40 ml alcohol per 100 m of solution (water + alcohol)
Mathematically, you find that as
Solving for
That's the total volume of the final solution. So that means to the 30 ml alcohol you already have, add 40 ml water.
Now the math of the solution by mass is bit more involved. First we must relate volume of substances to mass of them at a particular temperature (room temperature in this case). You use (solution) density constants in this case. Water is 1.0 g/ml which is easy enough in the math, but alcohol (ethanol) is about 0.8 g/ml. First set up the right equations
The goal is to compute the mass (in grams) of water added to 30 ml alcohol to get 40% (w/w) alcohol or
The equation will be
To solve for
Thus the equation for
And
Since you already have 24 g alcohol, you need to add
