A chemist wishes to mix a solution that is 4% acid. She has on hand 66 liters of a 2% acid solution and wishes to add some 8% acid solution to obtain the desired 4% acid solution. How much 8% acid solution should she add?
There is a chart that I have to fill out:
Liters of solution-% acid-liters of pure acid
6 - 0.02 - ?
x - 0.08 - ?
? - 0.04 - ?
.02*66+.08*Va=.04(Va+66)
solving for Va
Va(.08-.04)=66(.04-.02)
Va=66(.02)/.04=33 liters
so your chart should be...
66 - 0.02 - 1.32
x - 0.08 - .08x
66+x - 0.04 -2.64+.04x
Your x is my Vacid Va
I am not certain why your teacher is using these charts, most students get lost in them...as you did.
To solve this problem, we can set up an equation based on the given information.
The total volume of the solution will be the sum of the volume of the 2% acid solution (66 liters) and the volume of the 8% acid solution we need to add (x liters). This can be represented as:
66 + x = total volume of the solution
The equation for the amount of acid in the solution can be expressed as:
(0.02 * 66) + (0.08 * x) = 0.04 * (66 + x)
Now let's solve for x.
0.02 * 66 + 0.08x = 0.04 * (66 + x)
1.32 + 0.08x = 2.64 + 0.04x
0.08x - 0.04x = 2.64 - 1.32
0.04x = 1.32
x = 1.32 / 0.04
x = 33
Therefore, she should add 33 liters of the 8% acid solution to obtain the desired 4% acid solution.
To solve this problem, we need to use the concept of the acid solution's concentration. Concentration is typically expressed as a percentage of the amount of solute (in this case, acid) in a given amount of solution (in this case, liters).
Let's analyze the chart provided:
Liters of solution - % acid - liters of pure acid
6 - 0.02 - ?
x - 0.08 - ?
? - 0.04 - ?
The first row represents the initial solution the chemist has on hand, which is a 2% acid solution. So, in 6 liters of the initial solution, we have 0.02 liters (or 20 milliliters) of pure acid.
The second row represents the solution the chemist wants to add, which is an 8% acid solution. We don't know the number of liters, so we'll represent it as 'x.' Consequently, in 'x' liters of the 8% acid solution, we have 0.08 liters (or 80 milliliters) of pure acid.
The third row represents the desired 4% acid solution. We also don't know the number of liters here, so we'll represent it as '?.' In '?' liters of the 4% acid solution, we have 0.04 liters (or 40 milliliters) of pure acid.
Now, we can set up an equation using the information given. Since acid is conserved during the mixing process, the total amount of pure acid in the initial solution plus the amount of pure acid in the added solution should equal the amount of pure acid in the final solution.
From the chart, we know:
0.02 + 0.08 = 0.04 + ?
This equation can be simplified to:
0.1 = 0.04 + ?
By subtracting 0.04 from both sides of the equation, we find:
? = 0.1 - 0.04
? = 0.06
Therefore, the chemist should add 0.06 liters (or 60 milliliters) of the 8% acid solution to obtain the desired 4% acid solution.