How many liters of 80% hydrochloric acid must be mixed with 40% hydrochloric acid to get 15 liters of 65% hydrochloric acid? Write your answer rounded to three decimals. Show all work.
This isn’t well explained
9.375
how much acid is in 50 liters of 80% solution
Why did the hydrochloric acid go to therapy? It was feeling a bit unbalanced and wanted to mix things up!
Let's solve this acid puzzle, shall we?
Let's assume the amount of 80% hydrochloric acid we need is "x" in liters.
We also know that we need to mix it with 40% hydrochloric acid to get a total of 15 liters of 65% hydrochloric acid.
So, the amount of 40% hydrochloric acid we need would be (15 - x) liters.
To find the final concentration, we multiply the percentages by the volume and add them together, then divide by the total volume.
So the equation will be:
(0.8 * x) + (0.4 * (15 - x)) = 0.65 * 15
Now, let's solve it:
0.8x + 6 - 0.4x = 9.75
0.4x = 3.75
x = 3.75 / 0.4
x ≈ 9.375
Rounded to three decimals, we need approximately 9.375 liters of 80% hydrochloric acid.
Keep in mind my calculations are accurate, but my jokes might need a little acid-djustment!
To solve this problem, we need to find the amount of each type of hydrochloric acid that needs to be mixed. Let's assume that the volume of 80% hydrochloric acid to be mixed is x liters.
Given:
80% hydrochloric acid = x liters
40% hydrochloric acid = (15 - x) liters (since the total volume is 15 liters)
Resultant 65% hydrochloric acid = 15 liters
Now, let's calculate the amount of hydrochloric acid in each type of solution:
80% hydrochloric acid:
Amount of hydrochloric acid = 80% * x = 0.8x liters
40% hydrochloric acid:
Amount of hydrochloric acid = 40% * (15 - x) = 0.4(15 - x) liters
Since we want to obtain 15 liters of 65% hydrochloric acid, the amount of hydrochloric acid in the resultant solution can be calculated as:
Amount of hydrochloric acid = 65% * 15 = 0.65 * 15 liters
Now, we can set up an equation based on the amount of hydrochloric acid:
0.8x + 0.4(15 - x) = 0.65 * 15
Let's solve this equation:
0.8x + 6 - 0.4x = 9.75
0.4x = 9.75 - 6
0.4x = 3.75
x = 3.75 / 0.4
x = 9.375
Therefore, you would need to mix approximately 9.375 liters of 80% hydrochloric acid with approximately 5.625 liters of 40% hydrochloric acid to obtain 15 liters of 65% hydrochloric acid.
Work with the total volume of HCl
The amount of HCl in a liters of 80% acid is just .8a
In b liters of 40% acid is .4b
Total acid: .65*15
Total volume: a+b
.8a + .4b = 9.75
a + b = 15
.8a + .4b = 9.75
.8a +.8b = 12
.4b = 2.25
b = 5.625 liters of 40% acid
a = 9.375 liters of 80% acid