What quantity of 65 per cent acid solution must be mixed with a 25 percent solution to produce 384 mL of a 50 per cent solution?
Let there be x mL of 65% solution and y mL of 25% solution.
x + y = 384
Amount of acid:
0.50*384 = 192 = 0.65 x + 0.25 y
768 = 2.6 x + y
Subtract the first equation from the third.
1.6 x = 384
x = 240 mL
y = 144 mL
To find the quantity of each solution needed, let's set up an equation using the concept of mixtures.
Let's assume:
x = volume of the 65% acid solution needed (in mL)
384 - x = volume of the 25% acid solution needed (in mL)
Now, we can set up the equation based on the amount of acid in each solution:
0.65x + 0.25(384 - x) = 0.50 * 384
Let's solve this equation step-by-step:
0.65x + 0.25 * 384 - 0.25x = 192
Combine the x terms:
0.40x + 96 = 192
Subtract 96 from both sides of the equation:
0.40x = 96
Divide both sides by 0.40 to isolate x:
x = 96 / 0.40
Simplifying:
x = 240
Therefore, 240 mL of the 65% acid solution must be mixed with 144 mL (384 - 240) of the 25% acid solution to produce 384 mL of a 50% solution.
To find the quantity of the 65% acid solution needed, you can set up an equation based on the mixture rule:
Let's assume the quantity of the 65% acid solution needed is x mL.
The quantity of the 25% acid solution needed will be (384 - x) mL, as we want the sum of the quantities to be 384 mL.
Now, let's set up the equation based on the concentration of acid in the solution:
(65/100) * x + (25/100) * (384 - x) = (50/100) * 384
Here, we multiply the concentration of each solution (as a decimal) by its respective quantity. The sum on the left side of the equation represents the amount of acid in the mixture, while the right side represents the amount of acid in the desired 50% solution.
Let's solve this equation to find the value of x:
(0.65 * x) + (0.25 * 384 - 0.25 * x) = 0.5 * 384
0.65x + 96 - 0.25x = 192
0.4x + 96 = 192
0.4x = 96
x = 96 / 0.4
x = 240
Therefore, you would need 240 mL of the 65% acid solution to mix with the 25% acid solution to produce 384 mL of a 50% solution.