How much water in mL must be added to 40mL of a 10% acid solution to reduce its concentration to 4%?
x = 10% = 10 / 100 = 0.1
10% acid solution of 40 mL =
0.1 * 40 mL = 4 mL of acid
Volume of new acid solution = 40 mL + x
where x = volume of added wather
4 mL represent 4 %
4 % = 4 / 100 = 0.04
Now 4 mL of acid / new volume = 4 % =0.04
4 mL / ( 40 mL + x ) = 0.04
In mathematical form :
4 / ( 40 + x ) = 0.04 Multiply both sides by 40 + x
4 = 0.04 * ( 40 + x )
4 = 0.04 * 40 + 0.04 * x
4 = 1.6 + 0.04 x Subtract 1.6 to both sides
4 - 1.6 = 1.6 + 0.04 x - 1.6
2.4 = 0.04 x Divide both sides by 0.04
2.4 / 0.04 = x
60 = x
x = 60 mL
Proof :
New volume = 40 mL + 60 mL = 100 mL
4 mL of acid / new volume = 4 mL / 100 mL = 0.04 = 4 %
0.0x + .1(40) = .04(x+40)
0.0x + 4 = .04x + 1.6
.04x = 2.4
x = 60
60 ml of water must be added
or, you are reducing the concentration by a factor of 4/10, so you must increase the volume by a factor of 10/4.
10/4 * 40 = 100
So, you must wind up with 100ml, by adding 60ml of water.
To solve this problem, we need to find out the amount of water in milliliters (mL) that must be added to 40 mL of a 10% acid solution to reduce its concentration to 4%. Here's the step-by-step explanation:
1. Calculate the amount of acid in the initial solution:
In the 40 mL of the 10% acid solution, the amount of acid is 10% of 40 mL.
Amount of acid = (10/100) * 40 mL = 4 mL
2. Determine the desired amount of acid in the final solution:
To decrease the concentration to 4%, we need to calculate the amount of acid in the final solution.
Let the total volume of the final solution be (40 mL + x mL), where x is the amount of water to be added.
The desired amount of acid in the final solution is 4% of the total volume of the solution.
Amount of acid = (4/100) * (40 mL + x mL) = (2/50) * (40 mL + x mL) = (2/50) * (40 + x) mL
3. Set up the equation:
Since the amount of acid in the initial solution should equal the amount of acid in the final solution:
4 mL = (2/50) * (40 + x) mL
4. Solve for x:
Let's solve the equation to find the value of x:
4 mL = (2/50) * (40 + x) mL
Multiply both sides by 50 to eliminate the fraction:
200 mL = 2(40 + x) mL
200 mL = 80 + 2x mL
200 mL - 80 mL = 2x mL
120 mL = 2x mL
Divide both sides by 2 to isolate x:
x mL = 120 mL / 2
x mL = 60 mL
Therefore, 60 mL of water must be added to 40 mL of the 10% acid solution to reduce its concentration to 4%.