How many milliliters of a 75% acid solution must be added to 90 ml of a 10% acid solution to make a 25% acid solution?
To solve this problem, we can use the concept of the equation of the mixture.
Let's assume that x milliliters of the 75% acid solution need to be added to make a 25% acid solution.
First, let's calculate the amount of acid in the 90 ml of the 10% acid solution.
Amount of acid in the 10% solution = 10/100 * 90 ml
Next, let's calculate the amount of acid in the x ml of the 75% acid solution.
Amount of acid in the 75% solution = 75/100 * x ml
Now, let's calculate the amount of acid in the final mixture.
Amount of acid in the final mixture = 25/100 * (90 + x) ml
According to the equation of the mixture, the amount of acid in the 10% solution plus the amount of acid in the 75% solution should equal the amount of acid in the final mixture.
So, we can write the equation as:
10/100 * 90 + 75/100 * x = 25/100 * (90 + x)
Let's solve the equation to find the value of x.
10/100 * 90 + 75/100 * x = 25/100 * (90 + x)
Multiplying both sides of the equation by 100 to get rid of the denominators:
10 * 90 + 75x = 25 * (90 + x)
900 + 75x = 2250 + 25x
Now, let's simplify the equation:
75x - 25x = 2250 - 900
50x = 1350
Dividing both sides of the equation by 50:
x = 1350/50
x = 27
Therefore, to make a 25% acid solution, we need to add 27 milliliters of the 75% acid solution to 90 ml of the 10% acid solution.
To solve this problem, we can use the concept of mixture problems. Let's break down the steps:
Step 1: Determine the initial amount of acid in each solution
In the 10% acid solution, 90 ml of the solution contains 10% acid. Therefore, the initial amount of acid is 90 ml * 10% = 9 ml.
Step 2: Set up the equation
Let's assume that we need to add x ml of the 75% acid solution to obtain the final 25% acid solution.
The total amount of acid in the final solution will be the sum of the acid from the 10% solution and the acid from the 75% solution. So, we can set up the equation:
9 ml (acid in 10% solution) + (0.75 * x) ml (acid in 75% solution) = (90 ml + x ml) * 25% acid
In this equation, 0.75 represents 75% as a decimal, and 25% represents the target concentration of acid in the final solution.
Step 3: Solve the equation
Now we can solve the equation for x:
9 + 0.75x = (90 + x) * 0.25
Multiply both sides of the equation by 4 to eliminate the decimal:
36 + 3x = 22.5 + 0.25x
Subtract 0.25x from both sides:
2.75x = 13.5
Divide both sides by 2.75:
x = 13.5 / 2.75
x ≈ 4.91
Therefore, you would need to add approximately 4.91 ml of the 75% acid solution to the 90 ml of the 10% acid solution to obtain a 25% acid solution.