A pharmacist has an 18% alcohol solution. How much of this solution and how much water must be mixed together to make 10 liters of a 12% alcohol solution?
As usual, this is not hard if you understand what is going on.
The amount of alcohol is unchanged after adding water. So, if there are x liters of 18% solution, you have
.18x = .12*10
x = 20/3 L of 18% alcohol, and 10/3 L of water
Or, you can consider that you are reducing the concentration by a factor of 2/3, so you must increase the volume by a factor of 3/2. So, the volume v of 18% alcohol can be found by
3/2 v = 10
v = 20/3
To solve this problem, we need to use the concept of the concentration of the alcohol solution. Here are the steps to find the amount of the 18% alcohol solution and the amount of water needed to make 10 liters of a 12% alcohol solution:
Step 1: Define the variables:
Let's assume the volume of the 18% alcohol solution to be x liters.
The volume of water to be added will be (10 - x) liters.
Step 2: Write the equation using the concentration formula:
The concentration formula used here is:
(concentration of solution 1 * volume of solution 1) + (concentration of solution 2 * volume of solution 2) = (concentration of resulting solution * volume of resulting solution)
For our problem:
(0.18 * x) + (0 * (10 - x)) = 0.12 * 10
Step 3: Solve the equation:
0.18x + 0 = 1.2
0.18x = 1.2
x = 1.2 / 0.18
x = 6.7 liters (rounded to one decimal place)
Step 4: Determine the volume of water:
The volume of water to be added is:
10 - x = 10 - 6.7 = 3.3 liters
Therefore, to make 10 liters of a 12% alcohol solution, the pharmacist needs to mix 6.7 liters of the 18% alcohol solution with 3.3 liters of water.
To determine how much of the 18% alcohol solution and water is needed to make 10 liters of a 12% alcohol solution, we can use a basic formula:
Concentration × Volume = Amount of solute
Let's break down the information given in the question:
1. We have an 18% alcohol solution.
2. We want to make a 10-liter solution with a concentration of 12% alcohol.
Let's assume we need to mix x liters of the 18% alcohol solution with y liters of water. Since the total volume needs to be 10 liters, we can write the equation:
x + y = 10 (Equation 1)
Now, let's determine the amount of alcohol in the mixture. The amount of alcohol in the 18% solution is obtained by multiplying the concentration (0.18) by the volume (x):
0.18x
Since we want a 12% alcohol solution in 10 liters, the total amount of alcohol should be 10 liters multiplied by 0.12:
10 × 0.12 = 1.2
Now, we can create another equation for the amount of alcohol in the mixture:
0.18x + 0 × y = 1.2
Simplifying this equation, we have:
0.18x = 1.2
x = 1.2 / 0.18
x = 6.67
So, we need 6.67 liters of the 18% alcohol solution. Using Equation 1, we can find y:
6.67 + y = 10
y = 10 - 6.67
y = 3.33
Therefore, we need to mix 6.67 liters of the 18% alcohol solution with 3.33 liters of water to obtain 10 liters of a 12% alcohol solution.