I am assuming this is a 1,000g mixture.
42% H3BO3 = 420g H3BO3/(420g H3BO3+580g H2O)= 0.42 by mass.
420g H3BO3/(420g H3BO3+580g H2O+Xg H2O)= 0.06
Solve for X
Check my thinking. Check my work.
There is an alternative approach. You want to dilute it by a factor of seven. (42 to 6). So add six parts water.
Six liters of water added to the one liter of boric acid. It gives you the same answer.
Caleb has 1 liter of a mixture containing 42% boric acid. How much water must be added to make the mixture 6% boric acid?
I don't get how to do weighted averages
To solve this problem using weighted averages, you need to consider the amount of boric acid (H3BO3) and the amount of water present in the initial mixture, as well as the final desired concentration.
Let's start by understanding the given information:
- Caleb has 1 liter of a mixture containing 42% boric acid.
- Caleb wants to dilute the mixture by adding water to achieve a final concentration of 6% boric acid.
To find the amount of water that needs to be added, we'll use the concept of weighted averages. Here's how you can proceed:
Step 1: Calculate the amount of H3BO3 in the initial mixture:
In 1 liter of the initial mixture, the amount of H3BO3 can be found by multiplying the volume (1 liter) by the concentration (42%):
Amount of H3BO3 = 1 liter * 0.42 = 0.42 liters
Step 2: Determine the total volume of the initial mixture:
The initial mixture is 1 liter.
Step 3: Set up the equation using the weighted average formula:
The diluted mixture should have a final concentration of 6% boric acid. In this case, the amount of H3BO3 remains constant, while the total volume increases due to the addition of water. The equation can be written as follows:
0.42 liters H3BO3 / (0.42 liters H3BO3 + X liters water) = 0.06
Here, X represents the amount of water to be added.
Step 4: Solve the equation for X:
To solve for X, we can cross-multiply and rearrange the equation:
0.42 = 0.06 * (0.42 + X)
0.42 = 0.0252 + 0.06X
0.42 - 0.0252 = 0.06X
0.3948 = 0.06X
X = 0.3948 / 0.06
X ≈ 6.58 liters
So, approximately 6.58 liters of water must be added to Caleb's 1-liter mixture to achieve a final concentration of 6% boric acid.
To check your work, you can verify that the final concentration of the mixture is indeed 6% by recalculating it:
Amount of H3BO3 = 0.42 liters
Total volume after dilution = 1 liter + 6.58 liters = 7.58 liters
Concentration of boric acid in the diluted mixture = (0.42 liters / 7.58 liters) * 100% ≈ 5.53%
Therefore, with approximately 6.58 liters of water added, the mixture should have a final concentration close to 6% boric acid.