2 liters of cleaning solution is 65% ammonia. How much water must be added to dilute it to a 40% soulition?
So, you're going to want to set up an equation and the proper concentration formula for this problem would be C1(Q1)=C2(Q2). C1 is your given concentration is 65% (0.65) and your second concentration (the desired concentration) is 40% (0.40). Your solution is 2.0L so that would be your first quantity. Your second quantity is unknown so we can write it as X. So now plug everything in! 0.65(2)=0.40(X). Then you distribute! So 1.30=0.4X. Now you divide by 0.4! So you end up with X=3.25! That would be your second value but the question asks for HOW MUCH WATER YOU NEED TO ADD! So you would subtract Q2 with Q1. 3.25-2.0=1.25. You would add 1.25L!
1.25L of water
To find the amount of water that needs to be added to dilute the cleaning solution, we need to understand the concept of dilution.
Dilution is the process of reducing the concentration of a solute in a solution by adding more solvent (in this case, water). The key idea to remember is that the amount of solute (in this case, ammonia) remains constant throughout the dilution process.
Let's break down the information we have:
- We have 2 liters of cleaning solution.
- The solution is currently 65% ammonia.
- We want to dilute it to a 40% ammonia solution.
- We need to find out how much water should be added.
To solve this problem, we can set up an equation based on the concepts of concentration and dilution:
(Initial amount of solute) / (Total initial volume) = (Final amount of solute) / (Total final volume)
Let's solve the equation step by step:
Step 1: Calculate the initial amount of ammonia in the cleaning solution.
Initial amount of ammonia = 65% of 2 liters
Initial amount of ammonia = (65/100) * 2 liters
Initial amount of ammonia = 1.3 liters
Step 2: Calculate the final amount of ammonia required in the diluted solution.
Final amount of ammonia = 40% of (2 liters + x liters of water)
Final amount of ammonia = (40/100) * (2 liters + x liters of water)
Final amount of ammonia = 0.4 * (2 liters + x liters of water)
Final amount of ammonia = 0.8 + 0.4x liters
Since the initial amount of ammonia and the final amount of ammonia should be the same, we can set up an equation:
Initial amount of ammonia = Final amount of ammonia
1.3 liters = 0.8 + 0.4x liters
Step 3: Solve the equation for x to find the amount of water needed.
Subtracting 0.8 liters from both sides of the equation:
1.3 liters - 0.8 liters = 0.4x liters
0.5 liters = 0.4x liters
Dividing both sides of the equation by 0.4:
0.5 liters / 0.4 = x liters
x = 1.25 liters
Therefore, you need to add 1.25 liters of water to the 2 liters of cleaning solution to dilute it to a 40% ammonia solution.