1000g of a 55%(mass percentage) nitric acid solution is to be diluted to 20%(mass percentage) nitric acid solution.how many liters of water should be added to the starting solution?
you want to dilute it by a factor of 55/20=2.75 which means, you add 1.75 parts of water, and 1 part original.
one part: 1000g
water: 1.75 liters added.
Now check. You have 550g of HNO3 in 2.750kg solution, which is 550/2750 percent, or 20 percent.
1.75l
To solve this problem, we need to use the concept of mass percentage and the equation for dilution. The equation for dilution is as follows:
C1V1 = C2V2
Where,
C1 = initial concentration of the solution (55%)
V1 = initial volume of the solution (unknown)
C2 = final concentration of the solution (20%)
V2 = final volume of the solution (unknown)
Step 1: Convert the given mass percentages to decimal form.
For initial concentration (C1): 55% = 0.55
For final concentration (C2): 20% = 0.20
Step 2: Substitute the values into the dilution equation.
0.55 * V1 = 0.20 * (V1 + V_water)
Step 3: Solve for V_water (volume of water added).
0.35 * V1 = 0.20 * V_water
Dividing both sides by 0.20:
V_water = (0.35 / 0.20) * V1
Step 4: Convert the masses to volumes.
Since the density of water is approximately 1g/mL, we can assume that 1000g of water is equivalent to 1000 mL or 1 L.
Therefore, V_water = (0.35 / 0.20) * V1 = 1L
The volume of water that should be added to the starting solution is 1 liter.
To solve this problem, we need to use the concept of mass percentage.
We know that the starting solution is 1000g of a 55% nitric acid solution, which means that 55% of the solution's mass is nitric acid. We need to find out how many liters of water should be added to reach a final solution with a mass percentage of 20% nitric acid.
Let's first calculate the mass of nitric acid present in the starting solution:
Mass of nitric acid = 55% of 1000g
= 0.55 * 1000g
= 550g
Now, let's assume that x liters of water should be added to the starting solution. The total mass of the final solution will be the sum of the mass of nitric acid and the mass of water:
Total mass of final solution = Mass of nitric acid + Mass of water
We need to maintain a mass percentage of 20% nitric acid in the final solution. This means that the mass of nitric acid should be 20% of the total mass:
Mass of nitric acid = 20% of Total mass of final solution
Now, let's equate these two equations:
550g = 0.20 * (1000g + x)
Simplifying the equation:
550g = 200g + 0.20x
0.20x = 550g - 200g
0.20x = 350g
Now, solving for x:
x = 350g / 0.20
x = 1750g
Therefore, 1750g of water should be added to the starting solution to obtain a final solution with a mass percentage of 20% nitric acid.
Note: To convert the mass of water from grams to liters, we need to know the density of water, which is approximately 1g/mL. So, 1750g of water is equal to 1750mL, or 1.75 liters.