2.500 mL of ~3% w/v (i.e. 3 g in 100. mL) H2O2 solution is diluted with water to 25.00mL. If 40.05 mL of 0.02000 mol/L solution is required to completely react with 25.00 mL of diluted H2O2 solution, what is the mass concentration of the original (undiluted) H2O2 solution?
To find the mass concentration of the original H2O2 solution, we need to calculate the number of moles of H2O2 in the diluted solution and then convert it to mass.
First, let's calculate the number of moles of H2O2 in the diluted solution:
Volume of H2O2 solution = 2.500 mL = 0.002500 L
Concentration of H2O2 in diluted solution = 3% w/v = 3 g/100 mL = 30 g/L
Number of moles of H2O2 in diluted solution = Concentration x Volume
= 30 g/L x 0.002500 L
= 0.075 mol
Next, let's calculate the number of moles of H2O2 in the 0.02000 mol/L solution:
Volume of 0.02000 mol/L solution = 40.05 mL = 0.04005 L
Number of moles of H2O2 in 0.02000 mol/L solution = Concentration x Volume
= 0.02000 mol/L x 0.04005 L
= 0.000802 mol
Since the number of moles of H2O2 in the diluted solution and the 0.02000 mol/L solution are equal (they completely react with each other), we can set up the following equation:
Number of moles of H2O2 in diluted solution = Number of moles of H2O2 in 0.02000 mol/L solution
0.075 mol = 0.000802 mol
Now, let's find the volume of the original (undiluted) H2O2 solution:
Volume of the original (undiluted) H2O2 solution = Volume of diluted solution / Dilution factor
= 25.00 mL / (25.00 mL / 2.500 mL)
= 2.500 mL
Finally, let's calculate the mass concentration of the original H2O2 solution:
Mass of H2O2 in original solution = Number of moles x Molar mass
= 0.075 mol x 34.02 g/mol (molar mass of H2O2)
= 2.5525 g
Mass concentration of the original H2O2 solution = Mass of H2O2 / Volume of original solution
= 2.5525 g / 2.500 mL
= 1.021 g/mL
Therefore, the mass concentration of the original (undiluted) H2O2 solution is 1.021 g/mL.
To solve this problem, we'll follow these steps:
Step 1: Calculate the amount of H2O2 remaining in the diluted solution.
Step 2: Calculate the moles of H2O2 in the diluted solution.
Step 3: Determine the moles of H2O2 in the original (undiluted) solution.
Step 4: Calculate the mass of H2O2 in the original solution.
Step 5: Calculate the mass concentration of the original (undiluted) H2O2 solution.
Let's begin!
Step 1: Calculate the amount of H2O2 remaining in the diluted solution.
- We know that 2.500 mL of the diluted solution is used.
- The concentration of H2O2 in the diluted solution is 3% w/v, which means 3g of H2O2 is present in 100.0 mL of solution.
- We can calculate the amount of H2O2 in the diluted solution using a proportion:
(3g / 100.0 mL) = (x g / 2.500 mL)
- Cross-multiplying, we get:
(3g x 2.500 mL) = (100.0 mL x grams)
7.500 g = 100.0 mL x grams
- Dividing both sides by 100.0 mL, we find:
grams = 7.500 g / 100.0 mL
grams = 0.075 g
So, there are 0.075 grams of H2O2 remaining in the diluted solution.
Step 2: Calculate the moles of H2O2 in the diluted solution.
- We know the molar mass of H2O2 is 34.02 g/mol.
- We have calculated the mass of H2O2 in the diluted solution as 0.075 g.
- We can calculate the moles using the formula:
Moles = Mass / Molar Mass
- Substituting the values, we get:
Moles = 0.075 g / 34.02 g/mol
Moles = 0.002206 mol
So, there are 0.002206 moles of H2O2 in the diluted solution.
Step 3: Determine the moles of H2O2 in the original (undiluted) solution.
- We know that 40.05 mL of 0.02000 mol/L solution reacts with 25.00 mL of the diluted H2O2 solution.
- We can use the equation:
Moles1 x Volume1 = Moles2 x Volume2
- Substituting the values, we get:
Moles1 x 40.05 mL = 0.002206 mol x 25.00 mL
- Solving for Moles1, we find:
Moles1 = (0.002206 mol x 25.00 mL) / 40.05 mL
Moles1 = 0.001377 mol
So, there are 0.001377 moles of H2O2 in the original (undiluted) solution.
Step 4: Calculate the mass of H2O2 in the original solution.
- We know that 0.001377 moles of H2O2 is present in the original solution.
- We can calculate the mass using the formula:
Mass = Moles x Molar Mass
- Substituting the values, we get:
Mass = 0.001377 mol x 34.02 g/mol
Mass = 0.046855 g
So, the mass of H2O2 in the original (undiluted) solution is 0.046855 grams.
Step 5: Calculate the mass concentration of the original (undiluted) H2O2 solution.
- We know that the original solution was diluted to 25.00 mL.
- We can calculate the mass concentration using the formula:
Mass Concentration = Mass / Volume
- Substituting the values, we get:
Mass Concentration = 0.046855 g / 25.00 mL
Mass Concentration = 1.8742 g/mL
So, the mass concentration of the original (undiluted) H2O2 solution is 1.8742 g/mL.