starting with a 30% (W/W) SOLUTION OF HYDROGEN PEROXIDE, how many mL would you need to dilute on order to end up with 25.00ml of a 3.6M hydrogen peroxide solution?
To find out the volume of a 30% (w/w) hydrogen peroxide solution needed to obtain a 25.00 mL solution with a concentration of 3.6 M, we can use the concept of moles and the equation:
Molarity (M) = Moles (mol) / Volume (L)
First, we need to calculate the moles of hydrogen peroxide we want in the final solution. The molarity of the final solution is given as 3.6 M, and the volume is given as 25.00 mL. Therefore, we can calculate the moles:
Moles (mol) = Molarity (M) * Volume (L)
= 3.6 mol/L * (25.00 * 10^-3 L)
= 0.09 moles
Since the desired solution is 3.6 M, the number of moles of hydrogen peroxide is 0.09 mol.
The initial solution is 30% (w/w) hydrogen peroxide, which means that for every 100 grams of the solution, we have 30 grams of hydrogen peroxide.
To calculate the mass of hydrogen peroxide in our desired solution, we can use the equation:
Mass of Hydrogen Peroxide (g) = Percentage (w/w) * Total Mass (g)
Since we don't know the total mass of the initial solution, we assume it to be 100 grams for convenience. Therefore:
Mass of Hydrogen Peroxide (g) = 30% * 100g
= 30g
Next, we need to convert the mass of hydrogen peroxide to moles using its molar mass. The molar mass of hydrogen peroxide (H2O2) is:
Molar Mass (H2O2) = (2 * Molar Mass (H)) + (2 * Molar Mass (O))
= (2 * 1.008 g/mol) + (2 * 16.00 g/mol)
= 2.016 g/mol + 32.00 g/mol
= 34.016 g/mol
Now, we can calculate the number of moles of hydrogen peroxide in the 30% solution:
Moles (H2O2) = Mass (H2O2) / Molar Mass (H2O2)
= 30g / 34.016 g/mol
≈ 0.881 moles
We can use this information to calculate the volume of the 30% solution needed to obtain 0.09 moles of hydrogen peroxide:
Volume (L) = Moles (H2O2) / Molarity (M)
= 0.09 mol / 0.881 mol/L
≈ 0.102 L
Finally, we can convert the volume to milliliters:
Volume (mL) = Volume (L) * 1000
= 0.102 L * 1000
≈ 102 mL
Therefore, you would need to dilute approximately 102 mL of the 30% (w/w) hydrogen peroxide solution to obtain 25.00 mL of a 3.6 M hydrogen peroxide solution.