To calculate the amount of hydrogen peroxide (H2O2) needed to produce a 1.33 m (molal) solution, you'll need to use the formula:
molality (m) = moles of solute / mass of solvent (kg)
Since we want to find the mass of hydrogen peroxide (H2O2) needed and the volume of water given is in milliliters, we need to convert it to kilograms:
Mass of water (kg) = Volume of water (mL) / 1000
Mass of water (kg) = 1500 mL / 1000 = 1.5 kg
Next, we need to calculate the number of moles of hydrogen peroxide (H2O2) required:
molality (m) = moles of H2O2 / 1.5 kg
The molality is given as 1.33 m, so we can rearrange the formula to find the moles of H2O2:
moles of H2O2 = 1.33 m * 1.5 kg
moles of H2O2 = 1.995
Since the molar mass of hydrogen peroxide (H2O2) is approximately 34 g/mol, we can calculate the mass of H2O2 needed using the following formula:
mass of H2O2 (g) = moles of H2O2 * molar mass of H2O2
mass of H2O2 (g) = 1.995 mol * 34 g/mol
mass of H2O2 (g) = 67.83 g
Therefore, approximately 67.83 grams of hydrogen peroxide (H2O2) must be added to 1,500 mL of water to produce a concentration of 1.33 m (molal solution).