A solution of household bleach contains 5.25% sodium hypochlorite, NaOCl, by mass. Assuming that the density of bleach is the same as water, calculate the volume of household bleach that should be diluted with water to make 500.0 mL of a pH = 10.23 solution.
To calculate the volume of household bleach needed to make a 500.0 mL solution with a pH of 10.23, we need to use the concept of dilution and the given concentration of sodium hypochlorite in the bleach.
Here's how you can approach this problem step by step:
Step 1: Determine the concentration of sodium hypochlorite in the final solution.
The concentration of sodium hypochlorite in the bleach solution is given as 5.25% by mass. To convert this into a mass/volume concentration, divide the percentage by 100:
∴ Sodium hypochlorite concentration = 5.25% / 100 = 0.0525 g/mL
Step 2: Determine the mass and volume of sodium hypochlorite needed in the final solution.
To find the mass of sodium hypochlorite needed, multiply the desired final volume (500.0 mL) by the concentration:
Mass of sodium hypochlorite = Volume × Concentration
Mass of sodium hypochlorite = 500.0 mL × 0.0525 g/mL
Step 3: Determine the volume of bleach needed for the desired mass of sodium hypochlorite.
Since the density of bleach is assumed to be the same as water (1 g/mL), we can equate the mass of sodium hypochlorite obtained in Step 2 to the volume of bleach needed:
Volume of bleach = Mass of sodium hypochlorite / Density of bleach
Volume of bleach = (500.0 mL × 0.0525 g/mL) / 1 g/mL
Calculating the values:
Volume of bleach = 26.25 mL
Therefore, you would need to dilute 26.25 mL of household bleach with water to make a 500.0 mL solution with a pH of 10.23.