Question

Household bleach contains 5.25% (m/v) of sodium hypochlorite. It is often recommended that you dilute the household bleach to 0.110% (m/v) before using. If you need 1.00 gallons of diluted bleach, how many cups of household bleach should you measure?

Answer 1

First, we need to calculate how much sodium hypochlorite is in 1 gallon of 0.110% bleach solution:

0.110% (m/v) = 0.110 g/100 mL

1 gallon = 3,785 mL

So, the mass of sodium hypochlorite in 1 gallon of 0.110% bleach solution is:

0.110 g/100 mL x 3,785 mL = 4.1635 g

Now we can use this information to calculate how much undiluted household bleach we need:

5.25% (m/v) = 5.25 g/100 mL

Let's call the volume of undiluted bleach we need "V".

We can set up a proportion:

5.25 g/100 mL = 4.1635 g/3785 mL

Solving for V:

5.25 g/100 mL = x/3785 mL

x = 199.0425 g

Finally, we need to convert grams to cups. The density of household bleach is about 1.08 g/mL, so:

199.0425 g ÷ 1.08 g/mL = 184.31 mL

There are 48 teaspoons in a cup, and 5 mL in a teaspoon, so:

184.31 mL ÷ 5 mL/teaspoon ÷ 48 teaspoons/cup ≈ 0.77 cups

Therefore, you should measure approximately 0.77 cups of household bleach to make 1.00 gallon of diluted bleach solution.