A sample of 9.3 grams of NaOH is dissolved into 555 mL of aqueous 0.250 M NaOH (assume no volume change). This solution is then poured into 2.25 gallons of water. (You may assume that the two volumes can be added.) What is the concentration of NaOH in the final solution?

The concentration of NaOH in the final solution is 0.041 mol/L.

Explanation:

1. Solution A: 555 mL of 0.250 M NaOH

0.250 mol NaOH ___ 1000 mL

x ___ 555 mL

x = 0.139 mol NaOH

2. NaOH: 40 g/mol

40 g NaOH ___ 1 mol

9.3 g NaOH ___ y

y = 0.232 mol NaOH

3. Solution B: 0.139 + 0.232 mol NaOH in 555 mL

0.371 mol NaOH ___ 555 mL

4. Final solution: 0.371 mol NaOH in (555 mL + 2.25 gallons of water)

1 gallon ___ 3785.41 mL

2.25 gallon __ V

V = 8517.17 mL = 8.517 L

Total volume: 0.555 L + 8.517 L = 9.072 L

0.371 mol NaOH ___ 9.072 L

n ___ 1.000 L

n = 0.041 mol NaOH

The concentration of NaOH in the final solution is 0.041 mol/L.