Question

13. What is the pH of a solution made by combining 5.0 mL of 0.10 M HCl with 1.0 x 10^-6 L of water?

A. 10.00

B. 6.30

C. 7.00

D. 2.00

The answer is C why?

Answer 1

Ans. #Approach 1: Volume of water taken = 1.0 x 10^-6 L = 0.001 mL

Total volume of solution after mixing = 5.0 mL + (1.0 x 10^-6 L)

                                                                        = 5.0 mL + 0.001 mL

                                                                        = 5.001 mL

Now,

            [HCl] in mixed solution, C2 = ( 0.10 M x 5.0 mL) / 5.001 mL

                                                            = 0.09998 M

# Being monoprotic strong acid, 1 mol HCl yields 1 mol H⁺ in the aqueous solution.

So,       [H⁺] in mixed solution = 0.09998 M

# And, pH = -log [H⁺] = -log 0.09998 = 1.00

#Approach 2: Volume of water taken = 1.0 x 10⁺⁶ L

Total volume of solution after mixing = 5.0 mL + (1.0 x 10⁶ L)

                                                            = 10⁶ L (assuming 10⁶ L >> 5.0 mL)

# Amount of HCl taken = 5.00 mL of 0.10 M = 0.005 L of 0.10 L

# Now,

            [HCl] in mixed solution, C2 = (0.10 M x 0.005 L) / 10⁶ L

                                                            = 5.0 x 10^-10 M

# Since [HCl] is extremely diluted in final solution, it’s pH is close to 7.00.

# Or, the pH of solution can be calculated using ICE approach as shown below-

# Conclusion: It seems that there is a typo error in the written volume of water being mixed. It shall be 1.0 x 10⁶ L but NOT 1.0 x 10^-6 L to get a pH of 7.00.