# A buffer solution was prepared by mixing #"392 mL"# of #"0.301 M"# #"NaClO"# and #"181 mL"# of #"0.281 M"# #"HClO"#. Calculate the #"pH"# of the solution?

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Given that #K_a = 3.2 * 10^(-8)# . Express the answer rounded to 3 decimal places.

Given that

##### 1 Answer

#### Answer:

#### Explanation:

You're dealing with a weak acid - conjugate base buffer that has hypochlorous acid,

As you know, the **Henderson - Hasselbalch equation**.

#"pH" = "p"K_a + log ((["conjugate base"])/(["weak acid"]))#

Here

#"p"K_a = - log(K_a)#

Now, your goal here is to figure out the concentrations of the hypochlorous acid and of the hypochlorite anion **after** you mix the two solutions.

Right from the start, you know that the volume of the resulting solution will be

#"392 mL + 181 mL = 573 mL"#

Now, use the molarity and the volume of the hypochlorous solution to calculate how many moles of the weak acid are present.

#181 color(red)(cancel(color(black)("mL solution"))) * "0.281 moles HClO"/(10^3color(red)(cancel(color(black)("mL solution")))) = "0.050861 moles HClO"#

Next, do the same for the sodium hypochlorite solution, which as you know, dissociates in a

#392 color(red)(cancel(color(black)("mL solution"))) * "0.301 moles ClO"^(-)/(10^3color(red)(cancel(color(black)("mL solution")))) = "0.11799 moles ClO"^(-)#

To calculate the concentrations of the two species **after** the two solutions are mixed, use the total volume of the solution--do not forget to convert it to *liters*!

#["HClO"] = "0.050861 moles"/(573 * 10^(-3) quad "L") = "0.08876 M"#

#["ClO"^(-)] = "0.11799 moles"/(573 * 10^(-3) quad "L") = "0.2059 M"#

Plug your values into the Henderson - Hasselbalch equation to find the

#"pH" = - log(3.2 * 10^(-8)) + log ( (0.2059 color(red)(cancel(color(black)("M"))))/(0.08876 color(red)(cancel(color(black)("M")))))#

#color(darkgreen)(ul(color(black)("pH" = 7.860)))#

The answer is rounded to three **decimal places**, the number of **sig figs** you have for your values.

Notice that the **higher** than the

When this happens, the **higher** than the **lower** than the