Question #7f814
1 Answer
Here's what I got.
Explanation:
!! EXTREMELY LONG ANSWER !!
The idea here is that phosphate anion,
You have three possible reactions here, depending on how many hydrogen ions are present in the solution--I won't add the chloride anions here because they are not relevant.
# "PO"_ (4(aq))^(3-) + "H"_ ((aq))^(+) -> "HPO"_ (4(aq))^(2-)" " " "color(darkorange)((1))#
#"PO"_ (4(aq))^(3-) + 2"H"_ ((aq))^(+) -> "H"_ 2"PO"_ (4(aq))^(-) " " " "color(darkorange)((2))#
#"PO"_ (4(aq))^(3-) + 3"H"_ ((aq))^(+) -> "H"_ 3"PO"_ (4(aq)) " " " "color(darkorange)((3))#
Your goal here is to figure out which of these reactions will take place. In the first case, you're mixing
#50 color(red)(cancel(color(black)("mL"))) * ("0.10 moles PO"_4^(3-))/(10^3color(red)(cancel(color(black)("mL")))) = "0.0050 moles PO"_4^(3-)#
with
#50 color(red)(cancel(color(black)("mL"))) * ("0.30 moles H"^(+))/(10^3color(red)(cancel(color(black)("mL")))) = "0.0150 moles H"^(+)#
The phosphate anions and the hydrogen ions produced by the hydrochloric acid are present in a
The reaction will consume all the moles of phosphate anions and all the moles of hydrogen ions and leave you with
#"50 mL + 50 mL = 100 mL"#
The concentration of the phosphoric acid will be
#["H"_3"PO"_4] = "0.0050 moles"/(100 * 10^(-3) quad "L") = "0.05 M"#
To find the
#"H"_ 3"PO"_ (4(aq)) rightleftharpoons "H"_ 2"PO"_ (4(aq))^(-) + "H"_ ((aq))^(+)#
The acid dissociation constant for the first ionization of phosphoric acid is
#K_(a1) = 7.52 * 10^(-3)# Keep in mind that phosphoric acid ionizes two more times in aqueous solution--it's a triprotic acid-- but the acid dissociation constants for these ionizations are so small that you can assume that they will have no impact on the final
#"pH"# of the solution.
Now, if you take
#["H"_3"PO"_4] = (0.05 -x) quad "M"# This basically means that in order for the acid to ionize and produce
#x# #"M"# of hydrogen ions and#x# #"M"# of hydrogen phosphate anions, its concentration must decrease by#x# #"M"# .
By definition, the acid dissociation constant will be
#K_(a1) = (["HPO"_4^(2-)] * ["H"^(+)])/(["H"_ 3"PO"_4])#
Plug in your values to find
#7.52 * 10^(-3) = (x * x)/(0.05 - x)#
Rearrange to quadratic equation form to get
#x^2 + 7.52 * 10^(-3) * x - 0.376 * 10^(-3) = 0#
This quadratic equation will produce two values, one positive and one negative. Since
#x = 0.015992#
This means that the concentration of hydrogen ions in this solution will be
#["H"^(+)] = "0.015992 M"#
By definition, the
#color(blue)(ul(color(black)("pH" = - log(["H"^(+)]))))#
Plug in your value to find
#"pH" = - log(0.015992) = color(darkgreen)(ul(color(black)(1.80)))#
Now, for part (2), you once again examine the number of moles of phosphate anions and of hydrogen ions you're mixing.
This time, you're mixing
#50 color(red)(cancel(color(black)("mL"))) * ("0.25 moles H"^(+))/(10^3color(red)(cancel(color(black)("mL")))) = "0.0125 moles H"^(+)#
So you know for a fact that you don't have enough moles of hydrogen ions for reaction
This time, the reaction will consume all the moles of phosphate anions and only
#0.0050 color(red)(cancel(color(black)("moles PO"_4^(3-)))) * "2 moles HCl"/(1color(red)(cancel(color(black)("mole PO"_4^(3-))))) = "0.0100 moles H"^(+)#
and produce
So after the initial reaction takes place, the solution will contain
#overbrace("0.0125 moles")^(color(blue)("what you started with")) - overbrace("0.0100 moles")^(color(blue)("what was consumed")) = "0.0025 moles H"^(+)#
Now, these extra hydrogen ions will react with the dihydrogen phosphate anions to produce phosphoric acid.
#"H"_ 2"PO"_ (4(aq))^(-) + "H"_ ((aq))^(+) -> "H"_ 3"PO"_ (4(aq))#
This reaction will consume all the moles of hydrogen ions and only
#0.0025 color(red)(cancel(color(black)("moles H"^(+)))) * ("1 mole H"_ 2"PO"_ 4^(-))/(1color(red)(cancel(color(black)("mole H"^(+))))) = "0.0025 moles H"_ 2"PO"_ 4^(-)#
and produce
#overbrace("0.0050 moles")^(color(blue)("what was produced initially")) - overbrace("0.0025 moles")^(color(blue)("what was consumed")) = "0.0025 moles H"_2"PO"_4^(-)#
The total volume of the solution will once again be
#"50 mL + 50 mL = 100 mL"#
which means that the concentrations of the two chemical species will be
#["H"_2"PO"_4^(-)] = ["H"_3"PO"_4] = "0.0025 moles"/(100 * 10^(-3) quad "L") = "0.025 M"#
At this point, the fact that the solution contains phosphoric acid, a weak acid, and dihydrogen phosphate, its conjugate base, should tell you that you're now dealing with a buffer solution.
As you know, the
#color(blue)(ul(color(black)("pH" = "p"K_a + log ( (["conjugate base"])/(["weak acid"])))))#
In your case, you have
#"pH" = "p"K_(a1) + log( (["H"_2"PO"_4^(-)])/(["H"_3"PO"_4]))#
with
#"p"K_(a1) = - log(K_(a1))#
#"p"K_(a1) = - log(7.52 * 10^(-3)) = 2.12#
Now, because your buffer contains equal concentrations of the weak acid and of its conjugate base, you can say that its
This is the case because you have
#"pH" = 2.12 + log ((color(red)(cancel(color(black)("0.025 M"))))/(color(red)(cancel(color(black)("0.025 M")))))#
#"pH" = 2.12 + 0 = color(darkgreen)(ul(color(black)(2.12)))#
And there you have it. I'll leave the answers rounded to two decimal places, but keep in mind that you have one significant figure for almost all your values, so you should report the two