find the concentration

Question

1. what is the concentration of H+ ions in a 0.0356 M solution of hydriodic acid?

 

2. what is the concentration of H+ ions in a 0.0356 M solution of phosphoric acid?

Answer 1

1.  HI is a strong acid (K_a >> 1), and  therefore will ionize completely.  The H⁺ concentration will be 0.0356 M.

 

2.  Phosphoric acid is not a strong acid, and therefore will not ionize completely in water.  To find the H⁺ concentration, one needs to know the K₁ value.  This value is listed at one source as 7.25 x 10^-3.  The K₂ value is listed as 6.31 x 10^-8, and the K₃ value is listed as 4.80 x 10^-13.  In any case, only the K₁ value is needed to solve this problem.  The equilibrium constant expression is    K₁ = 7.25 x 10^-3 = [H⁺][H₂PO₄^-] / [H₃PO₄].  Let X be the molar concentration of H⁺ after equilibrium is established.  Since equal amounts of H⁺ and H₂PO₄^- are formed, [H₂PO₄^-] = X.  The equilibrium concentration of H₃PO₄ will be 0.0356 - X.  Now substitute these expressions into the equilibrium constant expression, and solve for X:

 

7.25 x 10^-3 = X² / (.0356 - X)  -->  -7.25 x 10^-3X + 2.581 x 10^-4 = X²  -->  X² + 7.25 x 10^-3X - 2.581 x 10^-4 = 0.  Now solve using the quadratic formula (ignore the negative value):  X = (-7.25 x 10^-3 + √(5.25625 x 10^-5 + (4)(2.581 x 10^-4))/2  -->  X = 0.0128.  Therefore, [H⁺] = 0.0128 M.

Answer 2

1, Hydroiodic acid is HI, or H⁺I^- when ionized.  Each molecule of HI contains one H⁺ ion, so the number of moles of H⁺ ions is the same as the number of moles of HI itself.  Therefore the concentration of H⁺ is 0.0356 M.

 

2. Phosphoric acid is H₃PO₄ (H⁺₃ PO₄^-).  Each molecule contains 3 H⁺ ions, so there are 3 times as many H⁺ ions as H₃PO₄ molecules.  So the concentration of H⁺ ions is 3 times the concentration of H₃PO_4, or 3 * 0.0356 = 0.1068 M.