Cubic equation in 1 unknown H Can be solved by trial error The correct solution

# Cubic equation in 1 unknown h can be solved by trial

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Cubic equation in 1 unknown {H + }. Can be solved by trial error. The correct solution is the one that yields the positive value ( {H + }=10 -3.963 and pH = 3.963 ) Follow the approach used in this solution to solve problem-1 using the spreadsheet approach, the mass balance (MB) and charge balance (CB) equations. Determine the pH of a solution obtained when H 3 C-COOH or HAc is added to water to a final concentration of 10 -2 M – Assume ideal solution. Just replace HPr by HAc, and Pr by Ac

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{ ? + ¿ } [ ? ] [ ?? ] = ? ? ¿ Fra ctions for m onop roti c acid
From the K w equation: And the CB equation can be rewritten as: Next, we know that for a monoprotic acid: and SOLUTION TO EXAMPLE PROBLEM-1: Using the spreadsheet approach, solve for pH by finding the point of charge balance, that is: S (+) = S (-) and S (+) – S (-) = 0 1. Species present Type (a): Type (b): Type (c): None Type (d): None Type (e): N/A 2. Relevant Chemical Reactions H 2 O = H + + OH - HAc = H + + Ac - 3. Equilibrium relationships 4. Mass Balance (MB) Equations TOTAc = [HAc] + [Ac - ] = 0.01 M 5. Charge Balance (CB) Equation [H + ] = [OH - ] + [Ac - ] SOLVING FOR pH

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pH [H+]=10 -pH [OH - ] = K w /[H + ] [Ac - ] = (TOTAc)(K a /(K a +[H + ])) Sum(+)-Sum(-) ([H+]) - ([OH-]-[Ac-]) 0 1 1E-14 1.79997E-07 0.9999998200 1 0.1 1E-13 1.79968E-06 0.0999982003 2 0.01 1E-12 1.79677E-05 0.0099820323 3 0.001 1E-11 0.000176817 0.0008231827 4 0.0001 1E-10 0.001525424 -0.0014254238 5 0.00001 0.000000001 0.006428571 -0.0064185724 6 0.000001 0.00000001 0.009473684 -0.0094726942 7 0.0000001 0.0000001 0.009944751 -0.0099447514 8 0.00000001 0.000001 0.009994448 -0.0099954375 9 0.000000001 0.00001 0.009999444 -0.0100094435 10 1E-10 0.0001 0.009999944 -0.0100999443 11 1E-11 0.001 0.009999994 -0.0109999944 12 1E-12 0.01 0.009999999 -0.0199999994 13 1E-13 0.1 0.01 -0.1099999999 14 1E-14 1 0.01 -1.0100000000
pH [H+]=10 -pH [OH - ] = K w /[H + ] [Ac - ] = (TOTAc)(K a /(K a +[H + ]) Sum(+)-Sum(-) 3.00 0.001 1E-11 0.000176817 0.0008231827 3.10 0.000794328 1.25893E-11 0.000221585 0.0005727429 3.20 0.000630957 1.58489E-11 0.000277368 0.0003535893 3.30 0.000501187 1.99526E-11 0.000346696 0.0001544915 3.40 0.000398107 2.51189E-11 0.000432581 -0.0000344737 3.50 0.000316228 3.16228E-11 0.000538555 -0.0002223272 3.60 0.000251189 3.98107E-11 0.000668676 -0.0004174875 3.70 0.000199526 5.01187E-11

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• Fall '08
• pH, HAc

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