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http://pages.suddenlink.net/drgriffinsmathcad/ Mathcad%20-%20Strong_acid_strong_base_titration%5B1%5D.pdf

1. concentration strong base [mol/L]
2. concentration strong acid [mol/L]
.....
3. ion product of water [mol/L]
4. Volume [mL] of acid solution being titrated. cNaOH 0.05 : cHCl 0.1 : Kw 1014 -^: vHCl 50 : 41 sys

vNaOH f H Kw H / - vHCl cHCl * vNaOH vHCl + / - vNaOH cNaOH * vNaOH vHCl + / + ≡

is implicit in H+ and is a function of the volume of the titrant added vNaOH f 0 ≡

Titration curve before Equivalence point x ≤ [100 mL] pH1 x 1100 1.1 range : i 1 x rows range sol i el H Kw H / - vHCl cHCl * x i el vHCl + / - x i el cNaOH * x i el vHCl + / + 0 ≡ H 1 roots : for sol sol rows el 1107 -^* : x sol log10 vectorize - augment 41 line :

1 mL * (100 mL * (1.1 mL * range

Titration curve beyond Equivalence point  x ≥ [100 mL] pH2 u 100.001 200 100.1 range : i 1 u rows range sol i el OH Kw OH / - u i el cNaOH * u i el vHCl + / - vHCl cHCl * u i el vHCl + / + 0 ≡ OH 1 roots : for u 14 sol log10 vectorize + augment 31 line :

100 mL * (200 mL * (100.1 mL * range

Titration curves: cNaOH[0.05mol/L], cHCl[0.1mol/L] ... vHCl[50 mL]

pH1 pH2 0 1 + 40 red 1 5 mat 100 7 + 40 black 1 5 mat 4 1 sys

pH1 pH2 01 + 40 red 15 mat 1007 + 40 black 15 mat 41 sys

Observe . . .

@ infinitesimal small roots, the

Equivalence point is => pH = 7

for both titrations curves pH1, pH2

managed wisely otherwise .

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In chemistry, pH is a logarithmic scale used to specify the acidity or basicity of an aqueous solution. It is approximately the negative of the base 10 logarithm of the molar concentration, measured in units of moles per liter, of hydrogen ions. More precisely it is the negative of the base 10 logarithm of the activity of the hydrogen ion.[1] Solutions with a pH less than 7 are acidic and solutions with a pH greater than 7 are basic. Pure water is neutral, at pH 7 (25 °C), being neither an acid nor a base. Contrary to popular belief, the pH value can be less than 0 or greater than 14 for very strong acids and bases respectively.[2]

Derive a titration curve of 50 mL of 0.5 M HCl [strong acid] with 0.1 M NaOH [strong base].

HCl + NaOH + H₂O <============> H⁺ + Cl^* + Na⁺ + OH^*

The charge balance equation for this titration is: H⁺ + Na⁺ = OH^* + Cl^*

We can solve the charge balance for the H⁺ [the pH] => H⁺ = OH^* + Cl^* - Na⁺

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Once the concentration of OH^* in solution exceeds H⁺ , the H⁺ concentration becomes negative.

We then have to rewrite the charge balance equation in term of OH^*

The charge balance is: H⁺+ Na⁺ ≡ OH^*+ Cl^*

OH^* ≡ Na⁺ - (Cl^* + H⁺)

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The procedure is the same as before, solve for a range of titrant volume using root function.

In this case, the starting value for the titrant volume will be approximately the same as the

ending value for the previous equation-solution.

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On-line interpolate titration

1. concentration strong base [mol/L]
2. concentration strong acid [mol/L]
.....
3. ion product of water [mol/L]
4. Volume [mL] of acid solution being titrated cNaOH 0.05 : cHCl 0.1 : Kw 1014 -^: vHCl 50 : 41 sys

x pH1 H Kw H / - vHCl cHCl * x vHCl + / - x cNaOH * x vHCl + / + 0 ≡ H 1 roots : u pH2 OH Kw OH / - u cNaOH * u vHCl + / - vHCl cHCl * u vHCl + / + 0 ≡ OH 1 roots : 21 sys

1 x ≤ (x 100 ≤ (&

100 u ≤ (u 200 ≤ (&

<= pH 25 pH1 log10 - 14115 pH2 log10 + 21 mat 1.30 11.66 21 mat

symmetric fraction ± Equivalence [100 = pH 7] f 5 :

<= pH 100 f - pH1 log10 - 14100 f + pH2 log10 + 21 mat 2.76 11.21 21 mat