Sea: X = [H+], Y= [OH-]
CASO
DATOS
L. A. M.
B. C.
B. M.
ECUACIONES POLINOMIALES
EC. LINEAL
Ácido fuerte
(HA)
Co
Kw = X Y
X = [A-] + Y
Co = [A-]
X2 – Co X – Kw = 0
X = Co
Base fuerte
(BOH)
Co
Kw = X Y
X + [B+] = Y
Co = [B+]
Y2 – Co Y – Kw = 0
Y = Co
Ácido débil
(Ha)
Co Ka
𝐾𝑤 = 𝑋. 𝑌
𝐾𝑎 = [𝑎−] 𝑋
[𝐻𝑎]
X= [a-] + Y
Co = [a-] + [Ha]
X3 + Ka.X2 -(Kw + CoKa)X – Kw Ka = 0
X2 + Ka.X - CoKa = 0
𝑋 = √𝐶𝑜.𝐾𝑎
Base débil
(bOH)
Co Kb
𝐾𝑤=𝑋𝑌
𝐾𝑏=[𝑏+]𝑌
[𝑏𝑂𝐻]
𝑋 + [𝑏+] = 𝑌
𝐶𝑜= [𝑏+] +[𝑏𝑂𝐻]
𝑌3+ 𝐾𝑏𝑌2− (𝐾𝑤+ 𝐶𝑜𝐾𝑏)𝑌 − 𝐾𝑤𝐾𝑏= 0
Y2 + Kb.Y - CoKb =0
𝑌 = √𝐶𝑜𝐾𝑏
Hidrólisis BFad
(Ba)
Cs Ka
𝐾𝑤=𝑋𝑌
𝐾ℎ=[𝐻𝑎] 𝑌
[𝑎−] = 𝐾𝑤
𝐾𝑎
𝑋 + [𝐵+]= 𝑌 + [𝑎−]
𝐶𝑠=[𝐵+]
𝐶𝑠=[𝑎−]+ [𝐻𝑎]
𝑌3+ 𝐾ℎ𝑌2− (𝐶𝑆𝐾ℎ+ 𝐾𝑤)𝑌 − 𝐾ℎ𝐾𝑤= 0
𝑌2+ 𝐾ℎ𝑌 − 𝐾ℎ𝐶𝑠= 0
𝑌 = √𝐶𝑠𝐾ℎ
GraHid = Y/Cs
Hidrólisis bdAF
(bA)
Cs Kb
𝐾𝑊= 𝑋. 𝑌
𝐾ℎ = [𝑏𝑂𝐻] 𝑋
[𝑏+] = 𝐾𝑤
𝐾𝑏
𝑋 + [𝑏+] = [𝐴−] + 𝑌
𝐶𝑠 = [𝐴−]
𝐶𝑠 = [𝑏+] + [𝑏𝑂𝐻]
X3+ 𝐾ℎX2− (𝐶𝑆𝐾ℎ+ 𝐾𝑤)X − 𝐾ℎ𝐾𝑤= 0
𝑋2+ 𝐾ℎ𝑋 − 𝐾ℎ𝐶𝑠= 0
𝑋 = √𝐶𝑠. 𝐾ℎ
GraHid = X/Cs
Hidrólisis bdad
(ba)
Cs
Ka Kb
𝐾𝑤=𝑋𝑌
𝑌[𝑎−]
[𝐻𝑎]= 𝐾𝑎
𝐾𝑤
𝐾𝑎𝐾𝑏 =[𝐻𝑎][𝑏𝑂𝐻]
[𝑎−][𝑏+]= 𝐾ℎ
𝑋 + [𝑏+] = 𝑌 + [𝑎−]
𝐶𝑠= [𝑏+] + [𝑏𝑂𝐻]
𝐶𝑠= [𝑎−] + [𝐻𝑎]
𝑋4+ (𝐾𝑎+ 𝐶𝑠+ 𝐾𝑤/𝐾𝑏) 𝑋3+
(𝐾𝑎𝐾𝑤/𝐾𝑏− 𝐾𝑤) 𝑋2
−(𝐾𝑎𝐾𝑤+ 𝐾𝑎𝐾𝑤𝐶𝑠/𝐾𝑏+ 𝐾𝑤2/𝐾𝑏) 𝑋
−𝐾𝑎𝐾𝑤2/𝐾𝑏= 0
𝑋 = √𝐾𝑤.𝐾𝑎/𝐾𝑏
GraHid = √𝐾ℎ
√𝐾ℎ +1
Tampón
“ácido”
(Ha + Ba)
Ca Cs
Ka
𝐾𝑤=𝑋𝑌
𝐾𝑎=[𝑎−]𝑋
[𝐻𝑎]
[𝐵+]+ 𝑋 = 𝑌 + [𝑎−]
𝐶𝑠=[𝐵+]
𝐶𝑎+ 𝐶𝑠=[𝐻𝑎]+[𝑎−]
X3+ (𝐶𝑆+ 𝐾a)X2− (𝐶a𝐾a+ 𝐾𝑤)X − 𝐾a𝐾𝑤= 0
𝑋2+ (𝐶𝑠+ 𝐾𝑎)𝑋 − 𝐾𝑎𝐶𝑎= 0
𝑋 = 𝐾𝑎𝐶𝑎
𝐶𝑠
Tampón
“básico”
(bOH + bA)
Cb Cs
Kb
𝐾𝑤 = 𝑋 𝑌
𝐾𝑏 = [𝑏+] 𝑌
[𝑏𝑂𝐻]
[𝑏+] + 𝑋 = [𝐴−] + 𝑌
𝐶𝑠 = [𝐴−]
𝐶𝑠 +𝐶𝑏 = [𝑏𝑂𝐻]+[𝑏+]
Y3+ (𝐶𝑆+ 𝐾a)Y2− (𝐶a𝐾a+ 𝐾𝑤)Y − 𝐾a𝐾𝑤= 0
𝑌2+ (𝐶𝑠 +𝐾𝑏)𝑌 − 𝐾𝑏.𝐶𝑏 = 0
Y=𝐾𝑏 .𝐶𝑏
𝐶𝑠
