Factors Independently Influencing Water Dissociation
After considering the factors that can influence the concentration
of hydrogen ions in a solution—strong ions, weak acids, and CO2
—we
can combine the derived equations to solve for [H+
]:
|
Water dissociation equilibrium: |
[H+
× [OH-
] = KW
|
|
Weak acid dissociation equilibrium: |
[H+
] × [A-
] = KA
×
[HA] |
|
Conservation of mass for weak acids: |
[HA] + [A-
] = [ATOT
] |
|
Bicarbonate ion formation equilibrium: |
[H+
] × [HCO3
-
] = KC
× PCO2
|
|
Carbonate ion formation equilibrium: |
[H+
] × [CO3
2-
] = K3
× [HCO3
-
] |
|
Electrical neutrality: |
[SID] + [H+
] - [HCO3
-
] - [A-
]
- [CO3
2-
] - [OH-
] = 0 |
There are six independent simultaneous equations and just six
unknown, dependent variables determined by them: [HA], [A-
], [HCO3
-
],
[CO3
2-
], [OH-
], and [H+
]. There are
three known independent variables: [SID], [ATOT
], and PCO2
.
Although these equations look relatively simple, they require
fourth-order polynomials for solution. This is not possible without computer technology.
Solving the equations for [H+
]:
[H+
]4
+ ([SID] + KA
)
× [H+
]3
+ (KA
× ([SID] −
[ATOT
]) − Kw
−
Kc
× PCO2
)
× [H+
]2
− (KA
× (Kw
+ Kc
× PCO2
) − K3
× Kc
× PCO2
)
× [H+
] − KA
× K3
× Kc
× PCO2
= 0
In other words, [H+
] is a function of SID, ATOT
, PCO2
,
and several constants. All other variables, most notably [H+
], [OH-
],
and [HCO3
-
], are dependent and cannot independently influence
the acid-base balance.
