An ICE table or RICE box or RICE chart is a tabular system of keeping track of changing concentrations in an
equilibrium reaction
In a chemical reaction, chemical equilibrium is the state in which both the reactants and products are present in concentrations which have no further tendency to change with time, so that there is no observable change in the properties of the sy ...
. ICE stands for ''initial, change, equilibrium''. It is used in chemistry to keep track of the changes in
amount of substance
In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the quantity or number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or entities may be molecules, atoms, ions, ...
of the reactants and also organize a set of conditions that one wants to solve with. Some sources refer to a RICE table (or box or chart) where the added R stands for the ''reaction'' to which the table refers. Others simply call it a concentration table (for the acid–base equilibrium).
Example
To illustrate the processes, consider the case of dissolving a
weak acid
Acid strength is the tendency of an acid, symbolised by the chemical formula HA, to dissociate into a hydron (chemistry), proton, H+, and an anion, A-. The Dissociation (chemistry), dissociation of a strong acid in solution is effectively comple ...
, HA, in water. The pH can be calculated using an ICE table. Note that in this example, we are assuming that the acid is not very weak, and that the concentration is not very dilute, so that the concentration of
−">H−ions can be neglected. This is equivalent to the assumption that the final pH will be below about 6 or so. See
Calculations of pH for more details.
First write down the equilibrium expression.
HA <=> +
The columns of the table correspond to the three species in equilibrium.
The first row shows the reaction, which some authors label R and some leave blank.
The second row, labeled I, has the initial conditions: the ''nominal concentration'' of acid is C
a and it is initially undissociated, so the concentrations of A
− and H
+ are zero.
The third row, labeled C, specifies the change that occurs during the reaction. When the acid dissociates, its concentration changes by an amount , and the concentrations of A
− and H
+ both change by an amount . This follows from consideration of ''mass balance'' (the total number of each atom/molecule must remain the same) and ''charge balance'' (the sum of the electric charges before and after the reaction must be zero).
Note that the coefficients in front of the "''x''" correlate to the mole ratios of the reactants to the product. For example, if the reaction equation had 2 H
+ ions in the product, then the "change" for that cell would be "2''x''"
The fourth row, labeled E, is the sum of the first two rows and shows the final concentrations of each species at equilibrium.
It can be seen from the table that, at equilibrium,
+">+= ''x''.
To find ''x'', the
acid dissociation constant
In chemistry, an acid dissociation constant (also known as acidity constant, or acid-ionization constant; denoted ) is a quantitative measure of the strength of an acid in solution. It is the equilibrium constant for a chemical reaction
:HA ...
(that is, the
equilibrium constant
The equilibrium constant of a chemical reaction is the value of its reaction quotient at chemical equilibrium, a state approached by a dynamic chemical system after sufficient time has elapsed at which its composition has no measurable tendency ...
for acid-base
dissociation
Dissociation, in the wide sense of the word, is an act of disuniting or separating a complex object into parts. Dissociation may also refer to:
* Dissociation (chemistry), general process in which molecules or ionic compounds (complexes, or salts) ...
) must be specified.
Substitute the concentrations with the values found in the last row of the ICE table.
With specific values for ''C
a'' and ''K''
a this
quadratic equation
In algebra, a quadratic equation () is any equation that can be rearranged in standard form as
ax^2 + bx + c = 0\,,
where represents an unknown (mathematics), unknown value, and , , and represent known numbers, where . (If and then the equati ...
can be solved for ''x''. Assuming
[Strictly speaking pH is equal to −log10 where is the activity of the hydrogen ion. In dilute solution concentration is almost equal to activity] that pH = −log
10 +">+the pH can be calculated as pH = −log
10''x''.
If the degree of dissociation is quite small, ''C
a'' ≫ ''x'' and the expression simplifies to
and pH = {{sfrac, 1, 2 (p''K''
a − log ''C
a''). This approximate expression is good for p''K''
a values larger than about 2 and concentrations high enough.
References
Equilibrium chemistry
Physical chemistry