RICE chart

RICE chart, or RICE box is a tabular system of keeping track of changing concentrations in an equilibrium reaction. RICE stands for "Reaction, Initial, Change, Equilibrium".^[1] It is used in chemistry to keep track of the changes in amount of substance of the reactants and also organize a set of conditions that one wants to solve with.

Example

To illustrate the processes, consider the case of dissolving a weak acid, HA, in water. How can the pH be calculated? 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 [OH⁻] 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. This is generally regarded as the 'R'.

{\ce {HA<=>{A^{-}}+{H+}}}

The columns of the table correspond to the three species in equilibrium.

R	[HA]	[A⁻]	[H⁺]
I	C_a	0	0
C	-x	+x	+x
E	C_a - x	x	x

The first 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 second row, labeled C, specifies the change that occurs during the reaction. When the acid dissociates, its concentration changes by an amount $-x$ , and the concentrations of A⁻ and H⁺ both change by an amount $+x$ . 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 "2x"

The third 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, [H⁺] = x.

To find x, the equilibrium constant must be specified.

K_{a}={\frac {\ce {[H^{+}][A^{-}]}}{\ce {[HA]}}}

Substitute the concentrations with the values found in the last row of the ICE table.

K_{a}={\frac {x^{2}}{C_{a}-x}}

x^{2}+K_{a}x-K_{a}C_{a}=0

With specific values for C_a and K_a this quadratic equation can be solved for x. Assuming^[2] that pH = -log₁₀[H⁺] the pH can be calculated as pH = -log₁₀x.

If the degree of dissociation is quite small, C_a ≫ x and the expression simplifies to

K_{a}={\frac {x^{2}}{C_{a}}}

and pH= 1/2( pK_a - log C_a). This approximate expression is good for pK_a values larger than about 2 and concentrations high enough.

References

↑ General Chemistry Concepts - YouTube
↑ Strictly speaking pH is equal to -log₁₀{H⁺} where {H⁺} is the activity of the hydrogen ion. In dilute solution concentration is almost equal to activity

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