- First, we will talk about
**equilibrium**and**equilibrium constant**. - Then, we will talk about the meaning of
**RICE table**. - After, we will look at some
**examples**involving RICE tables.

## RICE Tables equilibrium

Before diving into RICE table, let's review the basics of** dynamic equilibrium **and** equilibrium constant**. When a chemical reaction reaches a point where the reactant concentrations and the product concentrations are no longer changing (remains constant), it has reached **equilibrium**.

In **dynamic equilibrium**, the reactants and products are continuously reacting: reactants are being changed to products, while products are being changed back to reactants at the same rate.

When a reaction reaches **equilibrium **it does not mean that the reaction has stopped, it only means that it is reacting in both directions *at the same rate*. In other words, the **forward rate** and the **reverse rate** of the reaction are equal!

$$ A \rightleftharpoons B $$

Figure 1 shows a Concentration vs. time graph for reactant A and product B. Notice that reactant A went from having a 0.7 M concentration to a 0.3 M concentration, whereas product B went from having 0 M concentration to having a concentration of 0.2 M.

So, the change in concentration of A is equal to - 0.4 M, while the change in concentration of B is + 0.2 M. Since A, has decreased twice as much as B, has increases, then it means that to produce one B, we need two A's.

$$ \color {orchid} 2 \color {black} A_{(aq)} \to B_{(aq)} $$

Now, the **equilibrium constant (K _{eq})** is simply the ratio of concentration products to concentration of reactants at equilibrium.

- If K is greater than 1, then products are favored (and the forward direction is favored).
- If K is less than 1, then reactants are favored (and the reserve direction is favored).

$$ K_{eq} = \frac{[Products]}{[Reactants]} $$

In this case, the equilibrium constant is:

$$ K_{eq} = \frac{[Products]}{[Reactants]} = \frac{[B]}{[A]^{\color {orchid} \textbf{2}}} = \frac{[0.2]}{[0.3]^{\color {orchid}2}}=2.2 $$

**Chemical Equilibrium**" and "

**Equilibrium Constant**"!

Let's look at an example:

**For the following reaction, determine the equilibrium expression:**

$$ \color {orchid}\text{2 } \color{black}{N}_{2}\text{O}_{5} \text{ }(aq) \text{ }\rightleftharpoons \color {orchid} \text{4 } \color{black} {NO}_{2} \text{ } (aq) + \text{O}_{2} \text{ }(aq) $$

An equilibrium expression is just the formula for equilibrium constant (K_{eq}). So, in this case, the equilibrium expression will be:

$$K_{eq} = \frac{[Products]}{[Reactants]} = \frac{[NO_{2}]^{\color {orchid}\textbf{4}}[O_{2}]}{[N_{2}O_{5}]^{\color {orchid}\textbf{2}}} $$

When dealing which chemical equilibrium calculations, we can use **RICE tables **to show the initial concentration, the change in concentration and the concentration at equilibrium of reactants and products in a chemical reaction.

## RICE Tables: Meaning

Let's start by looking at the meaning of **RICE tables**. In the term RICE, R stands for "reaction", I stands for "initial concentrations", C stands for "change in concentration", and E stands for "equilibrium concentration".

A **RICE table** is a table that can be used to calculate the concentrations of reactants and products at equilibrium (provided that we know their initial concentrations), in the mixture, or to even calculate the equilibrium constant for a chemical reaction.

As an example, let's say that we have a chemical reaction where 1.50 mol of N_{2 }and 3.50 mol of H_{2} are allowed to come to equilibrium in a 1 L container at 700 °C to form NH_{3} as product. Let's calculate the equilibrium constant for this reaction if the equilibrium concentration of 2NH_{3} is 0.540 M.

$$ N_{2} (g) + \color {orchid}3 \color{black }\text{ }H_{2} (g)\rightleftharpoons \color {orchid}2 \color{black}\text{ }NH_{3}(g) $$

**Step 1: Construct a RICE table to find the equilibrium concentration of CO _{2}. **

The first thing we need to do is draw the RICE table, as seen in the figure below. The best place to construct it is under the chemical reaction.

**Step 2. Fill out the rows with the values for initial concentration, change in concentration, and equilibrium concentrations. **

In the* I *row, we need to add the initial concentrations of the reactants and products. The initial concentration of N_{2} is 1.50 mol/L whereas the initial concentration of H_{2} is 3.50 mol/L. For the product NH_{3}, we can just add 0 because at the start of the reaction, no product has been formed yet.

In the *C* row, we need to write the change in concentration due to reaction using the given reaction stoichiometric coefficients. "x" represents the change in concentration.

- N
_{2 }has a coefficient of 1. - H
_{2}has a coefficient of 3. - NH
_{3}has a coefficient of 2.

Lastly, we need to fill out the *E* row by adding the reactant and product concentrations at equilibrium in terms of the initial concentration and its change in x.

**Step 3. Determine the equilibrium expression for the reaction.**

Now, we need to write down the equilibrium expression for the chemical reaction.

$$ K_{eq} = \frac{[Products]}{[Reactants]} = \frac{[NH_{3}]^{\color {orchid}\textbf{2}}}{[N_{2}][H_{2}]^{\color {orchid}\textbf{3}}} $$

**Step 4. Solve for the equilibrium constant (K _{eq}) **

Now that we know the equilibrium equation for this chemical reaction, we can solve for K_{eq}. But first, notice that the problem tells us the equilibrium concentration of NH_{3} is 0.540 M. So, we can use it to solve for "x".

$$ [NH_{3}]_{eq} = + 2x = 0.540 \text { }M $$ $$x = 0.270\text{ } M$$

Now that we know the value for x, we can finally solve for the equilibrium constant (K_{eq}).

$$ K_{eq} = \frac{[NH_{3}]^{\color {orchid}\textbf{2}}}{[N_{2}][H_{2}]^{\color {orchid}\textbf{3}}} = \frac{[0.540 ]^{\color {orchid}\textbf{2}}}{[1.50 - 0.270][3.50 -0.270]^{\color {orchid}\textbf{3}}} = 0.0122 $$

Keep in mind that some chemistry textbooks might to refer to RICE table as ICE table or ICE chart instead.

## RICE Tables: examples

Now, let's solve another example using RICE tables.

**In a 1.0 L container, 4 moles of NO are added and allowed to reach equilibrium for the reaction below. At equilibrium, there are 1.98 moles of N _{2} present. Determine how many moles of NO are present in the mixture at equilibrium.**

$$ \color {orchid} 2 \color {black}\text{ NO} (g) \rightleftharpoons \text{N}_{2} (g)\text{ + O}_{2} (g) $$

First, we need to construct an ice table and fill it with the information given by the question. Notice that the only initial concentration that we have is that for NO because, at this point in the reaction, no products are present!

Since the amount of N_{2} at equilibrium is given to us, we can use it to solve for *x*.

$$ 0 +x = 1.98 $$ $$ x = 1.98 $$

Now that we have the value for x, we can determine the concentration of NO at equilibrium, which we determined was *4 - 2x*.

$$ [NO]_{eq} = 4 - 2x = 4-2(1.98) $$ $$ x = 0.04\text{ } M $$

## RICE Table: Practice Problems

Now that you have learned how to fill out a RICE table, let's look at a practice problem involving **partial pressures** and equilibrium.

In a gas mixture, **partial pressure** measures the concentration of the individual components.

Suppose that you have a container charged with 2 atm H₂_{ }and 2 atm Cl_{2}. At equilibrium, the partial pressure of HCl is said to be 3 atm. What is the equilibrium constant for the following reaction? Let's find out!

$$H_{2}(g)\text{ + }Cl_{2} (g) \rightleftharpoons \text{ } \color {orchid} 2\color{black} \text{ }HCl (g)$$

As with all other problems we looked at, we need to fill out a RICE table.

Since we were given the equilibrium partial pressure of HCl (3 atm), we can use it to solve for "x".

$$2x=3\text{ atm}$$ $$x = 1.5 \text{ atm}$$

Now that we have "x", we can solve for the equilibrium constant of the reaction.

$$ K_{P}=\frac{[P_{HCl}]^{\color {orchid}2}}{[P_{H_{2}}][P_{Cl_{2}}]}=\frac{[3 ]^{\color {orchid}2}}{[2-1.5][2-1.5]} = 36 $$

For a review of the partial pressure of gases, check out "**Partial Pressures**"!

## RICE Tables: Review

To make things simpler, let's make a simple review on RICE tables to help you revise for your chemistry exam.

- When dealing with equilibrium concentrations and equilibrium constants, you should always use a RICE table to help you with your calculations.
- When writing the equilibrium expression for a chemical reaction, ignores compounds/molecules in the solid or liquid states.

Now, I hope that you feel more confident in your ability to tackle problems involving RICE tables!

## RICE Tables - Key takeaways

- When a chemical reaction reaches a point where the reactant concentrations and the product concentrations are no longer changing (remains constant), it has reached
**equilibrium**. - In chemical equilibrium, the
**forward rate**and the**reverse rate**of the reaction are equal. - The
**equilibrium constant (K**is the ratio of concentration products to concentration of reactants at equilibrium._{eq}) - We can use
**RICE tables**to show the initial concentration, the change in concentration and the concentration at equilibrium of reactants and products in a chemical reaction, and also perform calculation involving concentrations at equilibrium and K_{eq}.

## References

- Chad’s Videos - Taking the Stress Out of Learning Science. (n.d.). Chad’s Prep -- DAT, MCAT, OAT & Science Prep. Retrieved October 11, 2022, from https://courses.chadsprep.com/
- Zumdahl, S. S., Zumdahl, S. A., & Decoste, D. J. (2019). Chemistry. Cengage Learning Asia Pte Ltd.
- Theodore Lawrence Brown, Eugene, H., Bursten, B. E., Murphy, C. J., Woodward, P. M., Stoltzfus, M. W., & Lufaso, M. W. (2018). Chemistry : the central science (14th ed.). Pearson.
- Moore, J. T., & Langley, R. (2021). McGraw Hill : AP chemistry, 2022. Mcgraw-Hill Education.

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##### Frequently Asked Questions about RICE Tables

What are RICE tables used for?

RICE tables can be used to calculate the concentrations of reactants and products at equilibrium (provided that we know their initial concentrations), in the mixture, or to even calculate the equilibrium constant for a chemical reaction.

How do you find the equilibrium on a RICE table?

There are some steps you can follow in order to find the equilibrium using a RICE table:

- Construct a RICE table.
- Fill out the rows with the values for initial concentration, change in concentration, and equilibrium concentrations.
- Determine for the equilibrium equilibrium expression for the reaction.
- Determine the concentration of the reactant or product at equilibrium.

How do you find the change in a RICE table?

The change in concentration can be found using the given reaction stoichiometric coefficients in the chemical reaction. Here, we use "x" to represent the change in concentration.

How do you solve RICE charts?

We can solve RICE charts by filling out the rows with the values for initial concentration, change in concentration, and equilibrium concentrations. Then, we can use it to solve problems involving chemical equilibrium.

What does the RICE table stand for?

In the term RICE, R stands for "reaction", I stands for "initial concentrations", C stands for "change in concentration", and E stands for "equilibrium concentration".

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