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# RICE Tables

In chemistry, Chemical Equilibrium is dynamic, meaning that when a chemical reaction reaches equilibrium, things continue to happen, but nothing really changes. When chemists want to solve problems involving reactants, products, and equilibrium, they use RICE tables

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• 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.

Figure 1. Concentration vs. Time graph for A and B, Isadora Santos - StudySmarter Originals.

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 (Keq) 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:

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

When writing an equilibrium expression, solids and liquids are ignored. For an in-depth explanation on equilibrium, check out "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 (Keq). 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 N2 and 3.50 mol of H2 are allowed to come to equilibrium in a 1 L container at 700 °C to form NH3 as product. Let's calculate the equilibrium constant for this reaction if the equilibrium concentration of 2NH3 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 CO2.

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.

Figure 2. An empty RICE table, Isadora Santos- StudySmarter Originals.

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 N2 is 1.50 mol/L whereas the initial concentration of H2 is 3.50 mol/L. For the product NH3, 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.

• N2 has a coefficient of 1.
• H2 has a coefficient of 3.
• NH3 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.

Figure 3. How to fill out a RICE table, Isadora Santos - StudySmarter Originals.

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 (Keq)

Now that we know the equilibrium equation for this chemical reaction, we can solve for Keq. But first, notice that the problem tells us the equilibrium concentration of NH3 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 (Keq).

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

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 N2 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!

Figure 4. RICE table example, Isadora Santos - StudySmarter Originals.

Since the amount of N2 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 Cl2. 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.

Figure 5. RICE table for an example using partial pressures, Isadora Santos - StudySmarter Originals.

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.

1. When dealing with equilibrium concentrations and equilibrium constants, you should always use a RICE table to help you with your calculations.
2. 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 (Keq) is the ratio of concentration products to concentration of reactants at equilibrium.
• 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 Keq.

## References

1. 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/
2. Zumdahl, S. S., Zumdahl, S. A., & Decoste, D. J. (2019). Chemistry. Cengage Learning Asia Pte Ltd.
3. 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.
4. Moore, J. T., & Langley, R. (2021). McGraw Hill : AP chemistry, 2022. Mcgraw-Hill Education.

#### Flashcards in RICE Tables 14

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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:

1. Construct a RICE table.
2. Fill out the rows with the values for initial concentration, change in concentration, and equilibrium concentrations.
3. Determine for the equilibrium equilibrium expression for the reaction.
4. 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".

## Test your knowledge with multiple choice flashcards

True or false: another name to RICE table is ICE chart.

In a 1.0 L container, 4 mol of NO are added and allowed to reach equilibrium for the reaction below. At equilibrium, there are 1.98 mol of N2 present. Determine how many moles of NO are present in the mixture at equilibrium.

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

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