However, sometimes our body isn't quite at an equilibrium. There might be too much glucose in our blood, or perhaps not enough. The **reaction quotient** is a handy way of looking at reversible reactions that haven't yet reached equilibrium.

- This article is about the
**reaction quotient**,**Q**, in chemistry. - We'll
**define the reaction quotient**and**expression**before seeing how it**differs from the****equilibrium constant, K**_{eq}. - We'll then go through an example of
**calculating the reaction quotient**. - Finally, we'll take a deep dive into how the reaction quotient relates to
**Gibbs free energy**.

## What is the Reaction Quotient?

If you've read the articles "Dynamic Equilibrium" and "Reversible Reactions", you'll know that if you leave a reversible reaction in a closed system for enough time, it will eventually reach a point of **dynamic equilibrium**. At this point, **the rate of the forward reaction equals the rate of the backward reaction** and **the relative amounts of products and reactants don't change**. Provided you keep the temperature the same, **the position of the equilibrium doesn't change** either.

It doesn't matter whether you start with lots of the reactants or lots of the products - as long as the temperature remains constant, **you'll always end up with fixed relative amounts of each**. This is analogous to your body always trying to bring your blood sugar levels back to a fixed point.

We can express **the ratio between the relative amounts of products and reactants** using the **equilibrium constant, K**_{eq}. Because the position of an equilibrium is always the same at a certain temperature, K_{eq} is always the same too. **At equilibrium, the value of K _{eq} is constant.**

However, reactions may take a while to get to equilibrium. What if we want to compare the relative amounts of reactants and products in a system that still isn't quite there? For this, we use the **reaction quotient**.

The **reaction quotient **is a value that tells us **the relative amounts of products and reactants in a system at a particular moment, at any point in the reaction**.

### Types of Reaction Quotient

You should be familiar with the different types of K_{eq}. They measure the amounts of substances in different systems of reversible reactions at equilibrium in different ways. For example, **K**_{c} measures the **concentration of aqueous or gaseous species** **in an equilibrium**, whilst **K _{p} **measures the

**partial pressure of gaseous species**

**in an equilibrium**. Likewise, we can also get different types of the reaction quotient. In this article, we'll focus on just two of them:

**Q**_{c}is similar to K_{c}. It measures the**concentration of aqueous or gaseous species****in a system at a particular moment**.- Q
_{p}is similar to K_{p}. It measures the**partial pressure of gaseous species****in a system at a particular moment**.

For a reminder of K_{eq}, check out "**Equilibrium Constant**". It's important that you understand the ideas within that article before you come to learn about Q.

Let's now move on to look at the **expressions** for Q_{c} and Q_{p}.

## Reaction Quotient Expression

The expressions for the reaction quotients Q_{c} and Q_{p} are very similar to the respective expressions for K_{c} and K_{p}. But whilst K_{c} and K_{p} take measurements at **equilibrium**, Q_{c} and Q_{p} take measurements **at any one time** - not necessarily at equilibrium.

### Q_{c} Expression

Take the reaction \(aA + bB \rightleftharpoons cC + dD\). Here, the capital letters represent **species** whilst the lowercase letters represent their **coefficients in the balanced chemical equation**. For the above reaction, Q_{c} looks a little something like this:

$$Q_C=\frac{[C]^c[D]^d}{[A]^a[B]^b}$$

Here's what that all means:

Square brackets show the

**concentration of a species at a given moment.**Therefore, [A]_{ }means the concentration of species A.The superscript lowercase letters are

**exponents**, based on the**coefficients of species in the balanced chemical equation**. Therefore, [A]^{a}means the concentration of species A, raised to the power of the number of moles of A in the balanced equation.Overall, the numerator represents the concentrations of the products, raised to the power of their coefficients, and then multiplied together. The denominator represents the concentrations of the reactants, raised to the power of their coefficients, and then multiplied together. To find Q

_{c}, you simply**divide the numerator by the denominator**.

Notice how similar this expression is to the expression for K_{c}. The only difference is that K_{c} uses **equilibrium concentrations**, whilst Q_{c} uses **concentrations at any given moment**:

$$K_c=\frac{[C]_{eq}^c[D]_{eq}^d}{[A]_{eq}^a[B]_{eq}^b}$$

$$Q_C=\frac{[C]^c[D]^d}{[A]^a[B]^b}$$

### Q_{p}^{ }Expression

Let's take the reaction again. But this time, instead of measuring concentration, let's measure the **partial pressure** of each species. This is the pressure it would exert on the system if it occupied the same volume on its own. To compare the ratio of partial pressures of gases in a system, we use **Q**_{p}. Here's the expression:

$$Q_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$$

Let's break that down:

*P*_{ }represents the**partial pressure of a species at a given moment**. Therefore, (*P*_{A}) means the partial pressure of species A.The superscript lowercase letters are

**exponents**, based on the**coefficients of species in the balanced chemical equation**. Therefore, (*P*_{A})^{a}means the partial pressure of species A, raised to the power of the number of moles of A in the balanced equation.Overall, the numerator represents the partial pressures of the products, raised to the power of their coefficients, and then multiplied together. The denominator represents the partial pressures of the reactants, raised to the power of their coefficients, and then multiplied together. To find K

_{p}, you simply**divide the numerator by the denominator**.

Once again, notice how similar this is to the expression for K_{p}. The only difference is that K_{p} uses **equilibrium partial pressures**, whilst Q_{p} uses **partial pressures at any given moment**:

$$K_p=\frac{(P_C)_{eq}^c(P_D)_{eq}^d}{(P_A)_{eq}^a(P_B)_{eq}^b}$$

$$Q_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$$

Like with the equilibrium constant, Q_{c} ignores any pure solids or liquids in the system, whilst Q_{p} ignores any species that aren't gaseous. It is simple, really - you leave them out of the equation altogether.

## Reaction Quotient Units

Q takes the same units as K_{eq} - which, as you might remember, doesn't have any units. **Both K _{eq} and Q are unitless**.

Like K_{eq}, Q is technically based on **activities**. A substance's concentration at any point in a reaction is actually its **concentration activity**, which is its concentration compared to the standard concentration of the species. Both values are typically measured in M (or mol dm^{-3}), and this means that the units cancel out, leaving a unitless quantity. Partial pressure is similar - we actually measure **pressure activity**, which is the substance's partial pressure compared to a standard pressure. Once again, pressure activity has no units. Because both forms of Q are made up of unitless values, Q itself is also unitless.

## Difference Between the Equilibrium Constant and the Reaction Quotient

Before we go any further, let's consolidate our learning by providing a summary of the **differences between the equilibrium constant ****and the**** ****reaction quotient**. We'll further break it down into K_{c}, K_{p}, Q_{c} and Q_{p}:

## Reaction Quotient Example

Before we finish, let's have a go at **calculating the reaction quotient** for a particular reaction at a given moment. In the article "Using the Reaction Quotient", we'll then compare this to the reaction's equilibrium constant and see what it tells us about the reaction.

**A mixture contains 0.5 M nitrogen, 1.0 M hydrogen and 1.2 M ammonia, all present as gases. Calculate Q _{c} at this particular instant. **The equation for the reversible reaction is given below:

$$N_{2\,(g)} + 3H_{2\,(g)} \rightleftharpoons 2NH_{3\,(g)}$$

Well, first we need to write an expression for Q_{c}. As the numerator, we find the concentrations of the products, all raised to the power of their coefficient in the chemical equation and then multiplied together. Here, our only product is NH_{3}, and we have two moles of it in the equation. Therefore, the numerator is [NH_{3}]^{2}.

As the denominator, we find the concentrations of the reactants, all raised to the power of their coefficient in the chemical equation and then multiplied together. Here, the reactants are N_{2} and H_{2}. We have one mole of N_{2} and 3 moles of H_{2}. Therefore, our denominator is [N_{2}] [H_{2}]^{3}. Putting this all together, we find an expression for Q_{c}:

$$Q_C=\frac{[NH_3]^2}{[N_2][H_2]^3}$$

Now, all we need to do is substitute in the concentrations given in the question, remembering that Q_{c} has no units:

$$Q_C=\frac{[NH_3]^2}{[N_2][H_2]^3}$$

$$Q_C=\frac{[1.2]^2}{[0.5][1.0]^3}=2.88$$

## Reaction Quotient and Gibbs Free Energy

In your studies, you might have come across **Gibbs free energy**. It is a measure of how **thermodynamically favorable** a reaction is, and relates to the reaction quotient Q with the following equation:

$$\Delta G=\Delta G^\circ +RTln(Q)$$

Note the following:

- ΔG is the
**change in Gibbs free energy**, measured in**J mol**^{-1}. - ΔG
**°**is the**change in**, measured in*standard*Gibbs free energy**J mol**^{-1}. - R is the
**gas constant**, measured in**J****mol**^{-1}K^{-1}. - T is the
**temperature**, measured in**K**.

This can help you identify an equilibrium! If ΔG equals 0, then the reaction is at equilibrium.

That's the end of this article. By now you should understand what we mean by the **reaction quotient** and be able to explain the **difference between the equilibrium constant and the reaction quotient**. You should also be able to derive an **expression** **for the reaction quotient** based on a system of reversible reactions then use your expression to **calculate the reaction quotient**.

## Reaction Quotient - Key takeaways

- The
**reaction quotient, Q**, is a value that tells us the**relative amounts of products and reactants in a system at a particular moment**. - Types of the reaction quotient include Q
_{c}and Q_{p}:**Q**_{c}measures**aqueous or gaseous concentration**at a particular moment.**Q**_{p}measures**gaseous partial pressure**at a particular moment.

- For the reaction \(aA + bB \rightleftharpoons cC + dD\) $$Q_C=\frac{[C]^c[D]^d}{[A]^a[B]^b}$$
- For the same reaction, $$Q_p=\frac{(P_C)^c(P_D)^d}{(P_A)^a(P_B)^b}$$
- The reaction quotient is
**unitless**.

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##### Frequently Asked Questions about Reaction Quotient

What is the reaction quotient?

The reaction quotient is a value that tells us the relative amounts of products and reactants in a system at any one time.

Can the reaction quotient equal zero?

The reaction quotient equals zero if your system consists of just the reactants and no products. As soon as you start producing some of the products, the reaction quotient will increase above zero.

How do you calculate the reaction quotient?

Calculating the value of the reaction quotient, Q, depends on the type of reaction quotient you want to find out. To calculate Q_{c}, you need to find the concentration of all of the aqueous or gaseous species involved in the reaction at any one moment. You find the numerator by taking the concentrations of the products and raising them to the power of their coefficients in the balanced chemical equation, and then multiplying them together. You find the denominator by repeating the process with the concentrations of the reactants. To find Q_{c}, you simply divide the numerator by the denominator. If that sounds complicated, don't worry - we've got you covered! Check out this article for a more detailed explanation and a worked example.

Are solids included in reaction quotient?

Solids aren't included in either Q_{c} or Q_{p}, the reaction quotients for concentration and partial pressure respectively. This is because pure solids have a concentration of 1 and no partial pressure.

What is the difference between reaction quotient and equilibrium constant?

Both measure the relative amounts of products and reactants in a reversible reaction. However, whilst the equilibrium constant K_{eq} measures the relative amounts of species *at equilibrium*, the reaction quotient Q measures the relative amounts of species *at any one moment*.

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