# Reaction Quotient

If you haven't eaten anything for a while, your blood glucose levels can drop. To fix this, your body releases glucagon, which makes your liver break down glycogen, raising your blood glucose levels. But when you eat a big meal, your blood glucose levels can increase. This time, your body releases insulin, which makes your cells take up glucose and store it as glycogen. The goal is to keep your blood glucose levels steady, but sometimes things go wrong. That's where the reaction quotient comes in handy. It helps us understand reversible reactions that haven't reached equilibrium yet. In this article, we'll explain what the reaction quotient is and how it's different from the equilibrium constant, Keq. We'll use an example to show you how to calculate the reaction quotient, and we'll also discuss how it relates to Gibbs free energy.

## What is the Reaction Quotient?

If you've read the articles "Dynamic Equilibrium" and "Reversible Reactions", you know that a reversible reaction in a closed system eventually reaches a point of dynamic equilibrium. At this point, the rates of the forward and backward reactions are equal, and the amounts of products and reactants don't change. But sometimes, reactions take a while to reach equilibrium. That's where the reaction quotient comes in. It's a value that tells us the relative amounts of products and reactants at any point in the reaction, not just at equilibrium.

The equilibrium constant, Keq, gives us the ratio of products to reactants at equilibrium, but the reaction quotient, Q, gives us the ratio of products to reactants at any moment in time. If Q is less than Keq, the reaction hasn't yet reached equilibrium and there are more reactants than products. If Q is greater than Keq, the reaction has gone past the equilibrium point and there are more products than reactants. And if Q equals Keq, the reaction is at equilibrium.

Using the reaction quotient helps us understand how far a reaction has progressed towards equilibrium and whether it's likely to shift towards products or reactants. So, while Keq is a constant value at equilibrium, Q gives us a snapshot of the reaction at any point in time.

**Types of Reaction Quotient**

To fully understand the reaction quotient, it's important to know the different types of Keq. These measure the amounts of substances in different systems of reversible reactions at equilibrium in different ways. For example, Kc measures the concentration of aqueous or gaseous species in an equilibrium, while Kp measures the partial pressure of gaseous species in an equilibrium. Similarly, there are two types of reaction quotient we'll focus on in this article:

Qc, which is like Kc, measures the concentration of aqueous or gaseous species in a system at a particular moment. Qp, which is like Kp, measures the partial pressure of gaseous species in a system at a particular moment.

But before delving into Qc and Qp, make sure to check out "Equilibrium Constant" to understand the concepts it covers. Now, let's look at the expressions for Qc and Qp.

## Reaction Quotient Expression

The expressions for the reaction quotients Qc and Qp are very similar to the respective expressions for Kc and Kp. But whilst Kc and Kp take measurements at equilibrium, Qc and Qp take measurements at any one time - not necessarily at equilibrium.

**Qc Expression**

Let's take the reaction A + 2B ⇌ C + 3D as an example. The expression for Qc would look like this:

Qc = [C]^1[D]^3 / [A]^1[B]^2

In this expression, the square brackets represent the concentration of a species at a given moment. The superscript lowercase letters are exponents based on the coefficients of species in the balanced chemical equation. For example, [A]^1 means the concentration of species A raised to the power of 1, which represents the coefficient of A in the balanced equation.

The numerator of the expression 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 calculate Qc, you simply divide the numerator by the denominator.

It's important to note that the expression for Qc is similar to the expression for Kc, but the difference lies in the use of equilibrium concentrations for Kc and any moment concentrations for Qc. This means that Qc can tell us whether a reaction is at equilibrium or not, and if it's not at equilibrium, in which direction the reaction needs to proceed to reach equilibrium.

**Qp Expression**

Now, let's consider the same reaction, A + 2B ⇌ C + 3D, but this time we'll measure the partial pressures of each species to calculate Qp. The expression for Qp would be:

Qp = (Pc)^1(Pd)^3 / (Pa)^1(Pb)^2

In this expression, the capital letters represent the species, and the lowercase letters represent their coefficients in the balanced chemical equation. The parentheses represent the partial pressure of each species at a given moment. For example, (Pa)^1 represents the partial pressure of species A raised to the power of 1, which represents the coefficient of A in the balanced equation.

The numerator of the expression 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 calculate Qp, you simply divide the numerator by the denominator.

Similar to Qc, the expression for Qp is similar to the expression for Kp, but the difference lies in the use of equilibrium partial pressures for Kp and any moment partial pressures for Qp. Qp can tell us whether a reaction is at equilibrium or not and in which direction the reaction needs to proceed to reach equilibrium based on the ratio of partial pressures of gases in the system. It is important to note that Qp ignores any species that aren't gaseous in the system.

## Reaction Quotient Units

Q takes the same units as Keq - which, as you might remember, doesn't have any units. Both Keq and Q are unitless.

Like Keq, 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 Kc, Kp, Qc and Qp:

## Reaction Quotient Example

To calculate Qc for the given reaction, we first need to write an expression for it. The equation for the reversible reaction is:

N2(g) + 3H2(g) ⇌ 2NH3(g)

Now, we can write an expression for Qc using the concentrations of the reactants and products at a particular moment. 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 NH3, and we have two moles of it in the equation. Therefore, the numerator is [NH3]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 N2 and H2. We have one mole of N2 and 3 moles of H2. Therefore, our denominator is [N2] [H2]3. Putting this all together, we find an expression for Qc:

Qc = [NH3]2 / [N2] [H2]3

Now, all we need to do is substitute in the concentrations given in the question:

Qc = (1.2 M)2 / (0.5 M)(1.0 M)3

Simplifying this expression, we get:

Qc = 1.44 / 0.5 = 2.88

The reaction quotient, Qc, for this reaction at this particular moment is 2.88.

This value can be compared to the equilibrium constant, Kc, for the reaction to determine whether the reaction is at equilibrium, and if not, which direction the reaction will proceed to reach equilibrium. If Qc is less than Kc, the reaction will proceed forward to reach equilibrium. If Qc is greater than Kc, the reaction will proceed in the reverse direction to reach equilibrium. If Qc is equal to Kc, the reaction is at equilibrium.

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 Qc and Qp: Qc measures aqueous or gaseous concentration at a particular moment. Qp measures gaseous partial pressure at a particular moment. For the reaction , For the same reaction, The reaction quotient is unitless.

## 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 Qc, 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 Qc, 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 Qc or Qp, 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 Keq measures the relative amounts of species at equilibrium, the reaction quotient Q measures the relative amounts of species at any one moment.