Reaction Quotient: Videos & Practice Problems

The reaction quotient, Q, is a ratio of product to reactant concentrations at a specific time, similar to the equilibrium constant, K, but not limited to equilibrium conditions. Both Q and K ignore solids and liquids in their expressions. Comparing Q to K determines the direction of a chemical reaction shift to maintain equilibrium. If Q < K, the reaction shifts right; if Q > K, it shifts left. At Q = K, the system is at equilibrium, with reactant and product amounts constant. This concept is crucial for understanding dynamic equilibrium in chemical reactions.

Reaction Quotient Q

The reaction quotient, denoted as Q, is a crucial concept in chemical equilibrium that represents the ratio of the concentrations of products to reactants at a specific moment in time. Unlike the equilibrium constant, K, which reflects the concentrations at equilibrium, Q can be calculated at any point during the reaction, whether it is at equilibrium or not. This distinction is essential for understanding the dynamic nature of chemical reactions.

To calculate Q, one must set up an expression similar to that of K, but it is important to note that both expressions exclude solids and liquids. This is because the concentrations of pure solids and liquids do not change during the reaction and do not affect the equilibrium position. The general form for calculating Q can be expressed as:

\[Q = \frac{[\text{Products}]}{[\text{Reactants}]}\]

Understanding how to set up this expression is vital for predicting the direction of the reaction and determining whether the system is at equilibrium. By comparing the value of Q to K, one can infer whether the reaction will proceed forward or reverse to reach equilibrium.

Reaction Quotient Calculation Example

The formation of gaseous ammonia can be represented by the balanced chemical equation:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

To determine the reaction quotient (Q) for this reaction, we use the expression that mirrors the equilibrium constant (K), which is defined as the ratio of the concentrations of the products to the reactants, each raised to the power of their coefficients in the balanced equation. For this reaction, the expression for Q is:

Q = \frac{[NH₃]^2}{[N₂][H₂]^3}

In this scenario, we are given the amounts of each component in moles and the volume of the vessel, which is 10 liters. To find the molarity (M) of each gas, we divide the number of moles by the volume in liters:

[NH₃] = \frac{n_{NH3}}{V} = \frac{0.529}{10} = 0.0529 \, M

[N₂] = \frac{n_{N2}}{V} = \frac{0.650}{10} = 0.0650 \, M

[H₂] = \frac{n_{H2}}{V} = \frac{0.330}{10} = 0.0330 \, M

Substituting these values into the Q expression gives:

Q = \frac{(0.0529)^2}{(0.0650)(0.0330)^3}

Calculating this yields:

Q = \frac{0.0028}{0.0650 \times 0.000036} = 1.3046

Considering significant figures, we round this value to three significant figures, resulting in:

Q = 1.30

This value represents the reaction quotient for the formation of ammonia under the given conditions.

Comparing Q to K and Equilibrium Shift

Understanding the relationship between the reaction quotient (q) and the equilibrium constant (K) is crucial for predicting the direction of a chemical reaction. The reaction quotient, q, is calculated using the concentrations of the reactants and products at any point in time, while K represents the concentrations at equilibrium.

When comparing q to K, the direction of the shift in the chemical reaction can be determined. If q is less than K, the reaction will shift to the right (toward the products) to reach equilibrium. For example, if q is 10 and K is 30, the reaction will favor the formation of products, increasing their concentration while decreasing that of the reactants. This shift continues until q equals K.

Conversely, if q is greater than K, the reaction will shift to the left (toward the reactants) to achieve equilibrium. For instance, if q is 75 and K is 30, the reaction will favor the reactants, leading to an increase in their concentration and a decrease in the products. This adjustment occurs until q aligns with K.

When q equals K, the system is at equilibrium, meaning the concentrations of reactants and products remain constant over time. In this state, there is no net change in the amounts of substances involved in the reaction.

In summary, the comparison of q and K is a powerful tool in chemical equilibrium analysis. By determining whether q is less than, greater than, or equal to K, one can predict the direction of the reaction shift and understand how the concentrations of reactants and products will change to maintain equilibrium.

Comparing Q to K Example

In the given chemical reaction, 4 moles of hydrogen bromide (HBr) gas react with 1 mole of oxygen (O₂) gas to produce 2 moles of bromine (Br₂) gas and 2 moles of water (H₂O) in liquid form. The equilibrium constant (K) for this reaction at 400 Kelvin is 0.063, while the reaction quotient (Q) is 0.100. Understanding the relationship between Q and K is crucial for predicting the direction of the reaction.

The equilibrium constant (K) represents the ratio of the concentrations of products to reactants at equilibrium, while the reaction quotient (Q) reflects the current state of the reaction. When comparing Q and K, if Q is greater than K, the reaction will shift to the left, favoring the formation of reactants to reach equilibrium. In this case, since Q (0.100) is greater than K (0.063), the reaction will shift in the reverse direction, meaning the concentration of reactants will increase while the concentration of products will decrease.

As a result, the amounts of HBr and O₂ will increase, while the amounts of Br₂ and H₂O will decrease. Therefore, among the statements provided, the assertion that the concentration of O₂ will increase is true, while the other statements regarding the changes in HBr, Br₂, and H₂O are false.

For the reaction: 2 CO₂ (g)  ⇌ 2 CO (g) + 2 O₂  (g), the equilibrium constant is 3.12 × 10⁻⁴ at 400 K, while the reaction quotient is 4.18 × 10⁻⁴. If initially we have 0.20 atm CO₂, 0.30 atm CO and 0.15 atm O₂, which of the following statements is not true? 
a) The pressure of CO₂ will be greater than 0.20 atm. 
b) The pressure of CO will be less than 0.30 atm. 
c) The pressure of O₂ will be greater than 0.15 atm. 
d) The pressure of O₂ will be less than 0.15 atm. 
e) The reaction will favor reactants. 

• A. The pressure of CO₂ will be greater than 0.20 atm.
• B. The pressure of CO will be less than 0.30 atm.
• C. The pressure of O₂ will be greater than 0.15 atm.
• D. The pressure of O₂ will be less than 0.15 atm.
• E. The reaction will favor reactants.

Answer: (C)

The equilibrium constant for the following gas phase reaction is 0.75 at 750 K. After a short time, analysis of a small amount of the reaction mixture shows the concentrations to be [NOBr] = 1.25 M, [NO] = 0.80 M and [Br₂] = 0.50 M. Which of the following statements is/are true? 
2 NOBr (g)  ⇌ NO (g) + Br₂ (g)
a) The reaction mixture is at equilibrium. 
b) No further reaction will occur. 
c) The partial pressure of NOBr will increase. 
d) The partial pressure of NO will increase. 
e) The reaction will shift to the left, the reactant side. 

• A. The reaction mixture is at equilibrium.
• B. No further reaction will occur.
• C. The partial pressure of NOBr will increase.
• D. The partial pressure of NO will increase.
• E. The reaction will shift to the left, the reactant side.

Answer: (D)

Here’s what students ask on this topic:

What is the reaction quotient (Q) and how is it different from the equilibrium constant (K)?

The reaction quotient, Q, is a measure of the ratio of product concentrations to reactant concentrations at a specific moment in a chemical reaction. It is similar to the equilibrium constant, K, which represents this ratio at equilibrium. The key difference is that Q can be calculated at any point during the reaction, not just at equilibrium. Both Q and K exclude solids and liquids from their expressions. By comparing Q to K, you can predict the direction in which the reaction will shift to reach equilibrium. If Q < K, the reaction shifts right, increasing products. If Q > K, it shifts left, increasing reactants. If Q = K, the system is at equilibrium, and concentrations remain constant.

How do you calculate the reaction quotient (Q) for a chemical reaction?

To calculate the reaction quotient, Q, you set up an expression similar to the equilibrium constant, K. For a general reaction aA + bB ⇌ cC + dD, the expression for Q is:

$\frac{C^c\times D^d}{A^a\times B^b}$

Here, [C], [D], [A], and [B] are the concentrations of the respective species at a given time. Solids and liquids are not included in the expression. By calculating Q, you can compare it to K to determine the direction of the reaction shift to achieve equilibrium.

What happens to a chemical reaction when Q < K?

When the reaction quotient, Q, is less than the equilibrium constant, K, the chemical reaction will shift to the right, towards the products, to reach equilibrium. This shift results in an increase in the concentration of products and a decrease in the concentration of reactants. The system adjusts itself to balance the ratio of product to reactant concentrations, moving towards the equilibrium state where Q equals K. This dynamic adjustment is crucial for understanding how reactions respond to changes in conditions and helps predict the outcome of such changes in a chemical system.

What does it mean when Q = K in a chemical reaction?

When the reaction quotient, Q, equals the equilibrium constant, K, the chemical reaction is at equilibrium. At this point, the concentrations of reactants and products remain constant, as the forward and reverse reaction rates are equal. There is no net change in the amounts of reactants and products, indicating a stable state. This equilibrium condition is essential for understanding the balance in chemical reactions and predicting how systems respond to external changes, such as temperature or pressure variations. It signifies that the system has reached a state of dynamic balance.

How does the reaction shift when Q > K?

When the reaction quotient, Q, is greater than the equilibrium constant, K, the chemical reaction will shift to the left, towards the reactants, to reach equilibrium. This shift results in an increase in the concentration of reactants and a decrease in the concentration of products. The system adjusts itself to balance the ratio of product to reactant concentrations, moving towards the equilibrium state where Q equals K. This dynamic adjustment is crucial for understanding how reactions respond to changes in conditions and helps predict the outcome of such changes in a chemical system.