Question

Balance each reaction and write its reaction quotient, \(Q_{c}\) (a) \(\mathrm{NO}_{2} \mathrm{Cl}(g) \rightleftharpoons \mathrm{NO}_{2}(g)+\mathrm{Cl}_{2}(g)\) (b) \(\mathrm{POCl}_{3}(g) \rightleftharpoons \mathrm{PCl}_{3}(g)+\mathrm{O}_{2}(g)\) (c) \(\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \rightleftharpoons \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\)

Short answer

(a) Balanced: \( \text{NO}_2\text{Cl}(g) \rightleftharpoons \text{NO}_2(g) + \text{Cl}_2(g) \), \( Q_c = \frac{[\text{NO}_2][\text{Cl}_2]}{[\text{NO}_2\text{Cl}]} \)(b) Balanced: \( \text{POCl}_3(g) \rightleftharpoons \text{PCl}_3(g) + \text{O}_2(g) \), \( Q_c = \frac{[\text{PCl}_3][\text{O}_2]}{[\text{POCl}_3]} \)(c) Balanced: \( 4\text{NH}_3(g) + 3\text{O}_2(g) \rightleftharpoons 2\text{N}_2(g) + 6\text{H}_2\text{O}(g) \), \( Q_c = \frac{[\text{N}_2]^2[\text{H}_2\text{O}]^6}{[\text{NH}_3]^4[\text{O}_2]^3} \)

Step-by-step solution

Write the unbalanced equation for reaction (a)

First, write out the chemical equation for reaction (a) as given:\( \text{NO}_2\text{Cl}(g) \rightleftharpoons \text{NO}_2(g) + \text{Cl}_2(g) \)

Balance reaction (a)

Inspect each element to ensure the equation is balanced.There is 1 nitrogen (N), 2 oxygen (O), and 1 chlorine (Cl) atom on each side of the equation, so the reaction is already balanced.

Write out the reaction quotient for reaction (a)

The reaction quotient, \( Q_c \), is defined as: \[ Q_c = \frac{[\text{NO}_2][\text{Cl}_2]}{[\text{NO}_2\text{Cl}]} \]

Write the unbalanced equation for reaction (b)

Write out the chemical equation for reaction (b) as given:\( \text{POCl}_3(g) \rightleftharpoons \text{PCl}_3(g) + \text{O}_2(g) \)

Balance reaction (b)

Inspect each element to ensure the equation is balanced.There is 1 phosphorus (P), 1 oxygen (O), and 3 chlorine (Cl) atom on each side of the equation, so the reaction is already balanced.

Write out the reaction quotient for reaction (b)

The reaction quotient, \( Q_c \), is defined as: \[ Q_c = \frac{[\text{PCl}_3][\text{O}_2]}{[\text{POCl}_3]} \]

Write the unbalanced equation for reaction (c)

Write out the chemical equation for reaction (c) as given:\( \text{NH}_3(g) + \text{O}_2(g) \rightleftharpoons \text{N}_2(g) + \text{H}_2\text{O}(g) \)

Balance reaction (c)

To balance the equation, count and adjust the number of atoms for each element. The balanced equation is:\( 4\text{NH}_3(g) + 3\text{O}_2(g) \rightleftharpoons 2\text{N}_2(g) + 6\text{H}_2\text{O}(g) \)

Write out the reaction quotient for reaction (c)

The reaction quotient, \( Q_c \), is defined as: \[ Q_c = \frac{[\text{N}_2]^2[\text{H}_2\text{O}]^6}{[\text{NH}_3]^4[\text{O}_2]^3} \]

Key concepts

reaction quotient

The reaction quotient, denoted as \( Q_c \), helps us understand the state of a chemical reaction at any given point in time. It's a great way to compare the current state of the reaction to its equilibrium state. You can think of it as a snapshot of the reaction's progress.
To calculate \( Q_c \), you simply use the following formula:

For a general reaction: \( aA + bB \rightleftharpoons cC + dD \)
The reaction quotient, \( Q_c \), is given by:
\[ Q_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
Here, the letters inside the square brackets represent the concentrations of the respective chemical species, raised to the power of their stoichiometric coefficients from the balanced equation.

By comparing \( Q_c \) to the equilibrium constant, \( K_c \), you can determine whether the reaction will proceed forward or backward to reach equilibrium:

• If \( Q_c < K_c \), the reaction will move forward to produce more products.
• If \( Q_c > K_c \), the reaction will shift in reverse, producing more reactants.
• If \( Q_c = K_c \), the reaction is at equilibrium and no net change will occur.

Understanding \( Q_c \) is key to predicting the direction of a chemical reaction and achieving chemical equilibrium.

balancing chemical reactions

Balancing chemical reactions is a fundamental skill in chemistry. A balanced chemical equation ensures that the number of each type of atom on the reactant side is equal to the number on the product side. This satisfies the Law of Conservation of Mass, which states that mass cannot be created or destroyed in a chemical reaction.

Here's a step-by-step approach to balance chemical reactions:

• Write the unbalanced equation with the correct formulas for all reactants and products.
• List and count the number of atoms for each element on both sides of the equation.
• Use coefficients (small whole numbers placed before the chemical formulas) to balance the atoms for each element, starting with the most complex molecule.
• Adjust coefficients as needed to ensure all elements are balanced.
• Double-check to make sure the same number of atoms of each element appears on both sides of the equation and that the coefficients are in the smallest possible integer ratios.

For example, let's balance the equation given in the problem:
\[ \text{NH}_3(g) + \text{O}_2(g) \rightleftharpoons \text{N}_2(g) + \text{H}_2\text{O}(g) \]
Count the atoms:

• Reactants: 1 N, 3 H, 2 O
• Products: 2 N, 2 H, 1 O

Balancing the nitrogen and hydrogen by adjusting coefficients:
\[ 4\text{NH}_3(g) + 3\text{O}_2(g) \rightleftharpoons 2\text{N}_2(g) + 6\text{H}_2\text{O}(g) \]
Check and confirm:

• Reactants: 4 N, 12 H, 6 O
• Products: 4 N, 12 H, 6 O

Success! All atoms balance out, fulfilling the Law of Conservation of Mass.

chemical equilibrium

Chemical equilibrium occurs when both the forward and reverse reactions in a chemical process occur at the same rate, resulting in no net change in the concentrations of reactants and products. This dynamic state is crucial for various chemical and biological processes.

Key features of chemical equilibrium:

• Dynamic Nature: Even though the macroscopic properties (like concentrations) remain constant, the reactions still proceed in both directions at equal rates.
• Position of Equilibrium: The ratio of the concentrations of products to reactants is constant for a given reaction at a specific temperature. This ratio is the equilibrium constant, \( K_c \).
• Perturbation: According to Le Chatelier’s Principle, if a system at equilibrium is disturbed, it will adjust to counteract the disturbance and restore equilibrium. This means if you add more reactants or products, or change temperature or pressure, the system will shift to re-establish equilibrium.

The equilibrium constant expression depends on the balanced equation of the reaction:
For the reaction: \( aA + bB \rightleftharpoons cC + dD \)
The equilibrium constant \( K_c \) is:
\[ K_c = \frac{[C]^c [D]^d}{[A]^a [B]^b} \]
If \( K_c \) is large (much greater than 1), products dominate at equilibrium. If \( K_c \) is small (much less than 1), reactants dominate.

For example, consider the equilibrium for the reaction in the exercise:
\[ \text{POCl}_3(g) \rightleftharpoons \text{PCl}_3(g) + \text{O}_2(g) \]
If at equilibrium the concentration ratio \( K_c \) is known, it gives valuable insight into the amounts of each substance present, helping predict and control the outcome of reactions.

Understanding chemical equilibrium is crucial to mastering reaction dynamics and designing systems where chemical reactions are efficiently managed.