Question

Write reaction quotients for the following reactions: (a) \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(g)\) (b) \(\mathrm{S}(s)+3 \mathrm{~F}_{2}(g) \rightleftarrows \mathrm{SF}_{6}(g)\) (c) \(\mathrm{Co}^{3+}(a q)+6 \mathrm{NH}_{3}(a q) \rightleftarrows \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}(a q)\) (d) \(\mathrm{HCOOH}(a q) \rightleftarrows \mathrm{HCOO}^{-}(a q)+\mathrm{H}^{+}(a q)\).

Short answer

(a) \( Q = \frac{[\mathrm{N}_{2} \mathrm{O}_{4}]}{[\mathrm{NO}]^2[\mathrm{O}_{2}]} \), (b) \( Q = \frac{[\mathrm{SF}_{6}]}{[\mathrm{F}_{2}]^3} \), (c) \( Q = \frac{[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}]}{[\mathrm{Co}^{3+}][\mathrm{NH}_{3}]^6} \), (d) \( Q = \frac{[\mathrm{HCOO}^{-}][\mathrm{H}^{+}]}{[\mathrm{HCOOH}]} \).

Step-by-step solution

Identify the reaction and write its expression

For each given equation, we need to write the expression for the reaction quotient \( Q \). The reaction quotient is calculated by using the equilibrium expression for the reaction, which includes concentrations of products raised to their stoichiometric coefficients over the concentrations of reactants raised to their stoichiometric coefficients.

Write the reaction quotient for part (a)

The balanced equation given is \( 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(g) \). The reaction quotient \( Q \) is calculated as follows: \[ Q = \frac{[\mathrm{N}_{2} \mathrm{O}_{4}]}{[\mathrm{NO}]^2[\mathrm{O}_{2}]} \] This expression takes into account the stoichiometry of 2 mol of \( \mathrm{NO} \) and 1 mol of \( \mathrm{O}_{2} \), which are raised to the power of their coefficients.

Write the reaction quotient for part (b)

The balanced equation is \( \mathrm{S}(s) + 3 \mathrm{~F}_{2}(g) \rightleftarrows \mathrm{SF}_{6}(g) \). Since \( \mathrm{S} \) is a solid, it is not included in the equilibrium expression. The reaction quotient \( Q \) is given by: \[ Q = \frac{[\mathrm{SF}_{6}]}{[\mathrm{F}_{2}]^3} \] Only gaseous and aqueous reactants and products are included in equilibrium expressions.

Write the reaction quotient for part (c)

The balanced equation is \( \mathrm{Co}^{3+}(a q) + 6 \mathrm{NH}_{3}(a q) \rightleftarrows \mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}(a q) \). The reaction quotient \( Q \) is: \[ Q = \frac{[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}^{3+}]}{[\mathrm{Co}^{3+}][\mathrm{NH}_{3}]^6} \] All reactants and products are aqueous and included.

Write the reaction quotient for part (d)

The balanced reaction is \( \mathrm{HCOOH}(a q) \rightleftarrows \mathrm{HCOO}^{-}(a q) + \mathrm{H}^{+}(a q) \). The reaction quotient \( Q \) is: \[ Q = \frac{[\mathrm{HCOO}^{-}][\mathrm{H}^{+}]}{[\mathrm{HCOOH}]} \] All species are aqueous and therefore are included in the expression for \( Q \).

Key concepts

Chemical Equilibrium

Chemical equilibrium is a state where the concentrations of all reactants and products remain constant over time. This occurs when the forward and reverse rates of a reaction are equal. At this point, the system is said to be at equilibrium. However, it's important to remember that equilibrium doesn't mean the reactions have stopped; rather, they are happening at the same rate.
In a chemical equation, we use a double arrow to signify this equilibrium state, like this: \( ightleftarrows \). This indicates that the reaction can proceed in both directions. Whether in a gas, liquid, or aqueous solution, reactions can reach equilibrium under certain conditions. These conditions can include temperature, pressure, and concentration of the substances involved.

• One key aspect of chemical equilibrium is the balance between reactants and products.
• Homeostasis in a chemical reaction can often be disrupted by changes in conditions, prompting shifts according to Le Chatelier's Principle.
• Understanding equilibrium helps inform how reactions behave over time and is crucial in fields like chemistry and biology for processes like metabolic pathways.

Stoichiometry

Stoichiometry involves using the balanced chemical equation to calculate the ratios of the reactants and products. It provides insights into the "recipe" of a chemical reaction, indicating how much of each substance is consumed or produced. This is vital when dealing with chemical reactions as it allows for accurate predictions and adjustments in processes involving chemical changes.
Each coefficient in a balanced equation corresponds to the amount needed or produced, often represented in moles. For example, in the reaction \( 2 \mathrm{NO}(g) + \mathrm{O}_{2}(g) \rightleftarrows \mathrm{N}_{2} \mathrm{O}_{4}(g) \), the coefficients tell us that two molecules of NO react with one molecule of \( \mathrm{O}_{2} \) to form one molecule of \( \mathrm{N}_{2} \mathrm{O}_{4} \).

• Stoichiometry can help determine how much product can be made from given reactants.
• It also plays a role in limiting reagents, where the amount of product is restricted by the reactant that's used up first.
• Through stoichiometry, one can ensure that chemical reactions occur as efficiently as possible.

Equilibrium Expression

An equilibrium expression is a mathematical representation of the concentrations of reactants and products at equilibrium. For the general reaction \( aA + bB \rightleftarrows cC + dD \), the equilibrium expression is: \[ K = \frac{[C]^c[D]^d}{[A]^a[B]^b} \] where \( K \) is the equilibrium constant, and the brackets \([ ]\) represent the concentration of each species. The powers correspond to the stoichiometric coefficients in the balanced equation.
Only gases and aqueous solutions appear in equilibrium expressions; solids and pure liquids are typically omitted since their concentrations do not change.

• Equilibrium expressions help in understanding the position of equilibrium—whether it favors products or reactants.
• The equilibrium constant, \( K \), provides insight into the reaction's extent and can also indicate the reaction's spontaneity.
• Understanding how to construct an equilibrium expression is crucial for predicting the outcomes of reactions in various conditions.

Aqueous Solution

An aqueous solution is a solution where water is the solvent. Many chemical reactions, including those in biological systems, occur in aqueous solutions. These solutions are formed when a substance dissolves in water, and the resulting mixture is homogeneous.
In writing reaction quotients or equilibrium expressions, the concentrations of aqueous substances are included, unlike solids and pure liquids. For instance, in the reaction \( \mathrm{Co}^{3+}(aq) + 6 \mathrm{NH}_{3}(aq) \rightleftarrows \mathrm{Co(NH}_3)_6^{3+}(aq) \), all substances are in the aqueous phase and therefore part of the equilibrium expression.

• Aqueous solutions are critical for reactions involving acids, bases, and salts, which often fully or partially ionize in water.
• These solutions provide a medium that facilitates the movement of ions and molecules, allowing reactions to proceed more efficiently.
• Understanding aqueous solutions assists in grasping concepts related to solubility, concentration, and chemical reactivity.