Question

Write an equilibrium constant, \(K_{c},\) for the formation from its gaseous elements of \((a) 1\) mol \(\mathrm{HF}(\mathrm{g})\) (b) \(2 \mathrm{mol} \mathrm{NH}_{3}(\mathrm{g}) ;(\mathrm{c}) 2 \mathrm{mol} \mathrm{N}_{2} \mathrm{O}(\mathrm{g}) ;(\mathrm{d}) 1 \mathrm{mol} \mathrm{ClF}_{3}(1)\)

Short answer

The equilibrium constants are as follows: (a) \(K_{c} = \frac{[HF]^2}{[H_2][F_2]}\) (b) \(K_{c} = \frac{[NH_3]^2}{[N_2][H_2]^3}\) (c) \(K_{c} = \frac{[N_{2O}]^2}{[N_2][O_2]}\) (d) \( K_{c} = \frac{[ClF_{3}]^2}{[Cl_{2}][F_{2}]^3}\)

Step-by-step solution

Write equation for formation of HF(g)

The formation reaction for hydrofluoric acid, \(HF(g)\), can be written as:\[ H_{2(g)} + F_{2(g)} \rightarrow 2HF_{(g)}\]

Establish the equilibrium constant expression for HF(g)

The equilibrium constant expression for \(HF(g)\) is the product of the concentrations of the products divided by the product of the concentrations of the reactants, each raised to the power of its stoichiometric coefficient, as follows:\[K_{c} = \frac{[HF]^2}{[H_2][F_2]}\]

Write equation for formation of NH3(g)

The formation reaction for ammonia, \(NH_{3(g)}\), is:\[N_{2(g)} + 3H_{2(g)} \rightarrow 2NH_{3(g)}\]

Establish the equilibrium constant expression for NH3(g)

The equilibrium constant for this reaction is:\[K_{c} = \frac{[NH_3]^2}{[N_2][H_2]^3}\]

Write equation for the formation of N2O(g)

The formation reaction for nitrous oxide, \(N_{2O(g)}\), is:\[N_2(g) + O_2(g) \rightarrow 2N_{2O(g)}\]

Establish the equilibrium constant expression for N2O(g)

The equilibrium constant for this reaction is:\[K_{c} = \frac{[N_{2O}]^2}{[N_2][O_2]}\]

Write equation for the formation of ClF3(g)

The formation reaction for chlorotrifluoride, \(ClF_{3(g)}\), is:\[Cl_{2(g)} + 3F_{2(g)} \rightarrow 2ClF_{3(g)}]\]

Establish the equilibrium constant expression for ClF3(g)

The equilibrium constant for this reaction is:\[ K_{c} = \frac{[ClF_{3}]^2}{[Cl_{2}][F_{2}]^3}\]

Key concepts

Chemical Equilibrium

Chemical equilibrium represents a state in which the rate of the forward reaction equals the rate of the reverse reaction, making the concentrations of reactants and products constant over time. This does not mean that the reactants and products are equal in concentration; rather, their ratios remain stable due to ongoing dynamic processes. In a chemical equilibrium, these processes happen simultaneously, allowing a reaction to balance between reactants turning into products and products reverting back into reactants.

To understand an equilibrium constant, denoted as \(K_{c}\), consider it as a snapshot of this delicate balance, providing insights into the extent of a reaction at equilibrium. The value of \(K_{c}\) is calculated using the concentration of the products and reactants, each raised to the power of their stoichiometric coefficients. A large \(K_{c}\) indicates a reaction favoring products, while a small \(K_{c}\) suggests a preference for reactants.

• Equilibrium is dynamic, with continuous motion at the molecular level.
• \(K_{c}\) provides a measure of a reaction's progress at equilibrium.
• Knowing \(K_{c}\) helps predict how changing conditions might affect a reaction.

Reaction Stoichiometry

Reaction stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. Understanding this concept is crucial as it determines the proportions in which different substances react and form products.

When writing balanced chemical equations, the stoichiometric coefficients indicate the relative amount of each substance involved. These coefficients are essential when calculating the equilibrium constant, since they dictate the exponents to which concentrations are raised in the \(K_{c}\) expression.

By using stoichiometry:

• You can predict the amount of products generated from given reactants.
• Determine limiting reactants to know the maximum yield possible.
• Understand how much of each reactant is needed to consume completely.

For example, in the formation of ammonia \( (NH_3) \), the balanced equation \( N_2 + 3H_2 \rightarrow 2NH_3 \) shows that one mole of \( N_2 \) requires three moles of \( H_2 \), producing two moles of \( NH_3 \).

Gaseous Reactions

Gaseous reactions involve reactants and products in the gas phase and are described by equations that account for the behavior and interactions of these gases. An essential aspect to understand here is how volume, pressure, and temperature can affect gaseous reactions at equilibrium.

The equilibrium constant for gaseous reactions, \( K_c \), can vary with temperature and is based on concentrations (moles per unit volume). In many cases, reactions involving gases might also be expressed in terms of partial pressures, known as \( K_p \).

Concepts related to gaseous reactions:

• Gases can be compressed and expanded significantly, affecting equilibrium position.
• When temperature changes, the reaction may shift to absorb or release heat.
• Ideal gas law equations often come in handy to relate different parameters involved.

Knowing how these factors interplay helps in predicting the direction of a reaction shift when external conditions change, according to Le Chatelier's principle.

Formation Reactions

Formation reactions describe how a compound forms from its elements, typically in their standard states. These reactions are fundamental in studying the thermodynamics and dynamics of chemical processes.

For every formation reaction, a corresponding chemical equation, like \( H_{2(g)} + F_{2(g)} \rightarrow 2HF_{(g)} \), provides the blueprint for calculating its equilibrium constant \( K_c \), crucial for understanding the reaction's feasibility and extent.

Key points about formation reactions:

• They allow calculation of standard enthalpy changes, essential for thermodynamic studies.
• Used to derive equilibrium constants, offering insight into the behavior of reactions.
• Integral for synthesis processes, especially in industrial chemistry.

Grasping formation reactions helps in predicting how different elements might combine and provides the foundation for constructing more complex chemical networks.