Question

Calculate \(\mathrm{K}_{\mathrm{p}}\) if the partial pressures of reactants and products in the dissociation of 1 mole of phosphorous pentachloride are \(0.3 \mathrm{~atm}, 0.4 \mathrm{~atm}\) and \(0.2 \mathrm{~atm}\) respectively.

Short answer

Question: Calculate the equilibrium constant Kp for the dissociation of phosphorous pentachloride if the partial pressures of PCl5, PCl3, and Cl2 are 0.3 atm, 0.4 atm, and 0.2 atm, respectively. Answer: The equilibrium constant Kp for the dissociation of phosphorous pentachloride is approximately 0.267.

Step-by-step solution

Write the expression for Kp

For the given chemical reaction, the expression for Kp can be written as: Kp = \frac{[PCl3][Cl2]}{[PCl5]}

Plug in the given partial pressures into the Kp expression

We have the partial pressures of PCl5, PCl3, and Cl2 as 0.3 atm, 0.4 atm, and 0.2 atm respectively. Now, substitute these values in the Kp expression: Kp = \frac{(0.4)(0.2)}{(0.3)}

Calculate the value of Kp

By calculating the values from the previous step, we get: Kp = \frac{(0.4)(0.2)}{(0.3)} = \frac{0.08}{0.3} = 0.267 Therefore, the value of Kp for the given dissociation is approximately 0.267.

Key concepts

Equilibrium Partial Pressures

Understanding equilibrium partial pressures is pivotal when examining reactions that occur in the gaseous phase. At chemical equilibrium, the rate of the forward reaction equals the rate of the reverse reaction, causing the pressures of the individual gases to remain constant over time. These pressures are known as 'equilibrium partial pressures'.

Each gas in a mixture has its own partial pressure, which is the pressure that the gas would exert if it were alone in the container. When dealing with reactions, the stoichiometry of the reaction must be considered to determine how the partial pressures of reactants and products are related. Keep in mind, changes in conditions, such as temperature or the addition of inert gases, can affect these pressures and thus the position of equilibrium.

Kp Calculation

The equilibrium constant for reactions involving gases is often represented by the symbol 'Kp'. This constant relates to the partial pressures of the gases at equilibrium. The general formula for calculating Kp is based on the balanced chemical equation and is a ratio of the product of partial pressures of the products raised to their stoichiometric coefficients to that for the reactants.

For example, given the equilibrium A + B ⇌ C + D, the expression for Kp would be \[ K_p = \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}} \]
where [C], [D], [A], and [B] represent the equilibrium partial pressures of the respective gases and a, b, c, and d are their stoichiometric coefficients. To find Kp, simply substitute the known equilibrium partial pressures into this expression and calculate.

Dissociation of Phosphorous Pentachloride

The dissociation of phosphorous pentachloride (PCl5) is an example of a chemical equilibrium that can be observed in gaseous systems. PCl5 dissociates into phosphorous trichloride (PCl3) and chlorine gas (Cl2) according to the balanced chemical equation: \[ PCl_5 ⇌ PCl_3 + Cl_2 \].

This process can be reversed; PCl3 and Cl2 can recombine to form PCl5. At equilibrium, the rate of dissociation of PCl5 is equal to the rate of recombination of PCl3 and Cl2, and their partial pressures do not change further. Understanding this behavior is crucial for predicting the outcome of reactions involving PCl5, as well as for manipulating conditions to favor the formation or dissociation of PCl5 in industrial processes.

Chemical Equilibrium

Chemical equilibrium is a state in a reversible chemical reaction where the rates of the forward and reverse reactions are equal. As a result, the concentrations of the reactants and products remain constant over time, although they are not necessarily equal. The equilibrium state can be described quantitatively by the equilibrium constant, K, which is unique for each chemical system at a given temperature.

It's important to note that while the macroscopic properties, such as concentration and pressure, are constant at equilibrium, reactions do persist at the molecular level. The concept of dynamic equilibrium captures this ongoing process where reactant molecules are continuously converted to products, and product molecules are continuously reverted to reactants. Understanding equilibrium is key when predicting the behavior of a system and controlling chemical reactions in various applications like pharmaceuticals, material science, and environmental engineering.