If 𝐾 𝑐 = 0.042 for PCl 3 (𝑔) + Cl 2 (𝑔) ⇌ PCl 5 (𝑔) at 500 K, what is the value of 𝐾 𝑝 for this reaction at this temperature?

everyone is never given the following value of K. C. For the reaction below. And it's 4.72 at 100 degrees Celsius. Were asked to determine its K. P. Value at this temperature. Since we're asked to find the K. P. And we're giving the K. C. We need to use the equation K. P. It was K C. R. T. The power of data. And where R. Is the gas constant T. Is the temperature and delta, N. Is the some of the most of the gaseous product minus to some of the most of the gas is reacting. Okay. Pete is what we're looking for for K. C. We're giving 4.72 Are we have 0.08206 later Times atmosphere about about malls times kelvin For temperature of 100°C. But we need to convert this into Kelvin. We need to add 273 115. Let me get 373 15 Kelvin and for delta. And we're one more nitrogen tetroxide -2 moles of nitrogen dioxide. Can we get negative 1? So now we can plug in the values and we get K. P. Equals 4. From 0.08206 letter sounds atmosphere about about malls. How's kelvin? 373 15 Kelvin. The Native one Power for K P. We get 0.154. Since K P. Doesn't have any units. We can disregard the units. Thanks for watching my video and I hope it was helpful

Ch.15 - Chemical Equilibrium

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Brown 14th Edition

Ch.15 - Chemical Equilibrium

Problem 21

Chapter 15, Problem 21

If 𝐾_𝑐= 0.042 for PCl₃(𝑔) + Cl₂(𝑔) ⇌ PCl₅(𝑔) at 500 K, what is the value of 𝐾_𝑝 for this reaction at this temperature?

Verified step by step guidance

Identify the balanced chemical equation for the reaction: PCl₃(g) + Cl₂(g) ⇌ PCl₅(g).

Note that the reaction involves gases, and the relationship between K_c and K_p is given by the equation K_p = K_c(RT)^Δn, where Δn is the change in moles of gas (moles of products - moles of reactants), R is the gas constant, and T is the temperature in Kelvin.

Calculate Δn for the reaction: Δn = moles of PCl₅ - (moles of PCl₃ + moles of Cl₂) = 1 - (1 + 1) = -1.

Substitute the values into the equation for K_p: K_p = K_c(RT)^Δn = 0.042(RT)^-1. Here, R is typically 0.0821 L·atm/K·mol, and T is given as 500 K.

Calculate K_p using the values of R, T, and Δn to find the effect of the negative exponent on (RT).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Equilibrium Constants

Equilibrium constants, denoted as Kc for concentrations and Kp for partial pressures, quantify the ratio of products to reactants at equilibrium. Kc is used when dealing with molar concentrations, while Kp is applicable for gases and is expressed in terms of their partial pressures. The relationship between Kc and Kp is crucial for converting between these two forms, especially when dealing with gaseous reactions.

Relationship Between Kc and Kp

The relationship between Kc and Kp is given by the equation Kp = Kc(RT)^(Δn), where R is the ideal gas constant, T is the temperature in Kelvin, and Δn is the change in moles of gas (moles of products minus moles of reactants). This equation allows for the conversion of Kc to Kp and vice versa, depending on the conditions of the reaction. Understanding this relationship is essential for solving equilibrium problems involving gases.

Change in Moles of Gas (Δn)

Δn represents the difference in the number of moles of gaseous products and reactants in a chemical reaction. It is calculated by subtracting the total moles of reactants from the total moles of products. This value is critical in the Kp and Kc relationship, as it influences the conversion factor (RT)^(Δn) when calculating the equilibrium constant for a reaction involving gases.