At 1000 K, 𝐾 𝑝 = 1.85 for the reaction SO 2 (𝑔) + 12 O 2 (𝑔) ⇌ SO 3 (𝑔) (c) What is the value of 𝐾𝑐 for the reaction in part (b)?

Hi everyone. So we have the action below. And the K. P. Value is 2.47. I'm sent to the third power or asked how the K. C. For the reaction at this temperature. Since we're asked to find the K. C. And we're giving the K. P. We're gonna need to use the occasion K. P. It was K. C. Times are T to the power of data. N. Where are as R gas constant T. Is our temperature in delta, N. Is the sum of the molds of the gaseous product minus is some of the molds of the gas is reacting. And if he rearranged this to solve for K. C, we get K. C equals K. P. About about R. T. The power of data. And so for K. P We're giving 2.47 lb 10 to the third. Okay. See is what we're looking for. Art is 0.08 leaders from atmosphere about about malls times kelvin. And for the temperature We have 1200 K. And for delta N. We have one mole of carbon monoxide. The three most passion gas -1 Mall of Methane Plus one more of H 20. Gas. Get two miles total. Now we can plug an advice into the equation. We get K. C. Equals 2.47 Times 10 to the 3rd, Divided by 0.08206. Later times atmosphere about about Moles Times Kelvin. I'm 1200 K. Into the power of two. Okay, see Is 0.255. Since K. C. Does not 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 25c

Chapter 15, Problem 25c

At 1000 K, 𝐾_𝑝= 1.85 for the reaction SO₂(𝑔) + 12 O₂(𝑔) ⇌ SO₃(𝑔) (c) What is the value of 𝐾𝑐 for the reaction in part (b)?

Verified step by step guidance

Step 1: Understand the relationship between Kp and Kc. The relationship between Kp and Kc is given by the equation Kp = Kc(RT)^(Δn), where R is the ideal gas constant (0.0821 L·atm/K·mol), T is the temperature in Kelvin, and Δn is the change in moles of gas in the reaction.

Step 2: Calculate Δn for the reaction. Δn is calculated as the difference between the total moles of gaseous products and the total moles of gaseous reactants. In this case, Δn = (moles of SO3) - (moles of SO2 + moles of O2) = 1 - (1 + 1/2) = -1/2.

Step 3: Substitute the known values into the equation. We know that Kp = 1.85, R = 0.0821 L·atm/K·mol, T = 1000 K, and Δn = -1/2. Substituting these values into the equation gives us 1.85 = Kc(0.0821*1000)^(-1/2).

Step 4: Solve the equation for Kc. To isolate Kc on one side of the equation, we need to divide both sides by (0.0821*1000)^(-1/2). This gives us Kc = 1.85 / (0.0821*1000)^(-1/2).

Step 5: Calculate the value of Kc. Now you can calculate the value of Kc using a calculator. Remember to follow the order of operations (PEMDAS/BODMAS) when performing the calculation.

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Key Concepts

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

Equilibrium Constant (Kp and Kc)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium. Kp is used for gas-phase reactions and is expressed in terms of partial pressures, while Kc is used for reactions in solution and is expressed in terms of molar concentrations. The relationship between Kp and Kc is given by the equation Kp = Kc(RT)^(Δn), where Δn is the change in moles of gas.

Relationship between Kp and Kc

The relationship between Kp and Kc is crucial for converting between the two constants. This relationship depends on the temperature and the change in the number of moles of gas during the reaction. Specifically, Kp can be calculated from Kc using the formula Kp = Kc(RT)^(Δn), where R is the ideal gas constant and T is the temperature in Kelvin.

Stoichiometry of the Reaction

Understanding the stoichiometry of the reaction is essential for determining Δn, which is the difference in moles of gaseous products and reactants. In the given reaction, the stoichiometry indicates that for every mole of SO2 and 12 moles of O2, 1 mole of SO3 is produced. This information is necessary to calculate the change in moles of gas, which directly affects the conversion between Kp and Kc.