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)?

검증된 단계별 안내

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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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

At 1000 K, 𝐾𝑝 = 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)?