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Question Video: Identifying the Expression for 𝐾_𝑝 for a Generic Equilibrium Reaction Chemistry

The following equation describes the reaction between different types of gases: 3W (g) + 5X (g) β‡Œ 4Y (g) + 6Z (g). Which of the following expressions can be used to determine the value of 𝐾_𝑝 for this reaction? [A] 𝐾_𝑝 = ((𝑝Z)⁢(𝑝Y)⁴)/((𝑝W)(𝑝X)) [B] 𝐾_𝑝 = ((𝑝Z)(𝑝Y))/((𝑝W)Β³(𝑝X)⁡) [C] 𝐾_𝑝 = ((𝑝Z)⁢(𝑝Y)⁴)/((𝑝W)Β³(𝑝X)⁡) [D] 𝐾_𝑝 = ((𝑝X)⁡(𝑝Y)⁴)/((𝑝W)Β³(𝑝Z)⁢) [E] 𝐾_𝑝 = ((𝑝Z)⁢(𝑝W)Β³/((𝑝X)⁡(𝑝Y)⁴)

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Video Transcript

The following equation describes the reaction between different types of gases. Three W gas plus five X gas are in equilibrium with four Y gas plus six Z gas. Which of the following expressions can be used to determine the value of 𝐾 𝑝 for this reaction? (A) 𝐾 𝑝 equals 𝑝Z to the sixth times 𝑝Y to the fourth divided by 𝑝W times 𝑝X. (B) 𝐾 𝑝 equals 𝑝Z times 𝑝Y divided by 𝑝W to the third times 𝑝X to the fifth. (C) 𝐾 𝑝 equals 𝑝Z to the sixth times 𝑝Y to the fourth divided by 𝑝W to the third times 𝑝X to the fifth. (D) 𝐾 𝑝 equals 𝑝X to the fifth times 𝑝Y to the fourth divided by 𝑝W to the third times 𝑝Z to the sixth. (E) 𝐾 𝑝 equals 𝑝Z to the sixth times 𝑝W to the third divided by 𝑝X to the fifth times 𝑝Y to the fourth.

To answer this question, we must determine an expression that can be used to calculate the value of 𝐾 𝑝 for the given reversible reaction. 𝐾 𝑝 is the equilibrium constant for partial pressures. The equilibrium constant for partial pressures is the ratio between the partial pressures of the products and reactants at equilibrium. To see how to calculate this constant, let’s take a look at a generic reaction equation.

In this equation, the lowercase letters represent stoichiometric coefficients and the uppercase letters represent chemical formulas. To construct an equation for the equilibrium constant for partial pressures, we write the partial pressures of the products, C and D, in the numerator and the partial pressures of the reactants, A and B, in the denominator. Then, to complete the expression, each individual partial pressure is raised to the power of the respective stoichiometric coefficient.

Now that we have a generic expression for 𝐾 𝑝, we can apply our understanding to the reaction equation given in the question. To construct the 𝐾 𝑝 expression, we write the partial pressures of the products, Y and Z, in the numerator. We write the partial pressures of the reactants, W and X, in the denominator. Then, we raise each of the partial pressures to the power of their corresponding stoichiometric coefficient. This is the correct expression for 𝐾 𝑝 for this reaction.

The answer choice that best matches the expression we have written is answer choice (C). The partial pressures of Y and Z are in the numerator, and the partial pressures of W and X are in the denominator. In addition, all of the partial pressures are raised to the correct power. In conclusion, the expression that can be used to determine the value of 𝐾 𝑝 for the given reaction is answer choice (C). 𝐾 𝑝 equals 𝑝Z to the sixth times 𝑝Y to the fourth divided by 𝑝W to the third times 𝑝X to the fifth.

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