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.
