Video Transcript
The given equation describes how
carbon monoxide can react with water vapor to produce carbon dioxide and
hydrogen. H2O gas plus CO gas are in
equilibrium with H2 gas plus CO2 gas. Which of the following expressions
can be used to determine the value of 𝐾 𝑝 for this reaction? (A) 𝐾 𝑝 equals pH2 times pCO2
divided by pH2O times pCO. (B) 𝐾 𝑝 equals pH2 squared times
pCO2 squared divided by pH2O times pCO. (C) 𝐾 𝑝 equals pH2 squared times
pCO2 squared divided by pH2O squared times pCO. (D) 𝐾 𝑝 equals pH2 squared times
pCO2 squared divided by pH2O squared times pCO squared. (E) 𝐾 𝑝 equals pH2 squared times
pCO2 divided by pH2O times pCO.
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. In a similar fashion to other
equilibrium constants, the equilibrium constant for partial pressures can most
simply be expressed as the partial pressures of the products divided by the partial
pressures of the reactants. So, when writing an expression for
𝐾 𝑝 for the provided reaction, we should write the partial pressures of the
products, H2 and CO2, in the numerator and the partial pressures of the reactants,
H2O and CO, in the denominator.
Looking at the answer choices, we
can see that this is the case for all of the expressions. We can also see that some of the
expressions contain superscript values. To understand where these
superscript values might come from, 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. We know that 𝐾 𝑝 for this
reaction will equal the partial pressures of the products, C and D, divided by the
partial pressures of the reactants, A and B. But the equilibrium constant for a
partial pressure’s expression, like other equilibrium constant expressions, needs to
take into account the stoichiometric coefficients.
So, to complete the expression,
each of the partial pressures must be raised to the power of the respective
stoichiometric coefficient. If we look at the reaction equation
given in the question, we can see that each species has a stoichiometric coefficient
of one. Therefore, each of the partial
pressures in the 𝐾 𝑝 expression should be raised to the power of one. But of course, an exponent of one
does not need to be explicitly written. So, this is the correct expression
for 𝐾 𝑝 for this reaction. We can see that this matches the
expression written in answer choice (A).
Therefore, the expression that can
be used to determine the value of 𝐾 𝑝 for the given reaction is the expression
shown in answer choice (A). 𝐾 𝑝 equals pH2 times pCO2 divided
by pH2O times pCO.
