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Question Video: Identifying the Expression for the Equilibrium Constant for Partial Pressures for the Reaction of Carbon Monoxide with Water Vapor Chemistry

The given equation describes how carbon monoxide can react with water vapor to produce carbon dioxide and hydrogen: Hโ‚‚O (g) + CO (g) โ‡Œ Hโ‚‚ (g) + COโ‚‚ (g) Which of the following expressions can be used to determine the value of ๐พโ‚š for this reaction? [A] ๐พโ‚š = (pHโ‚‚)(pCOโ‚‚)/((pHโ‚‚O)(pCO)) [B] ๐พโ‚š = (pHโ‚‚)ยฒ(pCOโ‚‚)ยฒ/((pHโ‚‚O)(pCO)) [C] ๐พโ‚š = (pHโ‚‚)ยฒ(pCOโ‚‚)ยฒ/((pHโ‚‚O)ยฒ(pCO)) [D] ๐พโ‚š = (pHโ‚‚)ยฒ(pCOโ‚‚)ยฒ/((pHโ‚‚O)ยฒ(pCO)ยฒ) [E] ๐พโ‚š = (pHโ‚‚)ยฒ(pCOโ‚‚)/((pHโ‚‚O)(pCO))

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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 ๐พ ๐‘ for this reaction? (A) ๐พ ๐‘ equals pH2 times pCO2 divided by pH2O times pCO. (B) ๐พ ๐‘ equals pH2 squared times pCO2 squared divided by pH2O times pCO. (C) ๐พ ๐‘ equals pH2 squared times pCO2 squared divided by pH2O squared times pCO. (D) ๐พ ๐‘ equals pH2 squared times pCO2 squared divided by pH2O squared times pCO squared. (E) ๐พ ๐‘ equals pH2 squared times pCO2 divided by pH2O times pCO.

๐พ ๐‘ 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 ๐พ ๐‘ 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, letโ€™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 ๐พ ๐‘ 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 pressureโ€™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 ๐พ ๐‘ 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 ๐พ ๐‘ 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 ๐พ ๐‘ for the given reaction is the expression shown in answer choice (A). ๐พ ๐‘ equals pH2 times pCO2 divided by pH2O times pCO.

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