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The ratio of \(K_{p} / K_{c}\) for the reaction \(\mathrm{CO}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{~g})\) is (a) \((\mathrm{RT})^{1 / 2}\) (b) \((\mathrm{RT})^{-1 / 2}\) (c) \(\mathrm{RT}\) (d) 1

Short Answer

Expert verified
The ratio \( \frac{K_p}{K_c} \) is \((RT)^{-1/2}\), matching option (b).

Step by step solution

01

Understand the Reaction

The given reaction is balanced as: \( \mathrm{CO} (\mathrm{g}) + \frac{1}{2} \mathrm{O}_{2} (\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2} (\mathrm{g}) \). It involves gases, so we use partial pressures for \( K_p \) and molar concentrations for \( K_c \).
02

Relate Kp and Kc Using the Formula

To find the relation between \( K_p \) and \( K_c \), use the formula: \[ K_p = K_c (RT)^{\Delta n} \] where \( \Delta n \) is the change in moles of gas from reactants to products.
03

Calculate Change in Moles (Δn)

Calculate \( \Delta n = (\text{moles of gaseous products}) - (\text{moles of gaseous reactants}) \). Here, \( \Delta n = 1 - \left( 1 + \frac{1}{2} \right) = 1 - \frac{3}{2} = -\frac{1}{2} \).
04

Substitute Δn in the Kp/Kc Formula

Substitute the value of \( \Delta n \) into the formula: \[ K_p = K_c (RT)^{-\frac{1}{2}} \]. Hence, \[ \frac{K_p}{K_c} = (RT)^{-\frac{1}{2}} \].
05

Choose the Correct Option

The expression \( \frac{K_p}{K_c} = (RT)^{-\frac{1}{2}} \) matches option (b), which is \((RT)^{-1/2}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reaction Quotients
The reaction quotient, denoted as \(Q\), is a valuable concept in chemistry that helps us determine the current state of a reaction compared to its equilibrium. It involves using the same formula as the equilibrium constant, but with the concentrations or pressures of the reactants and products at any given time, not just at equilibrium.

Here's why \(Q\) is so useful:
  • If \(Q < K\), the reaction will proceed forward, favoring the formation of products until equilibrium is reached.
  • If \(Q > K\), the reaction will shift backward, converting products into reactants to reach equilibrium.
  • If \(Q = K\), the reaction is at equilibrium, and no shift will occur.
Understanding \(Q\) helps predict which direction a reaction will proceed given the current concentrations or pressures, making it a fundamental tool in chemical analysis.
Le Chatelier's Principle
Le Chatelier's Principle is a key concept for understanding how systems at equilibrium respond to disturbances. When a change is applied to a system at equilibrium, the system will adjust to counteract the change and restore equilibrium. This principle covers changes in concentration, pressure, and temperature.

For example, if more reactants are added, the system will shift toward producing more products to re-establish balance. For gaseous reactions, changing the pressure by altering the volume can also shift equilibrium. Increasing pressure often favors the side with fewer moles of gas. In the context of temperature changes, the direction of shift depends on whether the reaction is exothermic or endothermic.
  • In exothermic reactions, increasing temperature shifts the equilibrium to favor the reactants.
  • In endothermic reactions, increasing temperature shifts the equilibrium to favor the products.
Le Chatelier's Principle provides a predictive tool for how chemical systems respond to external influences.
Ideal Gas Law
The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and amount of an ideal gas. It is represented as \(PV = nRT\), where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles of gas, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin.

Understanding this equation helps in predicting the behavior of gases under different conditions:
  • As pressure increases, the volume decreases if the temperature and moles remain constant (Boyle's Law).
  • As temperature rises, if pressure stays the same, the volume will increase (Charles's Law).
  • When moles of gas increase at constant temperature and pressure, the volume also increases (Avogadro's Law).
The Ideal Gas Law makes it simple to calculate any one of the variables—pressure, volume, or temperature—if the other three are known, and is a cornerstone in understanding gaseous reactions in chemistry.

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Most popular questions from this chapter

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Determine the value of equilibrium constant \(\left(\mathrm{K}_{\mathrm{C}}\right.\) ) for the reaction $$ \mathrm{A}_{2}(\mathrm{~g})+\mathrm{B}_{2}(\mathrm{~g}) \rightleftharpoons 2 \mathrm{AB}(\mathrm{g}) $$ If 10 moles of \(A_{2} ; 15\) moles of \(B_{2}\) and 5 moles of \(A B\) are placed in a 2 litre vessel and allowed to come to equilibrium. The final concentration of \(\mathrm{AB}\) is \(7.5 \mathrm{M}\) : (a) \(4.5\) (b) \(1.5\) (c) \(0.6\) (d) None of these

A vessel at equilibrium, contains \(\mathrm{SO}_{3}, \mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\), Now some helium gas is added, so that total pressure increases while temperature and volume remain constant. According to Le Chatelier's Principle, the dissociation of \(\mathrm{SO}_{3}\) (a) decreases (b) remains unaltered (c) increases (d) change unpredictably

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