Question

The ratio of \[{K_p}\]​/\[{K_c}\]for the reaction; \[CO(g) + \dfrac{1}{2}{O_2}(g) \rightleftharpoons C{O_2}(g)\], is:
A. TR​
B. RT
C. \[{(RT)^{1/2}}\]
D. \[{(RT)^{ - 1/2}}\]

Answer 1

Hint: \[{K_p}\] and \[{K_c}\] are the signs used to represent the equilibrium constant of an ideal gaseous mixture. \[{K_p}\] is the equilibrium constant that is used to denote equilibrium concentrations expressed in terms of atmospheric pressure. While “\[{K_c}\]” is an equilibrium constant used when equilibrium concentrations are expressed in terms of molarity.

Complete Step by Step Solution:
For an equation, we know the relationship, \[{K_p} = {K_c}{(RT)^{\Delta n}} \cdots \cdots \]equation (1)
\[CO(g) + \dfrac{1}{2}{O_2}(g) \to C{O_2}(g)\]
As we know, \[\Delta n = np - nr\]
\[\Delta n = 1 - (1 + \dfrac{1}{2}) = - \dfrac{1}{2}\]
So, \[\dfrac{{{K_p}}}{{{K_c}}} = {(RT)^{ - \dfrac{1}{2}}}\]\[ \cdots \cdots \] from, equation (1)
So, \[{(RT)^{ - 1/2}}\]is the correct answer.
Hence, the correct answer is option (D).

Additional information: Molarity is one of the most widely used units of concentration. It is denoted by the sign “M”. It is defined as the no. of moles of solute present in 1L of solution. An ideal gas is a hypothetical/imaginary gas that is made up of a group of randomly propagating very tiny/point particles that intermix only in the event of an elastic collision.

Note: The equilibrium constant of a chemical reaction which is denoted by the symbol K, provides information regarding the relationship that exists between the products and reactants when a chemical reaction reaches equilibrium. It is important to note that there are several different types of equilibrium constants that provide relationships between products and the reactants of equilibrium reactions in terms of different units..