Multiple Choice
For which of the following chemical equations would the value of K_c equal K_p at a given temperature?
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16. Chemical Equilibrium
Kp and Kc
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Which gas-phase reaction has equal to at the same temperature?
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Verified step by step guidance1
Recall the relationship between the equilibrium constants \(K_p\) and \(K_c\) for gas-phase reactions:
\[K_p = K_c (RT)^{\Delta n}\]
where \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(\Delta n\) is the change in moles of gas (moles of gaseous products minus moles of gaseous reactants).
To find when \(K_p = K_c\), set the equation equal and analyze the term involving \(\Delta n\):
\[K_p = K_c (RT)^{\Delta n} = K_c \implies (RT)^{\Delta n} = 1\]
Since \(R\) and \(T\) are positive and not equal to 1 in general, the only way for this to be true at all temperatures is if \(\Delta n = 0\).
For each given reaction, calculate \(\Delta n\) by subtracting the total moles of gaseous reactants from the total moles of gaseous products. For example, if the reaction is:
\[aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)\]
then
\[\Delta n = (c + d) - (a + b)\]
Identify the reaction where \(\Delta n = 0\). This means the number of moles of gaseous products equals the number of moles of gaseous reactants, so \(K_p\) will equal \(K_c\) at the same temperature.
Confirm that the chosen reaction has no change in moles of gas and thus satisfies the condition \(K_p = K_c\). This reaction is the one where the equilibrium constants are equal under the same temperature.
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