Chemistry Q60 – NEET-UG 2024

In which of the following equilibria,

K_{p}

and

K_{c}

are NOT equal?

Clue 1 of 3: Equilibrium Constants

Understand the relationship between the equilibrium constant in terms of partial pressures ( $K_{p}$ ) and the equilibrium constant in terms of molar concentrations ( $K_{c}$ ).

🧠 Full Solution Path

Step 1: Recall the relationship between

K_{p}

and

K_{c}

✦ Active

The relationship between the equilibrium constant in terms of partial pressures ( $K_{p}$ ) and the equilibrium constant in terms of molar concentrations ( $K_{c}$ ) for a gaseous equilibrium is given by the equation:

K_{p} = K_{c} (R T)^{Δ n_{g}}

Here, $R$ is the gas constant, $T$ is the absolute temperature, and $Δ n_{g}$ is the change in the number of moles of gaseous products minus the number of moles of gaseous reactants.

Step 2: Determine the condition for

K_{p} = K_{c}

○ Expand

For $K_{p}$ and $K_{c}$ to be equal, the term $(R T)^{Δ n_{g}}$ must be equal to 1. This condition is satisfied when $Δ n_{g} = 0$ .

💡 Teacher's Secret Hint

Remember that $R$ and $T$ are generally non-zero, so the only way for $(R T)^{Δ n_{g}}$ to be 1 is if the exponent $Δ n_{g}$ is 0.

Step 3: Calculate

Δ n_{g}

for each reaction○ Expand

We need to find the reaction where $Δ n_{g} \neq 0$ .

(1) $H_{2 (g)} + I_{2 (g)} ⇌ 2 {HI}_{(g)}$

$Δ n_{g} = (moles of gaseous products) - (moles of gaseous reactants) = 2 - (1 + 1) = 0$

(2) ${CO}_{(g)} + H_{2} O_{(g)} ⇌ {CO}_{2 (g)} + H_{2 (g)}$

$Δ n_{g} = (1 + 1) - (1 + 1) = 0$

(3) $2 {BrCl}_{(g)} ⇌ {Br}_{2 (g)} + {Cl}_{2 (g)}$

$Δ n_{g} = (1 + 1) - 2 = 0$

(4) ${PCl}_{5 (g)} ⇌ {PCl}_{3 (g)} + {Cl}_{2 (g)}$

$Δ n_{g} = (1 + 1) - 1 = 1$

Since $Δ n_{g} = 1 \neq 0$ for reaction (4), $K_{p}$ and $K_{c}$ are NOT equal for this equilibrium.

💡 Teacher's Secret Hint

Pay close attention to the stoichiometric coefficients of only the gaseous species when calculating $Δ n_{g}$ .

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Chemistry Question 60 – NEET-UG 2024

Clue 1 of 3: Equilibrium Constants

🧠 Full Solution Path