A vessel at 1000K contains CO₂ with a pressure of 0.5 atm. Some of the CO₂ is converted to CO on the addition of graphite. If the total pressure at equilibrium is 0.8 atm, the value of K is :-

To determine the equilibrium constant \( K \) for the reaction where carbon dioxide (\( CO_2 \)) is converted to carbon monoxide (\( CO \)) in the presence of graphite, we first need to understand the chemical reaction involved and how to set up the equilibrium expression. The reaction can be represented as follows:

The Reaction and Initial Conditions

The reaction can be written as:

• \( CO_2(g) + C(s) \rightleftharpoons 2CO(g) \)

In this reaction, solid carbon (graphite) reacts with gaseous carbon dioxide to produce gaseous carbon monoxide. Initially, we have:

• Pressure of \( CO_2 \) = 0.5 atm
• Pressure of \( CO \) = 0 atm
• Total pressure = 0.5 atm

Changes at Equilibrium

When the reaction reaches equilibrium, the total pressure is given as 0.8 atm. This means that some \( CO_2 \) has been converted to \( CO \). Let's denote the change in pressure of \( CO_2 \) that reacts as \( x \). At equilibrium, the pressures will be:

• Pressure of \( CO_2 \) = \( 0.5 - x \) atm
• Pressure of \( CO \) = \( 2x \) atm (since 1 mole of \( CO_2 \) produces 2 moles of \( CO \))

Setting Up the Equilibrium Expression

The total pressure at equilibrium is the sum of the pressures of \( CO_2 \) and \( CO \):

\( (0.5 - x) + 2x = 0.8 \)

Solving this equation:

• \( 0.5 + x = 0.8 \)
• \( x = 0.3 \) atm

Calculating Equilibrium Pressures

Now we can find the equilibrium pressures:

• Pressure of \( CO_2 \) = \( 0.5 - 0.3 = 0.2 \) atm
• Pressure of \( CO \) = \( 2 \times 0.3 = 0.6 \) atm

Equilibrium Constant Expression

The equilibrium constant \( K \) for the reaction is defined as:

\( K = \frac{[CO]^2}{[CO_2]} \)

Since we are dealing with pressures, we can substitute the equilibrium pressures into this expression:

\( K = \frac{(0.6)^2}{0.2} \)

Calculating this gives:

• \( K = \frac{0.36}{0.2} = 1.8 \)

Final Result

Thus, the equilibrium constant \( K \) for the reaction at 1000 K is:

K = 1.8