For the reaction, 1 g mole of CaCO₃ is
enclosed in 5 L container
CaCO₃(s) → CaO(s) + CO₂( g)
Kp = 1.16 at 1073 K then per cent
dissociation of CaCO₃ is

To determine the percent dissociation of calcium carbonate (CaCO3) in the given reaction, we first need to understand the equilibrium established when CaCO3 decomposes into calcium oxide (CaO) and carbon dioxide (CO2). The reaction can be represented as follows:

Understanding the Reaction

The balanced equation for the decomposition of calcium carbonate is:

CaCO3 (s) ⇌ CaO (s) + CO2 (g)

In this reaction, solid calcium carbonate decomposes into solid calcium oxide and gaseous carbon dioxide. The equilibrium constant, Kp, is given as 1.16 at a temperature of 1073 K.

Setting Up the Problem

We start with 1 mole of CaCO3 in a 5 L container. Since CaCO3 is a solid, it does not appear in the expression for Kp. The only gaseous product is CO2, which we will focus on.

Calculating Initial Conditions

Initially, we have:

• CaCO3: 1 mole (solid, not included in Kp)
• CaO: 0 moles (solid, not included in Kp)
• CO2: 0 moles (gaseous, included in Kp)

Defining Changes at Equilibrium

Let x be the amount of CaCO3 that dissociates at equilibrium. Therefore, at equilibrium, we have:

• CaCO3: 1 - x moles (still solid)
• CaO: x moles (solid, not included in Kp)
• CO2: x moles (gaseous)

Applying the Equilibrium Constant

The expression for Kp is given by:

Kp = P(CO2)

Since we have x moles of CO2 in a 5 L container, the partial pressure of CO2 can be calculated using the ideal gas law:

P(CO2) = (n/V)RT

Where:

• n = number of moles of CO2 = x
• V = volume of the container = 5 L
• R = ideal gas constant = 0.0821 L·atm/(K·mol)
• T = temperature = 1073 K

Thus, we can express the partial pressure as:

P(CO2) = (x / 5) * 0.0821 * 1073

Setting Up the Equation

Now, substituting this expression into the Kp equation:

1.16 = (x / 5) * 0.0821 * 1073

Calculating the right-hand side:

1.16 = (x / 5) * 88.4

1.16 = 17.68x / 5

Multiplying both sides by 5:

5.8 = 17.68x

Solving for x:

x = 5.8 / 17.68 ≈ 0.328 moles

Calculating Percent Dissociation

Percent dissociation is calculated using the formula:

Percent Dissociation = (moles dissociated / initial moles) * 100

Substituting the values:

Percent Dissociation = (0.328 / 1) * 100 ≈ 32.8%

Final Thoughts

The percent dissociation of CaCO3 at 1073 K in a 5 L container is approximately 32.8%. This means that about one-third of the initial calcium carbonate has decomposed into calcium oxide and carbon dioxide under the given conditions.