1 mole of caco3 is heated in 11.2 lit vessel so that equilibrium is established T 819K.If kp for caco3reversiblecao+co2 at this temperature is 2at,equilibruim concentration of co2 is?

To determine the equilibrium concentration of CO2 when 1 mole of CaCO3 is heated in an 11.2-liter vessel at 819 K, we can use the equilibrium constant (Kp) provided for the reaction. The reaction can be represented as follows:

Understanding the Reaction

The decomposition of calcium carbonate (CaCO3) can be expressed as:

• CaCO3 (s) ⇌ CaO (s) + CO2 (g)

In this reaction, solid calcium carbonate decomposes into solid calcium oxide and gaseous carbon dioxide. Since solids do not appear in the equilibrium expression, we focus only on the gaseous products.

Equilibrium Constant Expression

The equilibrium constant Kp for this reaction is given by:

• Kp = P(CO2)

Where P(CO2) is the partial pressure of CO2 at equilibrium. Given that Kp = 2 at 819 K, we can set up our calculations based on this information.

Calculating the Equilibrium Concentration

First, we need to relate the partial pressure of CO2 to its concentration. The ideal gas law states:

• P = (n/V)RT

Where:

• P = pressure (in atm)
• n = number of moles of gas
• V = volume of the container (in liters)
• R = ideal gas constant (0.0821 L·atm/(K·mol))
• T = temperature (in Kelvin)

We can rearrange this equation to find the concentration (C) of CO2:

• C = n/V

Finding Moles of CO2

Let x be the number of moles of CO2 produced at equilibrium. Since we start with 1 mole of CaCO3, and it decomposes to produce x moles of CO2, we can express the equilibrium condition as:

• Kp = P(CO2) = (x/V)RT

Substituting Values

Now, substituting the known values into the equation:

• Kp = 2
• V = 11.2 L
• R = 0.0821 L·atm/(K·mol)
• T = 819 K

We can express the pressure of CO2 in terms of x:

• 2 = (x / 11.2) * (0.0821 * 819)

Calculating x

Now, let’s calculate the right side:

• 0.0821 * 819 = 67.3089

Now substituting this back into the equation:

• 2 = (x / 11.2) * 67.3089

Rearranging gives:

• x = (2 * 11.2) / 67.3089

Calculating this yields:

• x ≈ 0.332 moles of CO2

Finding Concentration of CO2

Finally, to find the concentration of CO2 at equilibrium:

• C(CO2) = x / V = 0.332 / 11.2

This results in:

• C(CO2) ≈ 0.0296 moles/L

Thus, the equilibrium concentration of CO2 in the vessel is approximately 0.0296 M. This calculation illustrates how to apply the equilibrium constant and the ideal gas law to find concentrations in a chemical reaction at equilibrium.