find KP is sulfuryl chloride decomposes to the extent of 91.2% at 102 degree centigrade and total pressure 1 atmosphere

To find the equilibrium constant (KP) for the decomposition of sulfuryl chloride (SO2Cl2) under the given conditions, we first need to understand the reaction and the changes that occur during the decomposition process. The decomposition of sulfuryl chloride can be represented by the following balanced equation:

Decomposition Reaction

SO2Cl2(g) ⇌ SO2(g) + Cl2(g)

Understanding the Extent of Decomposition

The problem states that sulfuryl chloride decomposes to the extent of 91.2%. This means that 91.2% of the initial amount of SO2Cl2 has reacted to form products. If we assume we start with 1 mole of SO2Cl2, we can calculate the moles of reactants and products at equilibrium.

Calculating Moles at Equilibrium

• Initial moles of SO2Cl2 = 1 mole
• Moles decomposed = 91.2% of 1 mole = 0.912 moles
• Moles remaining of SO2Cl2 = 1 - 0.912 = 0.088 moles
• Moles of SO2 produced = 0.912 moles
• Moles of Cl2 produced = 0.912 moles

Calculating Total Moles at Equilibrium

At equilibrium, the total number of moles can be calculated as follows:

• Total moles = moles of SO2Cl2 + moles of SO2 + moles of Cl2
• Total moles = 0.088 + 0.912 + 0.912 = 1.912 moles

Finding Partial Pressures

Next, we need to calculate the partial pressures of each component at equilibrium. Since the total pressure is given as 1 atmosphere, we can use the mole fraction to find the partial pressures:

• Partial pressure of SO2Cl2 = (moles of SO2Cl2 / total moles) × total pressure = (0.088 / 1.912) × 1 atm ≈ 0.046 atm
• Partial pressure of SO2 = (moles of SO2 / total moles) × total pressure = (0.912 / 1.912) × 1 atm ≈ 0.477 atm
• Partial pressure of Cl2 = (moles of Cl2 / total moles) × total pressure = (0.912 / 1.912) × 1 atm ≈ 0.477 atm

Calculating KP

The equilibrium constant KP for the reaction can be expressed in terms of the partial pressures of the products and reactants:

KP = (P_SO2 × P_Cl2) / P_SO2Cl2

Substituting the values we calculated:

KP = (0.477 atm × 0.477 atm) / 0.046 atm

KP ≈ 4.66 atm

Final Result

Thus, the equilibrium constant KP for the decomposition of sulfuryl chloride at 102 degrees Celsius and a total pressure of 1 atmosphere is approximately 4.66 atm. This value indicates the extent to which the reaction favors the formation of products at the specified conditions.