CaCO‚ÄöCE(s) decomposes to produce CaO(s) and CO‚ÄöCC(g) when heated, as …

Chemistry Questions
Short Answer
Step by Step Solution
Chemistry Questions

CaCO‚CE(s) decomposes to produce CaO(s) and CO‚CC(g) when heated, as shown in the equation above. A 2.0 mol sample of CaCO‚CE(s) is placed in a rigid 100 L reaction vessel with all air evacuated. The vessel is heated to 898¬∞C, where the pressure of CO‚CC(g) is 1.00 atm, and some CaCO‚CE(s) remains. a. Calculate the number of moles of CO‚CC(g) at equilibrium. b. Write the Kp expression for the reaction and determine its value at 898¬∞C. c. If the experiment is repeated with a 4.0 mol sample of CaCO‚CE(s), sketch a curve on the provided graph showing how the pressure of CO‚CC(g) changes over time until equilibrium is reached at 898¬∞C.

Short Answer

The calculation of moles of CO‚ÄöCC at equilibrium using the ideal gas law yields approximately 1.1 moles at 1.00 atm and 1171 K. The equilibrium constant Kp for the reaction is simplified to the pressure of CO‚ÄöCC, which is established at 1.00 atm, and upon decomposition of 4.0 mol of CaCO‚ÄöCE, the CO‚ÄöCC pressure initially rises before stabilizing at the same equilibrium pressure.

Step-by-Step Solution

Step 1: Calculate Moles of CO2 at Equilibrium

To find the number of moles of CO2 at equilibrium, we can use the ideal gas law, which is expressed as P = 1.00 atm, V = 100 L, R = 0.0821 L.atm/mol.K, and T = 1171 K (898°C + 273). By rearranging the ideal gas law, we calculate:

  • n = PV/RT
  • n = (1.00 atm * 100 L) / (0.0821 L.atm/mol.K * 1171 K)
  • This results in approximately 1.1 moles of CO2 at equilibrium.

Step 2: Understand Equilibrium Constant (Kp)

The equilibrium constant, Kp, for the reaction can be expressed as Kp = [CO2]^p / ([CaCO3]^p * [CaO]^p). As both calcium carbonate (CaCO3) and calcium oxide (CaO) are solids, their concentrations do not change and are not included in the calculation. Thus, Kp simplifies to:

  • Kp = PCO2
  • Kp value at 898¬¨‚àûC is established as 1.00 atm.

Step 3: CO2 Pressure Dynamics with Initial CaCO3

When conducting the experiment using an initial amount of 4.0 mol of CaCO3, the pressure of CO2 will rise quickly at first due to the decomposition of calcium carbonate. As the reaction approaches equilibrium, the increase in pressure will decelerate until it stabilizes:

  • Initially high pressure of CO2
  • Pressure will stabilize just like in the previous scenario
  • Final equilibrium pressure remains at 1.00 atm.

Related Concepts

Ideal Gas Law

A mathematical relationship between the pressure, volume, temperature, and number of moles of an ideal gas, expressed as pv = nrt, where p is pressure, v is volume, n is the number of moles, r is the ideal gas constant, and t is temperature in kelvin.

Equilibrium Constant

A numerical value that expresses the ratio of the concentrations of products to the concentrations of reactants at equilibrium, denoted as k and can be expressed for gases as kp using partial pressures.

Pressure Dynamics

The changes in pressure of a gas during a reaction, particularly how the pressure increases rapidly during the initial stages of a reaction and then stabilizes as the system reaches equilibrium.

Table Of Contents
  1. CaCO‚CE(s) decomposes to produce CaO(s) and CO‚CC(g) when heated, as shown in the equation above. A 2.0 mol sample of CaCO‚CE(s) is placed in a rigid 100 L reaction vessel with all air evacuated. The vessel is heated to 898¬∞C, where the pressure of CO‚CC(g) is 1.00 atm, and some CaCO‚CE(s) remains. a. Calculate the number of moles of CO‚CC(g) at equilibrium. b. Write the Kp expression for the reaction and determine its value at 898¬∞C. c. If the experiment is repeated with a 4.0 mol sample of CaCO‚CE(s), sketch a curve on the provided graph showing how the pressure of CO‚CC(g) changes over time until equilibrium is reached at 898¬∞C.

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