Equilibrium Composition Calculation

Calculating Equilibrium Composition from an Equilibrium Constant

Introduction

  • The process of calculating equilibrium composition involves using the equilibrium constant, K, to determine the concentrations of reactants and products at equilibrium.

Reaction Overview

  • Given the reaction:
    • NO<em>2(g)+CO(g)⇌NO(g)+CO</em>2(g)NO<em>2(g) + CO(g) \rightleftharpoons NO(g) + CO</em>2(g)

Initial Conditions

  • A 500 mL flask contains the following initial amounts:
    • NO2: 1.4 mol
    • CO: 0.80 mol
    • NO: 1.8 mol
  • Volume of the flask: 500 mL = 0.500 L

Initial Molarity Calculation

  • The molarity (M) of each species can be calculated using the formula:
    • M=nVM = \frac{n}{V}
    • where ( n ) is the number of moles and ( V ) is the volume in liters.
    • Initial Molarities:
      • [NO<em>2]</em>0=1.4 mol0.500 L=2.8extM[NO<em>2]</em>0 = \frac{1.4 \text{ mol}}{0.500 \text{ L}} = 2.8 ext{ M}
      • [CO]0=0.80 mol0.500 L=1.6extM[CO]_0 = \frac{0.80 \text{ mol}}{0.500 \text{ L}} = 1.6 ext{ M}
      • [NO]0=1.8 mol0.500 L=3.6extM[NO]_0 = \frac{1.8 \text{ mol}}{0.500 \text{ L}} = 3.6 ext{ M}

Changes at Equilibrium

  • As the reaction proceeds, let ( x ) be the change in concentration for the reactants and products at equilibrium.
  • The changes for each species are as follows:
    • [NO2]=2.8−x[NO_2] = 2.8 - x
    • [CO]=1.6−x[CO] = 1.6 - x
    • [NO]=3.6+x[NO] = 3.6 + x
    • [CO2]=0+x[CO_2] = 0 + x

Equilibrium Expression

  • The equilibrium constant expression for the given reaction is:
    • K=[NO][CO<em>2][NO</em>2][CO]K = \frac{[NO][CO<em>2]}{[NO</em>2][CO]}
    • Given that ( K = 0.879 ), substituting the equilibrium concentrations gives:
    • 0.879=(3.6+x)(x)(2.8−x)(1.6−x)0.879 = \frac{(3.6 + x)(x)}{(2.8 - x)(1.6 - x)}

Setting Up the Equation

  • Rearranging gives:
    • 0.879(2.8−x)(1.6−x)=(3.6+x)(x)0.879 (2.8 - x)(1.6 - x) = (3.6 + x)(x)
  • Expanding both sides leads to a quadratic equation, which must be solved to find ( x ).

Solve the Quadratic Equation

  • Let's denote the equation derived from the arrangement as:
    • A=0.879imes[(2.8imes1.6)−(2.8imesx)−(1.6imesx)+x2]=(3.6x+x2)A = 0.879 imes [(2.8 imes 1.6) - (2.8 imes x) - (1.6 imes x) + x^2] = (3.6x + x^2)
    • Rearranging gives a structured quadratic equation in the standard form of ( ax^2 + bx + c = 0 ).
  • Solving the quadratic equation provides the value of ( x ).

Finding Molarity of CO at Equilibrium

  • After obtaining ( x ), calculate the equilibrium concentration of CO:
    • [CO]eq=1.6−x[CO]_{eq} = 1.6 - x

Rounding the Answer

  • The final molarity value for CO should be rounded to two decimal places for reporting purposes.
  • The resulting equilibrium molarity of CO is presented in the appropriate significant figures.

Conclusion

  • This process demonstrates the systematic approach in calculating equilibrium compositions by utilizing the equilibrium constant and initial concentrations to derive the necessary equilibrium concentrations.