15.2.5 An Equilibrium Problem Using the Quadratic Equation

Question 1

An Equilibrium Problem Using the Quadratic Equation

Answer 1

• When assumptions used to simplify math and make equilibrium problems easier to solve fail, the quadratic formula must be used.
• The quadratic formula always yields two solutions, but only one result will be physically meaningful.

Question 2

note

Answer 2

• When assumptions used to simplify math and make
  equilibrium problems easier to solve fail, the quadratic
  formula must be used.
• Problem: Graphite (C) reacts with carbon dioxide (CO 2 ) to form carbon monoxide (CO). If the total pressure at
  equilibrium is 1.40 atm, what are the partial pressures of CO 2 and CO?
• By Dalton’s law of partial pressures, the sum of the partial pressures of CO and CO 2 equals the total pressure. The partial pressure of CO is set equal to x. The law of mass action is then used to relate the expressions for the partial pressures of CO and CO 2 to the equilibrium constant (K p ).
• However, since K p is close to one, simplifying assumptions cannot be made. The quadratic formula must be used.
• The quadratic formula always yields two solutions, but only one result will be physically meaningful.
• Plugging the values of a, b, and c into the quadratic formula yields two solutions for x: 1.1 and –5.31. Since x represents the partial pressure of CO, the negative value can be eliminated—a negative partial pressure is not physically meaningful.
• Therefore, the partial pressure of carbon monoxide is 1.1 atm, and the partial pressure of carbon dioxide is 0.3 atm.
• When the equilibrium constant (K eq ) is less than 0.1 or greater than 10, approximations and simplifying assumptions can be used to make equilibrium problems easier to solve.
• When the equilibrium constant is between 0.1 and 10, the quadratic formula must be used to solve equilibrium problems.

Question 3

Which of the following correctly shows the relationship between the equilibrium constant, Kp, and the partial pressures for the following reaction: C(s) + CO2(g) ->

Answer 3

Kp = (PCO)^2/(PCO2)

Question 4

Which statement correctly describes Dalton’s law?

Answer 4

Gases in a mixture behave independently and exert the same pressure as if they were alone in the container. As a result, the total pressure exerted by a gaseous mixture is equal to the sum of the partial pressures.

Question 5

In this lesson, we learned about a reaction in which our previous assumptions about the value for x, the change in concentration, are no longer valid. Which of the following describes a situation in which we could still use these assumptions?

Answer 5

when the value of Kp is much less than 1 or much greater than 1

Question 6

Suppose that you are examining a calculation for the final partial pressures of a system that has a Gas 1 reactant and Gas 2 product. Their stoichiometric relationship is 1:2, where 1 represents the parts of Gas 1 reactant and 2 represent the parts of Gas 2 product. If you are told that the quadratic equation for finding the partial pressures of this reaction is x 2 + 2.8x − 4.8 = 0 (where x = partial pressure of the product Gas 2), what are the values for Kp and the final total pressure of the system?

Answer 6

2.8; 1.7 atm

Question 7

Suppose that you are examining a calculation for the final partial pressures of a system that has a Gas 1 reactant and Gas 2 product. Their stoichiometric relationship is 1:2, where 1 represents the parts of Gas 1 reactant and 2 represent the parts of Gas 2 product. The quadratic equation for finding the partial pressures of this reaction is x 2 + 1.3x − 1.83 = 0 (where x = partial pressure of the product Gas 2). What are the values for Kp, Ptotal (the final total pressure of the system), and the partial pressures for the two gases (PGas 2 and PGas 1 )?

Answer 7

Kp = 1.3;
Ptotal = 1.41 atm;
PGas 2 = 0.85 atm;
PGas 1 = 0.56 atm

Question 8

Which statement does not explain why a solid reactant, such as carbon, is not included in the equilibrium constant (and reaction quotient) expression that relates partial pressures?

Answer 8

The concentrations of solids in the products and the reactants are always balanced and that causes the terms to cancel in the equilibrium constant expression.

Question 9

Suppose that you are examining a calculation for the final partial pressures of a system that has a Gas 1 reactant and Gas 2 product. The hypothetical reaction is as follows: (Solid B) + (Gas 1) ->

Answer 9

Kp = 3.3; Ptotal = 3.21 atm; PGas 2 = 2.0 atm; PGas 1 = 1.2 atm

Question 10

In this lesson, we looked at the reaction C(s) + CO2(g) ->

Answer 10

The partial pressures of the gases at final equilibrium may not add up to 2.98 atm.

Question 11

Which statement about the partial pressures and the total pressure of a system is not correct?

Answer 11

The partial pressures are the individual contributions from each gas component of the system. When they are combined, they equal the total pressure when the system is at equilibrium.

Question 12

Suppose that we are looking at the reaction N2O4(g) ->

Answer 12

1.3 atm; 0.48 atm