Worksheet: Equilibrium Constants and Gibbs Free Energies

In this worksheet, we will practice converting between Gibbs free energies of equilibria and equilibrium constants by applying the equation ΔG = –RTlnK.

Q1:

Under certain conditions, gaseous ammonia can decompose into nitrogen and hydrogen gases: The partial pressures of N H 3 , H 2 , and N 2 are denoted 𝑃 ( N H ) 3 , 𝑃 ( H ) 2 , and 𝑃 ( N ) 2 respectively. When the initial partial pressure of each gas is equal to the standard value of 1.00 atm and the temperature is fixed at 298 K, the change in Gibbs free energy for the reaction, Δ 𝐺 ⦵ , is 33.00 kJ/mol. Calculate, to 3 significant figures, the change in Gibbs free energy, Δ 𝐺 , at 298 K when 𝑃 = 1 2 . 9 ( N H ) a t m 3 , 𝑃 = 0 . 2 5 0 ( H ) a t m 2 , and 𝑃 = 0 . 8 7 0 ( N ) a t m 2 .

Q2:

Which of the following is the best definition of Δ 𝐺 ⦵ , the standard change in Gibbs free energy for a reversible process?

  • AWhen the sum of the concentrations or partial pressures of reactants and products is equal to the standard value, Δ 𝐺 ⦵ is the energy that must be released for equilibrium to be reached.
  • BWhen the concentrations or partial pressures of reactants and products are all equal to the standard values, Δ 𝐺 ⦵ is the energy that must be released for equilibrium to be reached.
  • C Δ 𝐺 ⦵ is the difference in free energy between the pure reactants in their stoichiometric ratio and the equilibrium mixture of reactants and products.
  • DWhen the concentrations or partial pressures of reactants and products are all equal to the standard value, Δ 𝐺 ⦵ is the energy that must be absorbed for equilibrium to be reached.
  • E Δ 𝐺 ⦵ is the difference in free energy between the pure products in their stoichiometric ratio and the equilibrium mixture of reactants and products.

Q3:

The standard change in Gibbs free energy for a reversible process, Δ 𝐺 ⦵ , is measured for a standard solution of reactants and products. What are the initial concentrations of the reactants and products in this solution?

  • AReactants and products are present in the stoichiometric ratio and the sum of the reactant and product concentrations is 1 M.
  • BReactants are present in the stoichiometric ratio and the sum of the reactant concentrations is 1 M. Product concentrations are defined in the same way.
  • CReactants and products are present in the equilibrium ratio and the sum of the reactant and product concentrations is 1 M.
  • DThe concentration of each reactant and product is 1 M.
  • EReactants and products are present in the stoichiometric ratio and the sum of the reactant concentrations is 1 M.

Q4:

The equilibrium constant ( 𝐾 ) 𝑐 for the hydrolysis of adenosine triphosphate (ATP) to adenosine diphosphate (ADP) and phosphate is 1 . 6 7 × 1 0 / 5 3 m o l d m at 3 7 ∘ C , and the Δ 𝐻 𝑟 ⦵ for this reaction has a value of − 2 0 . 1 kJ/mol. Given this information, what is the value of Δ 𝑆 𝑟 ⦵ for the reaction?

Q5:

Consider the reaction g l y c e r o l ( ) + H P O ( ) D L - g l y c e r o l - - p h o s p h a t e + H O ( ) a q a q l 4 2 – 2 1 ( 𝑎 𝑞 ) 2 − . The equilibrium constant for this reaction at 3 7 ∘ C is 0.0120, and the value of Δ 𝐺 ⦵ r at 2 5 ∘ C is 9.37 kJ. Given this information, what is the equilibrium constant ( 𝐾 ) e q for the reaction at 2 5 ∘ C , and what is the value of Δ 𝐻 ⦵ r for the reaction? (You may assume that the Δ 𝐻 ⦵ r of the reaction is independent of temperature.)

  • A 𝐾 = 0 . 0 4 6 e q at 2 5 ∘ C ; Δ 𝐻 = 2 1 . 2 ⦵ r k J
  • B 𝐾 = 0 . 4 6 2 e q at 2 5 ∘ C ; Δ 𝐻 = 4 1 . 2 ⦵ r k J
  • C 𝐾 = 0 . 0 0 3 e q at 2 5 ∘ C ; Δ 𝐻 = − 2 1 . 2 ⦵ r k J
  • D 𝐾 = 0 . 0 2 3 e q at 2 5 ∘ C ; Δ 𝐻 = − 4 1 . 2 ⦵ r k J

Q6:

Consider the following two reactions: (1) g l u t a m a t e + N H g l u t a m i n e 4 + , for which Δ 𝐺 = 1 5 . 7 / ⦵ 𝑟 k J m o l at 3 7 ∘ C ; and (2) A T P A D P + P i , for which Δ 𝐺 = − 3 1 . 0 / ⦵ 𝑟 k J m o l at 3 7 ∘ C . (In reaction (2), A T P denotes adenosine triphosphate, A D P denotes adenosine diphosphate, and P i represents inorganic phosphate.) These two reactions can be coupled by an enzyme catalyst (glutamine synthetase), which leads to the following reaction: (3) g l u t a m a t e + N H + A T P g l u t a m i n e + A D P + P i 4 + . What is the equilibrium constant for reaction (3) at a temperature of 3 7 ∘ C ?

  • A1.1
  • B 2 . 3 × 1 0 − 3
  • CThere is not enough information provided to answer this question.
  • D 3 . 8 × 1 0 2

Q7:

Carbon tetrachloride is formed by the chlorination of methane at high temperature: The standard entropies and enthalpies of formation for the reactants and products are shown in the table.

Material Standard Molar Entropy 𝑆 ⦵    (J/K⋅mol) Standard Enthalpy of Formation Δ 𝐻 ⦵ f (kJ/mol)
C C l ( ) 4 l 214.4 − 1 2 8 . 2
C C l ( ) 4 g 309.7 − 9 5 . 7
C H ( ) 4 g 186.3 − 7 4 . 6
C l ( ) 2 g 223.1 0.0
H C l ( ) g 186.9 − 9 2 . 3

Assuming the thermodynamic parameters do not vary with temperature, calculate, to 1 significant figure, the equilibrium constant for this reaction at 2 5 0 ∘ C .

  • A 1 × 1 0  
  • B 1 × 1 0  
  • C 7 × 1 0  
  • D 7 × 1 0  
  • E 9 × 1 0  

Q8:

Hydrogen sulfide reacts reversibly with sulfur dioxide to form sulfur and water: The standard free energies of formation, Δ 𝐺 ⦵  , for hydrogen sulfide and other materials are shown in the table. These energies are measured at 2 5 ∘ C .

Material H S ( ) 2 g S O ( ) 2 g S O ( ) 3 g S ( ) 8 s S ( ) g H O ( ) 2 g H O ( ) 2 l
Standard Gibbs Free Energy of Formation Δ 𝐺 ⦵  (kJ/mol) − 3 3 . 4 − 3 0 0 . 1 − 3 7 1 . 1 0.0 238.3 − 2 2 8 . 6 − 2 3 7 . 1

Calculate, to 2 significant figures, the equilibrium constant for this reaction at 2 5 ∘ C .

  • A 6 . 6 × 1 0  
  • B 2 . 3 × 1 0 
  • C 1 . 4 × 1 0 
  • D 6 . 3 × 1 0  
  • E 4 . 5 × 1 0  

A student uses the values of Δ 𝐺 ⦵  at 2 5 ∘ C to calculate the equilibrium constant for this reaction at 9 0 ∘ C . Why are the results of this calculation likely to be inaccurate?

  • A Δ 𝐺 ⦵  values change with temperature.
  • BThe reaction may not occur at the higher temperature.
  • CThe equation Δ 𝐺 = − 𝑅 𝑇 ⦵ l n 𝐾 is only true at a standard temperature of 2 5 ∘ C .
  • DThe standard pressure changes with temperature.
  • EThe products of the reaction have different phases at the higher temperature.

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