Gibbs Free Energy MCQ Quiz - Objective Question with Answer for Gibbs Free Energy - Download Free PDF

at constant T

\(dG=VdP\)

\(\because\) for \(H_2O\) volume will be almost constant on increasing pressure.

\(\therefore \Delta G =V(\Delta P)\)

\(\Delta G =V(P_2-P-1)=5 \times 18\times 10^{-6}(101-1)\times 10^4 \, \text{Joule} =5 \times 18\times 10^{-1}\times 10^2=900 \, \text{Joule}\)

CONCEPT:

Gibbs Free Energy (ΔG) and Spontaneity

• Gibbs free energy change (ΔG) is a criterion for spontaneity at constant temperature and pressure.
• If ΔG is negative (ΔG < 0), the reaction is spontaneous.
• If ΔG is positive (ΔG > 0), the reaction is non-spontaneous.
• If ΔG is zero (ΔG = 0), the reaction is at equilibrium (reversible reaction).

Explantion:-

• 1) ΔG is negative for a spontaneous reaction:
  This statement is correct. A negative ΔG indicates a spontaneous reaction.
• 2) ΔG is positive for a spontaneous reaction:
  This statement is incorrect. A positive ΔG indicates a non-spontaneous reaction.
• 3) ΔG is zero for a reversible reaction:
  This statement is correct. ΔG = 0 indicates the reaction is at equilibrium and reversible.
• 4) ΔG is positive for a non-spontaneous reaction:
  This statement is correct. A positive ΔG indicates a non-spontaneous reaction.

Therefore, the incorrect statement is: 2) ΔG is positive for a spontaneous reaction

Concept:

• ΔG, or Gibbs free energy change, determines the spontaneity of a reaction. A negative ΔG indicates a spontaneous reaction.

• A catalyst speeds up the reaction by lowering the activation energy, but it does not change the overall Gibbs free energy change (ΔG) of the reaction.

• The Gibbs free energy change (ΔG) is a state function, which means it depends only on the initial and final states of the system, not on the path taken or the presence of a catalyst.

• Therefore, the value of ΔG for a reaction remains the same regardless of whether a catalyst is present.

Explanation:

1. Given:

   • ΔG for a reaction without a catalyst = x

   • ΔG for the same reaction with a catalyst = y

2. Since a catalyst does not alter the ΔG of a reaction:

   • x = y

3. Expressing the relationship using the options given:

   • -x = -y

Conclusion:

The correct relation between x and y, given the options provided, is: None of these.

Concept:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The nonavailable energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

Thus,

\(\Delta G = \Delta H - T\Delta S\)

\(dG = dq - d{q_{rev}}\)

• Gibbs free energy is denoted by ΔG and have the units J/mol.

Explanation:

\(\begin{array}{l} G = \;H - TS\\ \;or,\;dG = dH - TdS - SdT\\ \;when\;temperature\;and\;pressure\;is\;kept\;constant,\\ \;dH = dq\;and\;dT = 0\\ \;So,\;dS = \frac{{d{q_{rev}}\;}}{T}\;\\ or,\;dG = dq - d{q_{rev}} \end{array}\)

As \( dq > dq_{rev}\) in an irreversible process,

\(dG < 0\) for irreversible processes.

As all irreversible processes are spontaneous, \(dG < 0\) for spontaneous processes at constant temp and pressure.

Hence, ΔG for a spontaneous process at constant pressure and temperature is ΔG < 0.

Important Points

• Note that if the forward reaction is spontaneous and irreversible, the Gibbs free energy is negative.
• The backward reaction will have ΔG > 0 and will be non-spontaneous.
• ΔG = 0 at equillibrium ,i.e. reversible process.

Concept : 

• ∆G is the change in the Gibb's free energy 
• The value the spontaneity of a reaction is concluded
• For a reaction which is in equilibrium the value  of ∆G is zero
• For a spontaneous reaction ∆G is positive 
• For a non spontaneous reaction ∆G is negative 

Explanation :

• Option 1 says ∆G is zero for a reversible reaction .
• A reversible reaction always is in equilibrium
• And for equilibrium reaction the value of ∆G is zero.
• So it is true

• Option 2 says ∆G is positive for a spontaneous reaction .
• But for a spontaneous reaction value of  ∆G is negative.
• So it is wrong

• Option 3 says ∆G is negative for a spontaneous reaction .
• It is true. 

• Option 4 says  ∆G is positive for a non-spontaneous reaction .
• It is true. 

Conclusion :   

∆G is positive for a spontaneous reaction - the statement is incorrect.

so the correct option is 2

Concept:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The nonavailable energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

Thus,

\(\Delta G = \Delta H - T\Delta S\)

\(dG = dq - d{q_{rev}}\)

• Gibbs free energy is denoted by ΔG and have the units J/mol.

Explanation:

\(\begin{array}{l} G = \;H - TS\\ \;or,\;dG = dH - TdS - SdT\\ \;when\;temperature\;and\;pressure\;is\;kept\;constant,\\ \;dH = dq\;and\;dT = 0\\ \;So,\;dS = \frac{{d{q_{rev}}\;}}{T}\;\\ or,\;dG = dq - d{q_{rev}} \end{array}\)

As \( dq > dq_{rev}\) in an irreversible process,

\(dG < 0\) for irreversible processes.

As all irreversible processes are spontaneous, \(dG < 0\) for spontaneous processes at constant temp and pressure.

Hence, ΔG for a spontaneous process at constant pressure and temperature is ΔG < 0.

Important Points

• Note that if the forward reaction is spontaneous and irreversible, the Gibbs free energy is negative.
• The backward reaction will have ΔG > 0 and will be non-spontaneous.
• ΔG = 0 at equillibrium ,i.e. reversible process.

Concept : 

• ∆G is the change in the Gibb's free energy 
• The value the spontaneity of a reaction is concluded
• For a reaction which is in equilibrium the value  of ∆G is zero
• For a spontaneous reaction ∆G is positive 
• For a non spontaneous reaction ∆G is negative 

Explanation :

• Option 1 says ∆G is zero for a reversible reaction .
• A reversible reaction always is in equilibrium
• And for equilibrium reaction the value of ∆G is zero.
• So it is true

• Option 2 says ∆G is positive for a spontaneous reaction .
• But for a spontaneous reaction value of  ∆G is negative.
• So it is wrong

• Option 3 says ∆G is negative for a spontaneous reaction .
• It is true. 

• Option 4 says  ∆G is positive for a non-spontaneous reaction .
• It is true. 

Conclusion :   

∆G is positive for a spontaneous reaction - the statement is incorrect.

so the correct option is 2

at constant T

\(dG=VdP\)

\(\because\) for \(H_2O\) volume will be almost constant on increasing pressure.

\(\therefore \Delta G =V(\Delta P)\)

\(\Delta G =V(P_2-P-1)=5 \times 18\times 10^{-6}(101-1)\times 10^4 \, \text{Joule} =5 \times 18\times 10^{-1}\times 10^2=900 \, \text{Joule}\)

Concept:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The nonavailable energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

Thus,

\(\Delta G = \Delta H - T\Delta S\)

\(dG = dq - d{q_{rev}}\)

• Gibbs free energy is denoted by ΔG and have the units J/mol.

Explanation:

\(\begin{array}{l} G = \;H - TS\\ \;or,\;dG = dH - TdS - SdT\\ \;when\;temperature\;and\;pressure\;is\;kept\;constant,\\ \;dH = dq\;and\;dT = 0\\ \;So,\;dS = \frac{{d{q_{rev}}\;}}{T}\;\\ or,\;dG = dq - d{q_{rev}} \end{array}\)

As \( dq > dq_{rev}\) in an irreversible process,

\(dG < 0\) for irreversible processes.

As all irreversible processes are spontaneous, \(dG < 0\) for spontaneous processes at constant temp and pressure.

Hence, ΔG for a spontaneous process at constant pressure and temperature is ΔG < 0.

Important Points

• Note that if the forward reaction is spontaneous and irreversible, the Gibbs free energy is negative.
• The backward reaction will have ΔG > 0 and will be non-spontaneous.
• ΔG = 0 at equillibrium ,i.e. reversible process.

Concept:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The nonavailable energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

Thus,

\(\Delta G = \Delta H - T\Delta S\)

\(dG = dq - d{q_{rev}}\)

• Gibbs free energy is denoted by ΔG and have the units J/mol.

Explanation:

\(\begin{array}{l} G = \;H - TS\\ \;or,\;dG = dH - TdS - SdT\\ \;when\;temperature\;and\;pressure\;is\;kept\;constant,\\ \;dH = dq\;and\;dT = 0\\ \;So,\;dS = \frac{{d{q_{rev}}\;}}{T}\;\\ or,\;dG = dq - d{q_{rev}} \end{array}\)

As \( dq > dq_{rev}\) in an irreversible process,

\(dG < 0\) for irreversible processes.

As all irreversible processes are spontaneous, \(dG < 0\) for spontaneous processes at constant temp and pressure.

Hence, ΔG for a spontaneous process at constant pressure and temperature is ΔG < 0.

Important Points

• Note that if the forward reaction is spontaneous and irreversible, the Gibbs free energy is negative.
• The backward reaction will have ΔG > 0 and will be non-spontaneous.
• ΔG = 0 at equillibrium ,i.e. reversible process.

Concept:

• ΔG, or Gibbs free energy change, determines the spontaneity of a reaction. A negative ΔG indicates a spontaneous reaction.

• A catalyst speeds up the reaction by lowering the activation energy, but it does not change the overall Gibbs free energy change (ΔG) of the reaction.

• The Gibbs free energy change (ΔG) is a state function, which means it depends only on the initial and final states of the system, not on the path taken or the presence of a catalyst.

• Therefore, the value of ΔG for a reaction remains the same regardless of whether a catalyst is present.

Explanation:

1. Given:

   • ΔG for a reaction without a catalyst = x

   • ΔG for the same reaction with a catalyst = y

2. Since a catalyst does not alter the ΔG of a reaction:

   • x = y

3. Expressing the relationship using the options given:

   • -x = -y

Conclusion:

The correct relation between x and y, given the options provided, is: None of these.

Correct answer: -6.06)

Concept:

• A solution is created when two or more components mix homogeneously to form a single phase. 
• Most real gases behave like ideal gases at standard temperature and pressure.
• This allows us to combine our knowledge of ideal systems and solutions with standard state thermodynamics in order to derive a set of equations that quantitatively describe the effect that mixing has on a given gas-phase solution’s thermodynamic quantities.
• The Gibbs free energy of a mixture is defined as G=\(\sum_{j}^{}\mu_j n _j\) where μj is the chemical potential of species j, and it is temperature and pressure dependent, and n_j is the number of moles of species j.

Explanation:

• The expression of \(\Delta _{mix}G\)

\(\Delta G = RT \sum_{j}^{}n_j \ln x_j\)

\(\Delta _{mix}G = nRT(x_{1}lnx_{1} + x_{2}lnx_{2} + x_{3}lnx_{3})\)

• Here, x₁= 1/6; x₂=3/6; x₃= 2/6

\(\Delta _{mix}G/RT = 6 mol \times (\frac{1}{6}ln\frac{1}{6} +\frac{3}{6}ln\frac{3}{6} +\frac{2}{6}ln\frac{2}{6}))\)

\(\Delta _{mix}G = \) -6.06 J

Conclusion:

Thus, the value of ΔGmax is -6.06J.

Additional Information

CONCEPT:

Gibbs Free Energy (ΔG) and Spontaneity

• Gibbs free energy change (ΔG) is a criterion for spontaneity at constant temperature and pressure.
• If ΔG is negative (ΔG < 0), the reaction is spontaneous.
• If ΔG is positive (ΔG > 0), the reaction is non-spontaneous.
• If ΔG is zero (ΔG = 0), the reaction is at equilibrium (reversible reaction).

Explantion:-

• 1) ΔG is negative for a spontaneous reaction:
  This statement is correct. A negative ΔG indicates a spontaneous reaction.
• 2) ΔG is positive for a spontaneous reaction:
  This statement is incorrect. A positive ΔG indicates a non-spontaneous reaction.
• 3) ΔG is zero for a reversible reaction:
  This statement is correct. ΔG = 0 indicates the reaction is at equilibrium and reversible.
• 4) ΔG is positive for a non-spontaneous reaction:
  This statement is correct. A positive ΔG indicates a non-spontaneous reaction.

Therefore, the incorrect statement is: 2) ΔG is positive for a spontaneous reaction

Concept:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The nonavailable energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

Thus,

\(\Delta G = \Delta H - T\Delta S\)

\(dG = dq - d{q_{rev}}\)

• Gibbs free energy is denoted by ΔG and have the units J/mol.

Explanation:

\(\begin{array}{l} G = \;H - TS\\ \;or,\;dG = dH - TdS - SdT\\ \;when\;temperature\;and\;pressure\;is\;kept\;constant,\\ \;dH = dq\;and\;dT = 0\\ \;So,\;dS = \frac{{d{q_{rev}}\;}}{T}\;\\ or,\;dG = dq - d{q_{rev}} \end{array}\)

As \( dq > dq_{rev}\) in an irreversible process,

\(dG < 0\) for irreversible processes.

As all irreversible processes are spontaneous, \(dG < 0\) for spontaneous processes at constant temp and pressure.

Hence, ΔG for a spontaneous process at constant pressure and temperature is ΔG < 0.

Important Points

• Note that if the forward reaction is spontaneous and irreversible, the Gibbs free energy is negative.
• The backward reaction will have ΔG > 0 and will be non-spontaneous.
• ΔG = 0 at equillibrium ,i.e. reversible process.

Concept:

• The decrease in free energy is actually the amount of maximum work done by the system excluding the expansion work done when temp and pressure are kept constant.
• Free energy of a system is the difference in energy at the initial state and the equilibrium state energy.
• This free energy can be used to do external work.
• The nonavailable energy is the equilibrium state energy and is given by T × S, where T = temperature and S = Entropy.

Thus,

\(\Delta G = \Delta H - T\Delta S\)

\(dG = dq - d{q_{rev}}\)

• Gibbs free energy is denoted by ΔG and have the units J/mol.

Explanation:

\(\begin{array}{l} G = \;H - TS\\ \;or,\;dG = dH - TdS - SdT\\ \;when\;temperature\;and\;pressure\;is\;kept\;constant,\\ \;dH = dq\;and\;dT = 0\\ \;So,\;dS = \frac{{d{q_{rev}}\;}}{T}\;\\ or,\;dG = dq - d{q_{rev}} \end{array}\)

As \( dq > dq_{rev}\) in an irreversible process,

\(dG < 0\) for irreversible processes.

As all irreversible processes are spontaneous, \(dG < 0\) for spontaneous processes at constant temp and pressure.

Hence, ΔG for a spontaneous process at constant pressure and temperature is ΔG < 0.

Important Points

• Note that if the forward reaction is spontaneous and irreversible, the Gibbs free energy is negative.
• The backward reaction will have ΔG > 0 and will be non-spontaneous.
• ΔG = 0 at equillibrium ,i.e. reversible process.