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Calculate Delta G Using The Following Information 2hno3

Reviewed by Calculator Editorial Team

Calculating delta G (ΔG) for the reaction 2HNO3 involves determining the Gibbs free energy change using standard thermodynamic data. This calculation is essential in chemical thermodynamics to assess reaction spontaneity and equilibrium conditions.

Introduction to Gibbs Free Energy

Gibbs free energy (ΔG) is a thermodynamic property that measures the maximum amount of reversible work that a system can perform at constant temperature and pressure. For a chemical reaction, ΔG determines whether the reaction is spontaneous (ΔG < 0) or non-spontaneous (ΔG > 0).

The standard Gibbs free energy change (ΔG°) is calculated using the standard enthalpy change (ΔH°) and the standard entropy change (ΔS°) of the reaction at standard conditions (25°C and 1 atm).

Gibbs Free Energy Formula

The standard Gibbs free energy change is calculated using the following formula:

ΔG° = ΔH° - TΔS°

Where:

  • ΔG° = Standard Gibbs free energy change (kJ/mol)
  • ΔH° = Standard enthalpy change (kJ/mol)
  • T = Temperature in Kelvin (K)
  • ΔS° = Standard entropy change (J/mol·K)

For non-standard conditions, the actual Gibbs free energy change (ΔG) can be calculated using the reaction quotient (Q) and the equilibrium constant (K):

ΔG = ΔG° + RT ln(Q)

Where:

  • R = Universal gas constant (8.314 J/mol·K)

Calculation Steps

  1. Determine the standard enthalpy change (ΔH°) for the reaction from thermodynamic tables or experimental data.
  2. Determine the standard entropy change (ΔS°) for the reaction from thermodynamic tables or experimental data.
  3. Convert the temperature from Celsius to Kelvin (T = °C + 273.15).
  4. Calculate ΔG° using the formula ΔG° = ΔH° - TΔS°.
  5. If calculating for non-standard conditions, determine the reaction quotient (Q) and calculate ΔG using ΔG = ΔG° + RT ln(Q).

Worked Example

Let's calculate ΔG° for the reaction 2HNO3 → H2O + NO2 + O2 using the following data:

  • ΔH° = -100 kJ/mol
  • ΔS° = -200 J/mol·K
  • Temperature = 25°C (298.15 K)

ΔG° = ΔH° - TΔS°

ΔG° = (-100 kJ/mol) - (298.15 K)(-200 J/mol·K)

Convert ΔS° to kJ/mol·K: -200 J/mol·K = -0.200 kJ/mol·K

ΔG° = -100 - (298.15)(-0.200)

ΔG° = -100 + 59.63

ΔG° = -40.37 kJ/mol

The negative value indicates the reaction is spontaneous under standard conditions.

Interpreting Results

The sign of ΔG determines the spontaneity of the reaction:

  • ΔG < 0: The reaction is spontaneous and will proceed as written.
  • ΔG > 0: The reaction is non-spontaneous and will not proceed as written.
  • ΔG = 0: The reaction is at equilibrium.

For the example calculation, ΔG° = -40.37 kJ/mol indicates the reaction is spontaneous under standard conditions.

FAQ

What is the difference between ΔG and ΔG°?

ΔG° refers to the standard Gibbs free energy change at standard conditions (25°C and 1 atm), while ΔG is the actual Gibbs free energy change at specific conditions.

How do I find ΔH° and ΔS° values?

ΔH° and ΔS° values can be found in thermodynamic tables, chemistry textbooks, or experimental data sources. For the reaction 2HNO3, these values are typically obtained from standard thermodynamic databases.

What units should I use for ΔH° and ΔS°?

ΔH° should be in kJ/mol, and ΔS° should be in J/mol·K. Convert ΔS° to kJ/mol·K by dividing by 1000 if necessary.