Calculate Gibbs Free Energy of Mixing 0.2g Polystyrene
'/%3E%3Ccircle cx='48' cy='39' r='19' fill='%23f2c9a5'/%3E%3Cpath d='M27 35c3-16 39-17 42 2-8-8-27-9-42-2z' fill='%23374151'/%3E%3Cpath d='M21 86c5-24 49-28 56 0z' fill='%232563eb'/%3E%3Ccircle cx='41' cy='41' r='2' fill='%23111827'/%3E%3Ccircle cx='55' cy='41' r='2' fill='%23111827'/%3E%3Cpath d='M42 52c4 3 9 3 13 0' stroke='%2392400e' stroke-width='3' fill='none' stroke-linecap='round'/%3E%3C/svg%3E)
Reviewed by Calculator Editorial Team
Calculating the Gibbs free energy of mixing for 0.2g of polystyrene involves understanding the thermodynamic properties of polymer solutions. This calculation helps predict the spontaneity of mixing processes and is essential in polymer science and materials engineering.
Introduction
The Gibbs free energy of mixing (ΔGmix) is a fundamental thermodynamic property that describes the change in free energy when two substances are mixed. For polymers like polystyrene, this calculation helps understand the behavior of polymer solutions and blends.
In this guide, we'll walk through the calculation for 0.2g of polystyrene, explain the formula, and discuss how to interpret the results.
Gibbs Free Energy Formula
The Gibbs free energy of mixing can be calculated using the following formula:
Gibbs Free Energy of Mixing Formula
ΔGmix = RT Σ (xi ln xi)
Where:
- ΔGmix = Gibbs free energy of mixing (J)
- R = Universal gas constant (8.314 J/mol·K)
- T = Absolute temperature (K)
- xi = Mole fraction of component i
For a binary mixture, this simplifies to:
Binary Mixture Simplified Formula
ΔGmix = RT (x1 ln x1 + x2 ln x2)
Calculation Example
Let's calculate the Gibbs free energy of mixing for 0.2g of polystyrene in a binary mixture with another polymer.
Example Scenario
Assume we have 0.2g of polystyrene (Mw = 100,000 g/mol) mixed with 0.8g of another polymer (Mw = 50,000 g/mol) at 298K.
Step 1: Calculate the mole fractions
Mole Fraction Calculation
n1 = mass1 / Mw1 = 0.2g / 100,000 g/mol = 2 × 10-6 mol
n2 = mass2 / Mw2 = 0.8g / 50,000 g/mol = 1.6 × 10-5 mol
ntotal = n1 + n2 = 1.8 × 10-5 mol
x1 = n1 / ntotal = 0.111
x2 = n2 / ntotal = 0.889
Step 2: Calculate ΔGmix
Gibbs Free Energy Calculation
ΔGmix = (8.314 J/mol·K)(298 K) [0.111 ln(0.111) + 0.889 ln(0.889)]
ΔGmix ≈ (8.314 × 298) [0.111 × (-2.18) + 0.889 × (-0.123)]
ΔGmix ≈ 2494 [-0.244 + -0.109] ≈ 2494 × -0.353 ≈ -882 J
The negative value indicates that the mixing process is spontaneous under these conditions.
Interpreting Results
The Gibbs free energy of mixing provides several important insights:
- Spontaneity: A negative ΔGmix indicates a spontaneous process
- Energy Changes: The magnitude shows the energy available for work
- Miscibility: Large negative values suggest good miscibility
For our example, the negative value confirms that mixing polystyrene with the other polymer is thermodynamically favorable at 298K.
Frequently Asked Questions
What is the Gibbs free energy of mixing?
The Gibbs free energy of mixing is a thermodynamic property that describes the change in free energy when two substances are mixed. It helps predict the spontaneity of mixing processes.
How do I calculate the Gibbs free energy of mixing?
Use the formula ΔGmix = RT Σ (xi ln xi) where R is the gas constant, T is temperature, and xi are mole fractions.
What does a negative Gibbs free energy mean?
A negative Gibbs free energy indicates that the process is spontaneous and will occur without external energy input.