# Analysis Gibbs free energy of formation also

Analysis of Straight-Chain Alkane Thermodynamic and Physical PropertiesGibbs free energy of formation is the total difference in free energy of the elements that make up a substance and the substance itself.  To find the values of Gibbs free energy of formation, coefficients, which change depending on the substance, and temperature are used as in the following equation1:?G_f=A+BT+CT^2 (1)Gibbs free energy of formation is used to calculate the Gibbs free energy of a reaction, which defines the favorability of a reaction to occur.  The equation is expressed as1:?G_r=?G_(f,products)-?G_(f,reactants) (2)The table below shows the Gibbs free energy of formation for 12 different straight-chain alkanes.  As the data shows, as the number of carbons in an alkane increase, the Gibbs free energy of formation also increases.  When Gibbs free energy is below zero, the reaction is favorable and likely to happen.  When it is at zero, the reaction is in equilibrium, and when it is greater than zero, the reaction is unlikely to happen unless certain conditions are met1.  Essentially, a straight-chain alkane with more than 6 carbons is unlikely to form, since they will require energy to be formed, unlike the straight-chain alkanes with 6 or less carbons.Table 1: Gibb’s free energy of formation of straight-chain alkanes at 298K1 Number of Carbons ?G_f at 298k (kJ/mol)Methane 1 -50.84Ethane 2 -36.86Propane 3 -23.46n-Butane 4 -17.15n-Pentane 5 -8.37n-Hexane 6 -0.25n-Heptane 7 7.99n-Octane 8 16.4n-Nonane 9 24.81n-Decane 10 33.22n-Undecane 11 41.59n-Dodecane 12 50.04The plot with the Gibbs free energy of formation, Figure 1, shows the trend of increasing energy needed to form an alkane.  An alkane with more than 6 carbons requires energy to be formed, making it unlikely to be spontaneously formed.  An alkane with 6 carbons or less gives off energy when formed, meaning it can be formed spontaneously1.   Figure 1: Gibbs free energy of formation at 298K for straight-chain alkanes.  Data taken from Rules of Thumb for Chemical Engineers1.Heat capacity is the amount of energy, in joules, that it takes to raise the temperature of a mole of a substance one degree, in Kelvin5.  As shown in Table 2, the heat capacity of a straight-chain carbon increases as the number of carbons increase.  The reason for this is because the molecule is larger, has more bonds, and therefore will require more energy to heat each atom5.Table 2: Heat Capacity at 298K5Alkane Number of Carbons C_P (J/mol?K)Methane 1 35.69Ethane 2 52.47Propane 3 73.60n-Butane 4 98.49n-Pentane 5 120.0n-Hexane 6 142.6n-Heptane 7 165.2n-Octane 8 187.8n-Nonane 9 210.4n-Decane 10 233.1n-Undecane 11 267.1n-Dodecane 12 288.3The plot representing heat capacity, Figure 2, shows a trend with the amount of required energy to heat the alkane increasing linearly with the number of carbons in the alkane.  Figure 2 shows a positive relationship between the heat capacity and number of carbons, meaning that, the more carbons there are in a straight-chain alkane, the more energy is needed to raise the temperature of one mole5. Figure 2: Heat capacity of straight-chain alkanes at 298K.  Data from Perry’s Chemical Engineers’ Handbook5.Enthalpy of vaporization is the amount of energy needed, in kilojoules, to vaporize a substance without changing the temperature of the surroundings, for one mole4.  Table 3 shows that, relative to the heat capacity, the amount energy needed to do so is minimal, since the surrounding must stay constant.  Table 3: Enthalpies of vaporization of straight-chain alkanes at respective T¬¬min values4Alkane Number of Carbons Tmin (K) ?H_vap at Tmin ×10-7 (kJ/mol)Methane 1 90.69 0.8724Ethane 2 90.35 1.7879Propane 3 85.47 2.4787n-Butane 4 134.86 2.8684n-Pentane 5 143.42 3.3968n-Hexane 6 177.83 3.7647n-Heptane 7 182.57 4.2629n-Octane 8 216.38 4.5898n-Nonane 9 219.66 5.0545n-Decane 10 243.51 5.4168n-Undecane 11 247.57 5.9240n-Dodecane 12 263.57 6.2802Since enthalpy of vaporization is the amount of energy, in kilojoules, to take one mole of a substance from a liquid to a vapor without changing the surrounding temperature, the trend on a plot should be like the trend on heat capacity.  Figure 3 shows how the enthalpy of vaporization increases along with the number of carbons in a straight-chain alkane.  The value of enthalpy is small to keep the surrounding the same, but enough for the phase change to occur4. Figure 3: Enthalpy of Vaporization for straight-chain alkanes at respective Tmin.  Data from Research of the National Bureau Standards4.Viscosity is a fluids resistance to flow, due to internal friction, measured in Pa?s6. Both liquids and gases have viscosity.  Table 4 shows that larger alkanes have a lower viscosity, and therefore flow better because of the lower internal friction.Table 4: Viscosities of straight-chain alkanes at room temperature3Alkane Number of Carbons ? ×10-7(Pa?s)Methane 1 112.1Ethane 2 94.26Propane 3 83.07n-Butane 4 77.16n-Pentane 5 70.79n-Hexane 6 65.01n-Heptane 7 57.60n-Octane 8 54.77n-Nonane 9 48.84n-Decane 10 47.38n-Undecane 11 48.66n-Dodecane 12 46.61Figure 4 shows the inverse relationship between viscosity and the number of carbons in a straight-chain alkane.  This relationship is inverse because there is less internal friction in larger atoms with more bonds because there are less intermolecular forces attractions6. Figure 4: Viscosity of straight-chain alkanes at 298K.  Data from Viscosity of Selected n-alkane Liquids3.Information gathered from Knovel, and Google Scholar.?