2. Methanol, CH3OH, is used as fuel in race cars. This liquid fuel can be synthesized
using the following process
C(s)+ ½ O2(g) + 2H2(g) CH3OH(l)
Calculate delta G using the deta Gf of the reaction. Calculate Kp. What is the relation
between the magnitude of delta G and Kp?
To calculate ΔG for the given reaction using the ΔGf values, we need to know the ΔGf values of the reactants and products involved in the reaction. The ΔGf values represent the standard Gibbs free energy change for the formation of one mole of the substance from its elements in their standard states.
Assuming we have the ΔGf values for C(s), O2(g), H2(g), and CH3OH(l), we can calculate ΔG using the following equation:
ΔG = ΣnΔGf(products) - ΣnΔGf(reactants)
In this particular reaction, we have:
Reactants:
C(s) (graphite) ΔGf = 0 kJ/mol
O2(g) ΔGf = 0 kJ/mol
H2(g) ΔGf = 0 kJ/mol
Products:
CH3OH(l) ΔGf = -166 kJ/mol (assumed value)
Therefore, plugging in these values into the equation, we get:
ΔG = (1 × -166 kJ/mol) - (1 × 0 kJ/mol) - (2 × 0 kJ/mol) - (½ × 0 kJ/mol)
= -166 kJ/mol
ΔG = -166 kJ/mol
Now, to calculate Kp (the equilibrium constant in terms of partial pressures), we need to know the balanced chemical equation and the stoichiometric coefficients of the reactants and products.
The balanced chemical equation is:
C(s) + ½ O2(g) + 2H2(g) → CH3OH(l)
From this equation, we can conclude that the stoichiometric coefficients are 1 for C(s), ½ for O2(g), 2 for H2(g), and 1 for CH3OH(l).
The expression for Kp is given by:
Kp = (P(CH3OH))^1 / (P(C))^1 × (P(O2))^0.5 × (P(H2))^2
Since methanol is a liquid, its partial pressure doesn't affect the equilibrium and is considered to be constant. Therefore, we can simplify the equation to:
Kp = (P(CH3OH))^1 / (P(C))^1 × (P(O2))^0.5 × (P(H2))^2
= (P(CH3OH))^1 / (P(C))^1 × (P(O2))^0.5
The relation between the magnitude of ΔG and Kp is given by the equation:
ΔG = -RT ln(Kp)
where R is the ideal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin.
From this relation, we can understand that a negative ΔG means the reaction is spontaneous and favored in the forward direction. For Kp, a value greater than 1 indicates that the products prevail at equilibrium.
Thus, in general, the magnitude of ΔG and Kp have an inverse relationship. If ΔG is more negative, Kp will be larger, indicating a greater preference for the formation of products.