Consider the evaporation of methanol at 25.0 C:
CH3OH(l)--->CH3OH(g)
Delta G= 4.3 kJ
Find Delta G at 25.0 C under the following nonstandard conditions:
Pressure of CH3OH= 108.0 mmHg.
To find Delta G at 25.0 C under the given nonstandard conditions, we need to use the equation:
Delta G = Delta G standard + RT ln(Q)
Where:
- Delta G is the change in Gibbs free energy
- Delta G standard is the standard Gibbs free energy change at standard conditions
- R is the gas constant (8.314 J/(mol*K) or 0.008314 kJ/(mol*K))
- T is the temperature in Kelvin
- Q is the reaction quotient
First, let's convert the pressure from millimeters of mercury (mmHg) to atmospheres (atm), since the standard conditions use atm.
1 atm = 760 mmHg
So, the pressure of CH3OH in atm is:
108.0 mmHg / 760 mmHg/atm = 0.14211 atm
Next, we need to calculate the reaction quotient Q. The reaction quotient is the ratio of the concentrations (or pressures) of the products and reactants at nonstandard conditions.
Since the reaction is from liquid (CH3OH(l)) to gas (CH3OH(g)), the concentration of CH3OH(l) is essentially 1 (since it is the pure substance). The concentration of CH3OH(g) can be calculated using the ideal gas law.
PV = nRT
Where:
- P is the pressure of CH3OH(g)
- V is the molar volume of the gas (we assume 22.4 L/mol at standard temperature and pressure)
- n is the number of moles of CH3OH(g)
- R is the gas constant
- T is the temperature in Kelvin
Solving for n, we get:
n = PV / RT
Using the given pressure of CH3OH(g) (0.14211 atm), the molar volume (22.4 L/mol), the gas constant (0.008314 kJ/(mol*K)), and the temperature (25.0 C = 25.0 + 273.15 K = 298.15 K), we can calculate n.
n = (0.14211 atm) * (22.4 L/mol) / (0.008314 kJ/(mol*K) * 298.15 K) = 9.72 mol
Now that we know the number of moles, we can calculate Q.
Q = (concentration of CH3OH(g)) / (concentration of CH3OH(l))
= n(CH3OH(g)) / n(CH3OH(l))
= 9.72 mol / 1 mol
= 9.72
Now, we can substitute the values into the equation:
Delta G = Delta G standard + RT ln(Q)
Given that Delta G standard = 4.3 kJ, R = 0.008314 kJ/(mol*K), and T = 298.15 K, we can calculate Delta G:
Delta G = 4.3 kJ + (0.008314 kJ/(mol*K) * 298.15 K) * ln(9.72)
Solving this expression will give you the value of Delta G at 25.0 C under the given nonstandard conditions.