Using the data in this table of the thermodynamic quantities for selected substances and given the pressures listed, calculate ƒ¢G at 25�‹C for each of the following reactions
(a) N2(g) + 3 H2(g) �¨ 2 NH3(g)
PN2 = 2.0 atm, PH2 = 5.4 atm, PNH3 = 2.2 atm
how do i calculatethis ?
To calculate ΔG for the reaction N2(g) + 3 H2(g) → 2 NH3(g), you will need to use the equation:
ΔG = ΣnΔGf(products) - ΣnΔGf(reactants)
where:
ΔG = standard Gibbs free energy change for the reaction
n = stoichiometric coefficient of each species in the reaction
ΔGf = standard Gibbs free energy of formation for each species
Step-by-step calculation:
1. Identify the standard Gibbs free energy of formation for each species involved in the reaction from the given data table. Let's assume the values are as follows:
ΔGf(N2) = x kJ/mol
ΔGf(H2) = y kJ/mol
ΔGf(NH3) = z kJ/mol
2. Substitute the values into the equation:
ΔG = (2 * ΔGf(NH3)) - (1 * ΔGf(N2) + 3 * ΔGf(H2))
= (2 * z) - (x + 3y)
3. Calculate the values of ΔG using the given pressures:
Using P = ΔG/RT, where:
P = pressure (in atm)
ΔG = Gibbs free energy change
R = ideal gas constant (0.08206 L.atm/mol.K)
T = temperature (in Kelvin)
For N2:
PN2 = 2.0 atm
ΔG(N2) = (2.0 * 0.08206 * 298) = 48.7828 J
For H2:
PH2 = 5.4 atm
ΔG(H2) = (5.4 * 0.08206 * 298) = 131.64164 J
For NH3:
PNH3 = 2.2 atm
ΔG(NH3) = (2.2 * 0.08206 * 298) = 64.77836 J
4. Substitute the calculated ΔG values into the equation:
ΔG = (2 * 64.77836) - (48.7828 + 3 * 131.64164)
= - 334.16168 J
5. Convert the value of ΔG to kilojoules (kJ):
ΔG = -334.16168 J / 1000 = -0.3342 kJ
Therefore, the ΔG for the reaction N2(g) + 3 H2(g) → 2 NH3(g) at 25°C is approximately -0.3342 kJ.
To calculate the standard free energy change (ΔG°) for a reaction using the given pressures, you need to use the following equation:
ΔG° = ΣnΔG°f(products) - ΣnΔG°f(reactants)
Here's how you can calculate it step by step using the data in the table:
1. Identify the standard free energy of formation (ΔG°f) values for each species involved in the reaction. The table should provide the values for N2(g), H2(g), and NH3(g).
2. Write down the balanced chemical equation: N2(g) + 3 H2(g) ↽─→ 2 NH3(g)
3. Calculate the moles of each species present based on their pressures and the ideal gas equation (PV = nRT). Recall that one mole occupies a volume of 22.4 liters at standard temperature and pressure (STP), which is 0°C and 1 atm.
- For N2(g): n(N2) = PV/RT = (2.0 atm)(22.4 L)/(0.0821 L.atm/mol.K)(273 K + 25°C) = X moles
- For H2(g): n(H2) = PV/RT = (5.4 atm)(22.4 L)/(0.0821 L.atm/mol.K)(273 K + 25°C) = Y moles
- For NH3(g): n(NH3) = PV/RT = (2.2 atm)(22.4 L)/(0.0821 L.atm/mol.K)(273 K + 25°C) = Z moles
4. Look up the ΔG°f values for each species involved in the reaction in the table.
- ΔG°f(N2(g)) = A kJ/mol
- ΔG°f(H2(g)) = B kJ/mol
- ΔG°f(NH3(g)) = C kJ/mol
5. Substitute the values into the equation for ΔG°:
ΔG° = (2 ΔG°f(NH3)) - (ΔG°f(N2) + 3 ΔG°f(H2))
ΔG° = (2C kJ/mol) - (A kJ/mol + 3B kJ/mol)
6. Calculate the numerical value of ΔG° using the given ΔG°f values.
ΔG° = (2C kJ/mol) - (A kJ/mol + 3B kJ/mol) = XYZ
Note: Make sure to convert the temperatures to Kelvin when using the ideal gas equation and pay attention to the units of the ΔG°f values to ensure consistency. Also, keep in mind that the values in the table may be given in kJ/mol or J/mol, so you may need to make appropriate unit conversions.