For the reaction below, the thermodynamic equilibrium constant is K = 2.30×10−4 at 25 °C.
NH4CO2NH2(s) ⟶ 2 NH3(g) + CO2(g)
Suppose that 0.0156 moles of NH4CO2NH2, 0.0312 moles of NH3, and 0.0156 moles of CO2 are added to a 5.00 L container at 25 °C.
(a) What are Q and ΔrG (kJ mol−1) for the initial reaction mixture?
(NH3) = 0.0312 mols/5 L = approx 0.006
(CO2) = 0.0156 mols/5 L = approx 0.003
Note that concn NH4CO2NH2 doesn't matter since it doesn't appear in the Q expression.
NH4CO2NH2(s) ⟶ 2 NH3(g) + CO2(g)
dG = -RTlnQ
dG = -RTln(NH3)^2*(CO2)
Substitute and solve for Q and dG.
BTW, what does r stand for in delta r G?
Note that my calculations are approx. You need to recalculate all.
Also note that dG will be in joules and you will need to convert to kJ.
r stands for reaction! thanks for ur help
Oh, let me whip out my thermodynamic humor calculator! *beep boop beep* Ah, here we go:
For the equation NH4CO2NH2(s) ⟶ 2 NH3(g) + CO2(g), we can use the formula:
ΔrG = ΔrG° + RT ln(Q)
where ΔrG is the Gibbs free energy change, ΔrG° is the standard Gibbs free energy change, R is the gas constant, T is the temperature in Kelvin, and Q is the reaction quotient.
Now, to calculate Q, we can simply divide the molar amounts of the products by the molar amount of the reactant:
Q = [NH3]^2 * [CO2] / [NH4CO2NH2]
Substituting the given values:
Q = (0.0312 mol)^2 * (0.0156 mol) / (0.0156 mol) = 0.0312 mol
But wait! We need to convert this to Kelvin for the temperature. So, 25 °C = 298 K.
Now, plugging everything into the formula:
ΔrG = ΔrG° + (8.314 J/mol·K) * (298 K) * ln(0.0312 mol)
*clown honks* Oops, I misplaced a unit! But don't worry, I'll fix it right away. Let's convert the Joules to kilojoules, just for convenience:
ΔrG = ΔrG° + (8.314 J/mol·K * 0.001 kJ/J) * (298 K) * ln(0.0312 mol)
Now that's cleared up, you can plug your numbers into the equation and have a good laugh at the result. Enjoy!
To determine Q and ΔrG (kJ mol−1) for the initial reaction mixture, we need to calculate the reaction quotient (Q) and the standard Gibbs free energy change (ΔrG) using the given moles and the equilibrium constant (K).
The balanced chemical equation for the reaction is:
NH4CO2NH2(s) ⟶ 2 NH3(g) + CO2(g)
(a) Calculation of Q:
Q is calculated in the same way as K, but using the initial concentrations instead of the equilibrium concentrations.
Q = [NH3]² · [CO2] / [NH4CO2NH2]
The given moles of substance are:
[NH4CO2NH2] = 0.0156 moles
[NH3] = 0.0312 moles
[CO2] = 0.0156 moles
Plugging in the values:
Q = (0.0312)² · (0.0156) / (0.0156)
Q = 0.0624 · 0.0156 / 0.0156
Q = 0.0624
Therefore, Q = 0.0624.
(b) Calculation of ΔrG:
ΔrG is calculated using the equation:
ΔrG = ΔrG° + RT · ln(Q)
Where ΔrG° is the standard Gibbs free energy change, R is the ideal gas constant (8.314 J mol⁻¹ K⁻¹), T is the temperature in Kelvin (25 + 273 = 298 K), and ln(Q) is the natural logarithm of Q.
Given that K = 2.30×10⁻⁴ and R = 8.314 J mol⁻¹ K⁻¹, we need to convert ΔrG° from kJ to J:
ΔrG° = -RT · ln(K) = -8.314 J mol⁻¹ K⁻¹ · 298 K · ln(2.30×10⁻⁴)
ΔrG° = -8.314 J mol⁻¹ K⁻¹ · 298 K · (-8.682)
ΔrG° = 20,673.13 J mol⁻¹
Converting ΔrG° to kJ:
ΔrG° = 20,673.13 J mol⁻¹ / 1000 J/kJ = 20.67 kJ mol⁻¹
Now we can calculate ΔrG:
ΔrG = 20.67 kJ mol⁻¹ + 8.314 J mol⁻¹ K⁻¹ · 298 K · ln(0.0624)
ΔrG = 20.67 kJ mol⁻¹ + 8.314 J mol⁻¹ K⁻¹ · 298 K · (-2.776)
ΔrG = 20.67 kJ mol⁻¹ - 6,246.43 J mol⁻¹
ΔrG = 20.67 kJ mol⁻¹ - 6.246 kJ mol⁻¹
Therefore, ΔrG = 14.43 kJ mol⁻¹.
To calculate Q and ΔrG (Gibbs free energy change) for the initial reaction mixture, we need to use the concentrations of the reactants and products.
(a) Q is the reaction quotient, which is calculated using the concentrations of reactants and products. It is determined by comparing the molar concentrations of the reactants and products at a given point during the reaction. In this case, the balanced chemical equation is:
NH4CO2NH2(s) ⟶ 2 NH3(g) + CO2(g)
The coefficients in the balanced equation represent the stoichiometry of the reaction. Therefore, the Q can be calculated as follows:
Q = [NH3]^2 * [CO2]
Where [NH3] and [CO2] are the concentrations of NH3 and CO2 respectively. Since the concentration of NH4CO2NH2 is given as 0.0156 moles in a 5.00 L container, we need to convert it to concentration using the formula:
Concentration (M) = moles / volume (L)
Concentration of NH4CO2NH2 = 0.0156 moles / 5.00 L
Now, we know that the coefficient of NH4CO2NH2 in the balanced equation is 1. Therefore, the concentration of NH4CO2NH2 is 0.0156 moles / 5.00 L.
For the concentration of NH3, we have 0.0312 moles in a 5.00 L container, so the concentration is 0.0312 moles / 5.00 L.
The concentration of CO2 is given as 0.0156 moles in a 5.00 L container, so the concentration is 0.0156 moles / 5.00 L.
Plugging these values into the equation for Q:
Q = (0.0312/5)^2 * (0.0156/5)
Q = 2.4384 × 10^-4
(b) ΔrG is the change in Gibbs free energy (kJ/mol) for a reaction. It is related to the equilibrium constant (K) using the equation:
ΔrG = -RT * ln(K)
Where R is the gas constant (8.314 J/(mol K)), T is the temperature in Kelvin, and ln denotes the natural logarithm.
Given that the equilibrium constant (K) is 2.30 × 10^-4, and the temperature (T) is 25 °C (which is 298 Kelvin), we can calculate ΔrG:
ΔrG = - (8.314 J/(mol K)) * (298 K) * ln(2.30 × 10^-4 / 1)
Converting ΔrG from J/mol to kJ/mol:
ΔrG = - (8.314 J/(mol K)) * (298 K) * ln(2.30 × 10^-4 / 1) / 1000
This will give you the value of ΔrG in kJ/mol.