When the oxide of generic metal M is heated at 25.0 °C, only a negligible amount of M is produced. MO2(s)<-->M(s)+O2(g) DeltaS= 287.5 kJ/mol When this reaction is coupled to the conversion of graphite to carbon dioxide, it becomes spontaneous. What is the chemical equation of this coupled process? Show that the reaction is in equilibrium, include physical states, and represent graphite as C(s). MO2(s)+C(s)<-->M(s)+CO2(g) What is the thermodynamic equilbrium constant for the coupled reaction?
Didn't I do this for you last week? As I remember you didn't understand my explanation. Or am I wrong?
It's the first time I ask this question on here actually.
Will you check that dS = -287.5? I may have it mixed up with another problem but I seem to remember that as being delta G or something like that but not dS. Thanks.
I looked at one of your description of one of the previous questions asked that are similar to mine and it made perfect sense. Thanks!
To determine the chemical equation of the coupled process and calculate the thermodynamic equilibrium constant, we need to consider the concept of Gibbs free energy (ΔG) and the relationship with thermodynamic equilibrium.
The Gibbs free energy change (ΔG) at a given temperature is related to the equilibrium constant (K) of a chemical reaction through the equation:
ΔG = -RT ln(K)
Where:
- ΔG is the change in Gibbs free energy.
- R is the gas constant (8.314 J/(mol·K)).
- T is the temperature in Kelvin (K).
- ln represents the natural logarithm.
Let's start by analyzing the given equation:
MO2(s) + C(s) ⇌ M(s) + CO2(g)
We know from the information provided that the reaction:
MO2(s) ⇌ M(s) + 1/2 O2(g)
Has ΔS = 287.5 kJ/mol, indicating an increase in entropy. Therefore, the reaction is spontaneous.
To determine the equilibrium constant for the coupled reaction, we need to find the value of ΔG at equilibrium.
We can write the overall reaction as the sum of two reactions:
Reaction 1: MO2(s) ⇌ M(s) + 1/2 O2(g)
Reaction 2: C(s) + O2(g) ⇌ CO2(g)
The overall reaction is then the sum of the two reactions:
MO2(s) + C(s) ⇌ M(s) + CO2(g)
Now, let's calculate the value of ΔG for each reaction using the equation:
ΔG = ΔH - TΔS
For Reaction 1:
ΔS1 = +287.5 kJ/mol (from the information given)
ΔG1 = ΔH1 - TΔS1
Since ΔG1 is negligible (as stated in the question), we assume ΔH1 is close to zero. Hence, the term - TΔS1 can be neglected.
For Reaction 2:
The conversion of graphite to carbon dioxide is a well-known reaction with a known value of ΔG. At 25.0°C, the value of ΔG for this reaction is -393.5 kJ/mol.
Next, we add the ΔG values for both reactions to obtain the overall ΔG for the coupled reaction:
ΔG = ΔG1 + ΔG2
Since ΔG1 is negligible, the overall ΔG is approximately equal to the value of ΔG for Reaction 2:
ΔG ≈ ΔG2 = -393.5 kJ/mol
Now, we can calculate the equilibrium constant (K) using the equation:
ΔG = -RT ln(K)
K = e^(-ΔG/RT)
Plugging in the values:
ΔG = -(-393.5 × 10^3 J/mol) = 393.5 × 10^3 J/mol
R = 8.314 J/(mol·K)
T = 25.0 + 273.15 K = 298.15 K
K = e^(-393.5 × 10^3 / (8.314 × 298.15))
Using a calculator, we can find that the equilibrium constant (K) for the coupled reaction is approximately 1.095 × 10^64.
Therefore, the chemical equation for the coupled process is:
MO2(s) + C(s) ⇌ M(s) + CO2(g)
The reaction is at equilibrium, and the thermodynamic equilibrium constant is approximately 1.095 × 10^64.