Estimate the value of the equilibrium constant at 550 K for each of the following reactions.
1) 2CO(g)+O2(g)--->2CO2(g)
2) 2H2S(g)--->2H2(g)+S2(g)
i used the equation K=e^(delta G/RT) for the first problem and got K=1.40*10^-49 but it was wrong. Is there a different equation i need to use?
To estimate the value of the equilibrium constant at a certain temperature, you need to consider the Gibbs Free Energy change (ΔG) for the reaction. The equation K = e^(ΔG/RT) is the correct equation to use, where R is the gas constant and T is the temperature in Kelvin.
However, care must be taken with the signs and units of ΔG. The ΔG value in the equation should correspond to the products minus the reactants. Also, the units of ΔG must be in joules (J), not kilojoules (kJ).
Let's calculate the correct values for the two reactions you provided:
1) The reaction is 2CO(g) + O2(g) ---> 2CO2(g)
To determine the ΔG value at 550 K, you need to know the ΔG value at standard conditions (ΔG^o, usually given in kJ/mol) and the standard Gibb's free energy change of formation (ΔGf^o) for each compound involved in the reaction.
For this equation, let's assume the given ΔGf^o values are as follows:
ΔGf^o(CO2) = -394 kJ/mol
ΔGf^o(CO) = -283 kJ/mol
ΔGf^o(O2) = 0 kJ/mol
First, calculate the ΔG value for the reaction at standard conditions:
ΔG^o = (2 × ΔGf^o(CO2)) - (2 × ΔGf^o(CO)) - (1 × ΔGf^o(O2))
= (2 × (-394 kJ/mol)) - (2 × (-283 kJ/mol)) - (1 × 0 kJ/mol)
= -196 kJ/mol
Next, convert the ΔG value from kJ/mol to J/mol:
ΔG = ΔG^o × 1000
= -196 kJ/mol × 1000
= -196000 J/mol
Finally, substitute the values into the equilibrium constant equation at 550 K (convert K to Kelvin):
K = e^(ΔG/RT)
= e^(-196000 J/mol / (8.314 J/(mol·K) × 550 K))
≈ 0 (since the exponent is very large and negative)
Based on the value of K being approximately 0, we can infer that the equilibrium heavily favors the reactants at 550 K for the reaction 2CO(g) + O2(g) ---> 2CO2(g).
2) The reaction is 2H2S(g) ---> 2H2(g) + S2(g)
Following a similar process as above, calculate the ΔG value at standard conditions and convert it to J/mol. Then, substitute the values into the equilibrium constant equation at 550 K to estimate K for this reaction.
I would try the following:
Determine delta Go at 25 C for the reaction, calculate K at 25 C, then use the van't Hoff equation to convert from K at 298 to K at 550 K.