# Chemical equilibrium: Enthelpies and equilibrium contsants

• Coastal
In summary, the equilibrium constants for CO2 decomposition change depending on temperature. At 1500K, the equilibrium constants are 5.5 x 10-9 J/K mol and at 3000K, the equilibrium constants are 4.03 x 10-1 J/K mol.
Coastal

## Homework Statement

For the system 2 CO2 = 2 CO + O2, ∆H= 510 kJ
the percentage decomposition of CO2 changes w/ temperature as follows.
Temp, K...% Decomposition
1500...0.048
2500...17.6
3000...54.8
Calculate the equilibrium constants, plot lnK vs. 1/T. In the graph, find the slope and confirm ∆H. Also, using average bond enthalpies, calculate ∆H(it should come out the same for both approaches).

## Homework Equations

1.) Slope = ∆H / R
2.) R(constant) = 8.314 J/k-mol
3.) ∆Hrxn = Sum of bond enthalpies of broken bonds - Sum of bond enthalpies of formed bonds

## The Attempt at a Solution

I started by calculating K at each temperature. We also did this part in class so I know all the K's are correct.
K at 1500=5.5 x 10-9
K at 2500=4.01 x 10-1
K at 3000=4.03 x 10

I plugged all these #s into the calculator to figure out lnK and 1/T. I plotted them on a graph and got a straight line with a negative slope. This threw me because lnK vs. 1/T should not be straight because this isn't a first order reaction. The slope was something like -40,000, which would then be multiplied by the constant R and ∆H came out to be -330,000(wrong).

Then I tried the 2nd approach. Using equation #3 above, I got ∆H= (4x799)-((2x1072)+495). I'm well aware of how to draw Lewis structures, and am positive I got all the bond enthalpies right and ∆H came out to be 557kJ, which is much closer to the 510kJ given in the problem description.

Where I am stuck is getting ∆H through the graph. Supposedly ∆H=Slope x R(constant)... but with such a small different in 1/T's or the ∆x value or the denominator in the rise/run slope formula, the slope always comes out enormous. How am I supposed to get ∆H for the first method? I looked over the numbers many times and they all seem correct.

I have a feeling you’re plotting your data in joules and comparing it to an answer in kilojoules. Just a hunch.

## 1. What is chemical equilibrium?

Chemical equilibrium is the state in which the forward and reverse reactions of a chemical reaction occur at equal rates, resulting in no net change in the concentrations of reactants and products.

## 2. What is the role of enthalpy in chemical equilibrium?

Enthalpy is the measure of the total energy of a system. In chemical equilibrium, the enthalpy change of the forward and reverse reactions must be equal in order for the system to remain at equilibrium.

## 3. How is equilibrium constant calculated?

The equilibrium constant (K) is calculated by taking the ratio of the concentrations of products to reactants, with each concentration raised to the power of its respective coefficient in the balanced chemical equation. K can also be calculated using the partial pressures of gases in the reaction.

## 4. How does temperature affect equilibrium constants?

According to Le Chatelier's principle, an increase in temperature will favor the endothermic reaction and decrease the equilibrium constant, while a decrease in temperature will favor the exothermic reaction and increase the equilibrium constant.

## 5. Can equilibrium constants be altered?

Equilibrium constants are characteristic of a specific chemical reaction at a given temperature. They can be altered by changing the temperature, pressure, or concentrations of reactants and products. However, the value of K will always remain the same for a specific reaction at a specific temperature under ideal conditions.

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