Consider the reaction: 2 NO(g)+O2(g) ⇌2 NO2(g) The following data show the equilibrium constant

step 1 Okay, so from the given table in the question, we make a new table. So we invert the temperature

Consider the reaction: 2 NO(g)+O2(g) ⇌2 NO2(g) The following...

Consider the reaction: $$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$ The following data show the equilibrium constant for this reaction measured at several different temperatures. Use the data to find $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}$ for the reaction. $$\begin{array}{lc} \text { Temperature } & \boldsymbol{K}_{\mathbf{p}} \\ 170 \mathrm{~K} & 3.8 \times 10^{-3} \\ \hline 180 \mathrm{~K} & 0.34 \\ \hline 190 \mathrm{~K} & 18.4 \\ \hline 200 \mathrm{~K} & 681 \end{array}$$

Consider the reaction:
$$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g)$$
The following data show the equilibrium constant for this reaction measured at several different temperatures. Use the data to find $\Delta H_{\mathrm{rxn}}^{\circ}$ and $\Delta S_{\mathrm{rxn}}^{\circ}$ for the reaction.
$$\begin{array}{lc}
\text { Temperature } & \boldsymbol{K}_{\mathbf{p}} \\
170 \mathrm{~K} & 3.8 \times 10^{-3} \\
\hline 180 \mathrm{~K} & 0.34 \\
\hline 190 \mathrm{~K} & 18.4 \\
\hline 200 \mathrm{~K} & 681
\end{array}$$

Key Concepts

Linearization of Thermodynamic Data

By plotting ln(K) against 1/T, the data from experiments can be linearized, enabling the use of linear regression to determine the slope and intercept. These are directly related to the standard enthalpy (via the slope, -?H°/R) and the standard entropy (via the intercept, ?S°/R), making this method a powerful tool in analyzing temperature-dependent equilibrium data.

Gibbs Free Energy, Enthalpy, and Entropy Relationship

The relationship ?G° = -RT ln(K) = ?H° - T?S° connects the standard Gibbs free energy change with the standard enthalpy and entropy changes. This equation is fundamental in understanding how the spontaneity of a reaction and its equilibrium constant change with temperature under standard conditions.

van't Hoff Equation

The van't Hoff equation provides a relationship between the equilibrium constant and temperature. By expressing ln(K) as a linear function of 1/T, it allows us to extract thermodynamic parameters like the standard enthalpy change (?H°) from the slope and the standard entropy change (?S°) from the intercept, assuming these values remain constant over the temperature range considered.

Equilibrium Constant

The equilibrium constant quantifies the ratio of the concentrations or partial pressures of products to reactants at equilibrium. It is a central concept in chemical thermodynamics that helps determine the position of equilibrium and is a function of temperature for a given reaction.

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