Question
The dependence of the equilibrium constant of a reaction on temperature is given by the van't Hoff equation:$$\ln K=\frac{-\Delta H^{\circ}}{R T}+C$$where $C$ is a constant. The following table gives the equilibrium constant $\left(K_{P}\right)$ for the reaction at various temperatures.$$2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftarrows 2 \mathrm{NO}_{2}(g)$$$$\begin{array}{l|rrrrr}K_{P} & 138 & 5.12 & 0.436 & 0.0626 & 0.0130 \\\hline T(\mathrm{K}) & 600 & 700 &800 & 900 & 1000\end{array}$$Determine graphically the $\Delta H^{\circ}$ for the reaction.
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The values are: For $\ln K_{P}$, the corresponding values are 4.93, 1.63, -0.83, -2.77, and -4.34. For $1/T$, the corresponding values are 0.00167, 0.00143, 0.00125, 0.00111, and 0.00100. Show more…
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The dependence of the equilibrium constant of a reaction on temperature is given by the van't Hoff equation: $$ \ln K=-\frac{\Delta H^{\circ}}{R T}+C $$ where $C$ is a constant. The following table gives the equilibrium constant $\left(K_{P}\right)$ for the reaction at various temperatures $$ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}_{2}(g) $$ $$\begin{array}{llllll} K_{p} & 138 & 5.12 & 0.436 & 0.0626 & 0.0130 \\ T(\mathrm{K}) & 600 & 700 & 800 & 900 & 1000 \end{array}$$
The van't Hoff equation $$d \ln K=\frac{\Delta H^{0}}{\bar{R} T^{2}} d T_{p^{0}}$$ relates the chemical equilibrium constant $K$ to the enthalpy of reaction $\Delta H^{0} .$ From the value of $K$ in Table A. 11 for the dissociation of hydrogen at $2000 \mathrm{~K}$ and the value of $\Delta H^{0}$ calculated from Table A.9 at $2000 \mathrm{~K}$, use the van't Hoff equation to predict the equilibrium constant at $2400 \mathrm{~K}$.
The van't Hoff equation $$d \ln K=\frac{\Delta H^{0}}{\bar{R} T^{2}} d T_{p^{0}}$$ relates the chemical equilibrium constant $K$ to the enthalpy of reaction $\Delta H^{0}$. From the value of $K$ in Table A.11 for the dissociation of hydrogen at $2000 \mathrm{K}$ and the value of $\Delta H^{0}$ calculated from Table A.9 at $2000 \mathrm{K}$, use the van't Hoff equation to predict the equilibrium constant at $2400 \mathrm{K}$
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