For the reaction C2 H4(g)+Cl2(g) ⟶C2 H4 Cl2(1) determine Δr...

For the reaction $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)$ determine $\Delta_{\mathrm{r}} H^{\circ},$ given that $$\begin{array}{l} 4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1) \\ \qquad \begin{aligned} \Delta_{\mathrm{r}} H^{\circ} &=-202.4 \mathrm{kJ} \mathrm{mol}^{-1} \\ 2 \mathrm{HCl}(\mathrm{g})+\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow & \\ \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)+\mathrm{H}_{2} \mathrm{O}(1) & \Delta_{\mathrm{r}} H^{\circ}=-318.7 \mathrm{kJ} \mathrm{mol}^{-1} \end{aligned} \end{array}$$

For the reaction $\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)$ determine $\Delta_{\mathrm{r}} H^{\circ},$ given that $$\begin{array}{l}
4 \mathrm{HCl}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{Cl}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(1) \\
\qquad \begin{aligned}
\Delta_{\mathrm{r}} H^{\circ} &=-202.4 \mathrm{kJ} \mathrm{mol}^{-1} \\
2 \mathrm{HCl}(\mathrm{g})+\mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) \longrightarrow & \\
\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}(1)+\mathrm{H}_{2} \mathrm{O}(1) & \Delta_{\mathrm{r}} H^{\circ}=-318.7 \mathrm{kJ} \mathrm{mol}^{-1}
\end{aligned}
\end{array}$$

Key Concepts

Hess's Law

This is the principle that the total enthalpy change for a reaction is independent of the pathway between the initial and final states. Hess's Law allows one to determine unknown reaction enthalpies by adding, subtracting, or otherwise manipulating known enthalpy changes from other reactions. It relies on the fact that enthalpy is a state function, meaning its change depends only on the initial and final states of the system, not on how the change occurs.

Standard Reaction Enthalpy

This concept refers to the enthalpy change when a reaction occurs under standard conditions (usually 1 atm pressure and a specified temperature, commonly 298 K). Knowing the standard reaction enthalpy helps in comparing energy changes of different reactions and is crucial for understanding thermodynamic favorability.

Thermochemical Equation Manipulation

Manipulating thermochemical equations involves algebraically adding, subtracting, or reversing reactions to obtain a target reaction while simultaneously adjusting their enthalpy changes. This skill is essential for solving problems where the enthalpy change of a reaction must be derived from other known reactions.

Stoichiometry in Thermochemistry

Stoichiometry in thermochemistry involves using the mole ratios from a balanced chemical equation to ensure that all added or subtracted reactions are scaled correctly. This guarantees that the combined enthalpy changes accurately reflect the formation or consumption of the specific amounts of reactants and products involved in the target reaction.

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