The enthalpy changes for the following reactions can be...

The enthalpy changes for the following reactions can be measured: $$ \begin{array}{l} \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ \left.\quad \Delta_{r} H^{\circ}=-802.4 \mathrm{k}\right] / \mathrm{mol}-\mathrm{r} \mathrm{xn} \\ \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+3 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\ \Delta_{\mathrm{r}} \mathrm{H}^{\circ}=-676 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn} \end{array}$$(a) Use these values and Hess's law to determine the enthalpy change for the reaction$$ \mathrm{CH}_{4}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})$$ (b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.

The enthalpy changes for the following reactions can be measured:
$$
\begin{array}{l}
\mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\
\left.\quad \Delta_{r} H^{\circ}=-802.4 \mathrm{k}\right] / \mathrm{mol}-\mathrm{r} \mathrm{xn} \\
\mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})+3 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \\
\Delta_{\mathrm{r}} \mathrm{H}^{\circ}=-676 \mathrm{kJ} / \mathrm{mol}-\mathrm{rxn}
\end{array}$$(a) Use these values and Hess's law to determine the enthalpy change for the reaction$$
\mathrm{CH}_{4}(\mathrm{g})+1 / 2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CH}_{3} \mathrm{OH}(\mathrm{g})$$
(b) Draw an energy level diagram that shows the relationship between the energy quantities involved in this problem.

Key Concepts

Enthalpy Change

Enthalpy change is a measure of the total heat content of a system, and it is used to quantify the energy absorbed or released during a chemical reaction under constant pressure. It is typically expressed in kilojoules per mole and can be determined experimentally or calculated via Hess's Law, reflecting the difference in energy between reactants and products.

Energy-level Diagram

An energy-level diagram graphically represents the energy changes during a chemical reaction, illustrating the relative energies of reactants, intermediates, and products. It is a visual tool that helps in understanding endothermic and exothermic processes, showing how energy is absorbed or released as the system moves from reactants to products in a stepwise fashion.

Hess's Law

Hess's Law is a principle in thermochemistry that states the total enthalpy change of a chemical reaction is the same no matter how many steps the reaction is carried out in, because enthalpy is a state function. This allows the calculation of unknown reaction enthalpies by algebraically combining the known enthalpy changes of other reactions, as demonstrated in the problem where the given reactions are manipulated to yield the desired reaction.

Transcript

00:01 Hi guys, in this problem, we need to find to use the values and heslo to determine the unsolver change for the reaction.

00:11 And then we need to draw the energy level diagram that shows the relationship between the energy quantities involved in this problem.

00:20 Okay, so the first step here is heslo states that we can adopt the standard reaction in the talbi values for individual steps to determine the insult value for a problem.

00:30 Multiple step process.

00:32 To accomplish this, we must first reverse the second equation, which will change the sign of the enthalpy value.

00:40 So here we have co2 gas plus 2h2 gas.

00:49 This gives us ch3 oh gas plus 3 over 2 -02 gas.

01:01 Okay.

01:03 Now we can add the two individual steps together to derive the overall reaction.

01:09 Okay, so here we have ch4 plus 2o2.

01:19 And this is co2 plus 2h2 okay and the second equation is co2 plus 2h2 o2 okay so this is ch3oh2 okay so now we have of ch4 plus 1 over 2 o2 this gives us ch3 oh each this is the result term equation so in the same way we can add up the insolvary values to determine the value for the overall process okay so delta h delta r h total this is delta r h1 plus delta r h2 okay so this is just negative 802 .4 plus 676 so this is negative 1 to 6 kilojoules per more this is an solid change for the given reaction okay, for part p we need to draw the energy diagram, okay? so the first reaction begins with with exothermic conversion of ch4 and 202, to co2 and to h2o, releasing 802 .4 kilogram per moon...

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