Theoretical justification for the definition of standard enthalpy of reaction

Question

I've been reading the book Chemistry: Core Concepts by Allan Blackman, Daniel Southam, Gwendolyn Lawrie, Natalie Williamson, Christopher Thompson and Adam Bridgeman. They give the following definition for standard enthalpy of reaction:

The standard enthalpy of reaction ($\Delta_r H^\circ$) at temperature $T$ is the value of $\Delta H$ for a reaction in which the pure, separated reactants in their standard states are converted to the pure separated products in their standard states, all at temperature $T$, and in which the stoichiometric coefficients in the balanced chemical equation refer to actual number of moles.

The theoretical justification for this definition isn't clear to me. With this definition, would the standard enthalpy of reaction be equal to the heat absorbed or released during the reaction? In other words, can the standard enthalpy of reaction be measured by just measuring the heat absorbed or released during the reaction? I'm particularly confused regarding cases where you have more than one gas involved in the reactants as well as in the products.

Answer 1

...would the standard enthalpy of reaction be equal to the heat absorbed or released during the reaction? In other words, can the standard enthalpy of reaction be measured by just measuring the heat absorbed or released during the reaction? I'm particularly confused regarding cases where you have more than one gas involved in the reactants as well as in the products.

The standard enthalpy of reaction would be equal to the heat absorbed or released during the reaction at isobaric and isothermal conditions (the initial p($\pu{1 bar}$),T = final p,T), if the respective amounts of reactants in standard state reacts completely, forming products in their standard state.

That cannot be obviously the case if the equilibrium constant is not very big or if products are mixed.

It is the case for $\ce{2 H2(g) + O2(g) ->[\pu{1 bar}][25 ^{\circ}C] H2O(l)}$

It is not the case for $\ce{CO(g) + H2O(g) <=> CO2(g) + H2(g)}$

For the latter, one can measure (isothermal, isobaric conditions $p = \pu{1 bar}$)

$\ce{CO(g,pure) + H2O(g,pure) -> \text{equilibrium}} \tag{$\Delta_\text{r} H_\text{fw}$}$ $\ce{CO2(g,pure) + H2(g,pure) -> \text{equilibrium}} \tag{$\Delta_\text{r} H_\text{bw}$}$

and then

$$\Delta_\text{r} H^{\circ} = \Delta_\text{r} H_\text{fw} - \Delta_\text{r} H_\text{bw}$$