To determine which graph can be used to represent the reaction pathway for the given chemical reaction, we need to follow these steps:
1. Identify the given enthalpy changes:
- The enthalpy of formation for the reactants is given as [tex]\(\Delta H_f, \text{reactants} = -1023 \ \text{kJ}\)[/tex].
- The enthalpy of formation for the products is given as [tex]\(\Delta H_f, \text{products} = -935.3 \ \text{kJ}\)[/tex].
2. Calculate the enthalpy change of the reaction ([tex]\(\Delta H_{\text{reaction}}\)[/tex]):
- The enthalpy change of the reaction is the difference between the enthalpy of the products and the enthalpy of the reactants:
[tex]\[
\Delta H_{\text{reaction}} = \Delta H_f, \text{products} - \Delta H_f, \text{reactants}
\][/tex]
3. Substitute the given values:
[tex]\[
\Delta H_{\text{reaction}} = -935.3 \ \text{kJ} - (-1023 \ \text{kJ})
\][/tex]
Since subtracting a negative number is the same as adding its positive counterpart:
[tex]\[
\Delta H_{\text{reaction}} = -935.3 \ \text{kJ} + 1023 \ \text{kJ}
\][/tex]
4. Perform the addition:
[tex]\[
\Delta H_{\text{reaction}} = 87.7 \ \text{kJ}
\][/tex]
5. Interpret the result:
- The positive value of [tex]\(\Delta H_{\text{reaction}} = 87.7 \ \text{kJ}\)[/tex] indicates that the reaction is endothermic. This means that the reaction absorbs energy from the surroundings.
6. Draw the reaction pathway graph:
- In an endothermic reaction, the reactants have lower energy compared to the products. Therefore, a graph representing the reaction pathway would show the energy of the reactants on the y-axis, starting at a lower value, and the energy of the products at a higher value, with an upward slope indicating the absorption of energy.
Here is a simplified version of how the graph might look:
```
Energy
|
| ___________
|
| (Products)
| /
| /
| (Reactants)
|_______________________________ Time
```
In summary, since the enthalpy change is positive ([tex]\(\Delta H_{\text{reaction}} = 87.7 \ \text{kJ}\)[/tex]), the graph representing this reaction pathway should show an increase in energy from the reactants to the products, indicative of an endothermic reaction.
