To determine what graph would have a similar shape to the given chemical reaction, we need to calculate the enthalpy change of the reaction, [tex]\(\Delta H\)[/tex], using the provided enthalpy of formation values. Here is the step-by-step process:
1. Identify the enthalpy of formation ([tex]\(\Delta H_f\)[/tex]) values given:
- The enthalpy of formation for the reactants is [tex]\(\Delta H_f = -256 \, \text{kJ/mol}\)[/tex].
- The enthalpy of formation for the products is [tex]\(\Delta H_f = -321 \, \text{kJ/mol}\)[/tex].
2. Recall the definition of enthalpy change of the reaction ([tex]\(\Delta H_{reaction}\)[/tex]):
[tex]\[
\Delta H_{reaction} = \Delta H_f \text{(products)} - \Delta H_f \text{(reactants)}
\][/tex]
3. Substitute the given values into the equation:
[tex]\[
\Delta H_{reaction} = (-321 \, \text{kJ/mol}) - (-256 \, \text{kJ/mol})
\][/tex]
4. Simplify the expression:
[tex]\[
\Delta H_{reaction} = -321 \, \text{kJ/mol} + 256 \, \text{kJ/mol}
\][/tex]
[tex]\[
\Delta H_{reaction} = -65 \, \text{kJ/mol}
\][/tex]
5. Interpret the enthalpy change:
The enthalpy change of [tex]\(-65 \, \text{kJ/mol}\)[/tex] signifies that the reaction releases energy (it is exothermic).
6. Describe the shape of the related graph:
An exothermic reaction typically features a curve where the enthalpy decreases from reactants to products. Specifically:
- The y-axis represents the enthalpy ([tex]\(H\)[/tex]).
- The x-axis represents the progression of the reaction.
- The graph starts higher for the reactants and ends lower for the products.
- The difference in height between the starting and ending points of the graph reflects the enthalpy change of -65 kJ.
Thus, a graph of this reaction would show an initial high point corresponding to the enthalpy of the reactants, and it would slope downwards to a lower point corresponding to the enthalpy of the products, indicating that the reaction releases energy ([tex]\(\Delta H = -65 \, \text{kJ/mol}\)[/tex]). The slope and the difference in heights between the starting and ending points are representative of the exothermic nature of the reaction.
