Answer :
To find the enthalpy of the reaction ([tex]\Delta H_{\text{rxn, MgO+HCl}}[/tex]) in kJ/mol, we need to consider the heat change of the reaction and the stoichiometry of the reactants involved.
Calculate the heat absorbed or released by the solution (q):
The formula to calculate the heat change is:
[tex]q = m \cdot c \cdot \Delta T[/tex]
Where:- [tex]m[/tex] is the mass of the solution, which can be calculated from the density and volume of the HCl solution.
- [tex]c[/tex] is the specific heat capacity of the solution (given as 4.184 J/g-deg).
- [tex]\Delta T[/tex] is the change in temperature (given as 4.4 degrees Celsius).
First, calculate [tex]m[/tex] (mass of the solution):
[tex]m = \text{volume} \times \text{density} = 101.2 \text{ mL} \times 1.016 \text{ g/mL} = 102.59 \text{ g}[/tex]Now, calculate [tex]q[/tex]:
[tex]q = 102.59 \text{ g} \times 4.184 \text{ J/g-deg} \times 4.4 \text{ deg} = 1893.1 \text{ J}[/tex]
Convert [tex]q[/tex] to kJ: [tex]q = 1.8931 \text{ kJ}[/tex]Determine moles of MgO used:
The formula for moles is:
[tex]\text{moles of MgO} = \frac{\text{mass of MgO}}{\text{MW of MgO}} = \frac{0.511 \text{ g}}{40.304 \text{ g/mol}} \approx 0.01267 \text{ mol}[/tex]Calculate [tex]\Delta H_{\text{rxn, MgO+HCl}}[/tex]:
The enthalpy change for the reaction is then calculated per mole of MgO:
[tex]\Delta H_{\text{rxn, MgO+HCl}} = \frac{q}{\text{moles of MgO}} = \frac{-1.8931 \text{ kJ}}{0.01267 \text{ mol}} \approx -149.4 \text{ kJ/mol}[/tex]The negative sign indicates the reaction is exothermic, meaning it releases heat.
In conclusion, the enthalpy change for the reaction [tex]\Delta H_{\text{rxn, MgO+HCl}}[/tex] is approximately [tex]-149.4 \text{ kJ/mol}[/tex]. This value signifies the energy change associated with the reaction of one mole of [tex]\text{MgO}[/tex] with [tex]\text{HCl}[/tex].
