To determine the enthalpy of the reaction, let's follow a step-by-step approach:
1. Given Data:
- The number of moles of [tex]\( \text{BaCl}_2 \)[/tex] formed is [tex]\( 0.050 \)[/tex] mol.
- The amount of energy released in the solution ([tex]\( q_\text{soln} \)[/tex]) is [tex]\( 5934 \)[/tex] Joules.
2. Understanding the Concept:
- The enthalpy of the reaction ([tex]\( \Delta H \)[/tex]) represents the amount of energy change associated with the reaction. This is typically given in Joules per mole (J/mol).
- We know how much energy ([tex]\( q_\text{soln} \)[/tex]) is released for a known quantity of substance (moles of [tex]\( \text{BaCl}_2 \)[/tex]).
3. Calculation of Enthalpy Change:
- To find the enthalpy change per mole of [tex]\( \text{BaCl}_2 \)[/tex] formed, we will divide the total energy released by the number of moles formed.
[tex]\[
\Delta H = \frac{q_\text{soln}}{\text{moles of } \text{BaCl}_2}
\][/tex]
4. Substitute the Given Values:
- Given [tex]\( q_\text{soln} = 5934 \)[/tex] J and moles of [tex]\( \text{BaCl}_2 = 0.050 \)[/tex] mol,
[tex]\[
\Delta H = \frac{5934 \text{ J}}{0.050 \text{ mol}}
\][/tex]
5. Perform the Division:
[tex]\[
\Delta H = 118680 \text{ J/mol}
\][/tex]
6. Interpret the Result:
- The positive value indicates the energy release per mole, meaning the reaction is exothermic, releasing energy to the surroundings.
Conclusion:
The enthalpy of the reaction, when [tex]\( \text{Ba(OH)}_2 \)[/tex] reacts with [tex]\( \text{HCl} \)[/tex] to form [tex]\( \text{BaCl}_2 \)[/tex] and water, is [tex]\( 118680 \)[/tex] Joules per mole of [tex]\( \text{BaCl}_2 \)[/tex] formed.
