Final answer:
To calculate the enthalpy change for this reaction, use the equation q = m * c * ∆T. The enthalpy change per mole of HCl is 64.4 kJ/mol.
Step-by-step explanation:
To calculate the enthalpy change for this reaction, we can use the equation:
q = m * c * ∆T
where q is the heat released or absorbed, m is the mass of the solution, c is the specific heat capacity of the solution, and ∆T is the change in temperature. In this case, we have a total volume of 99.2 mL, which corresponds to a mass of 99.2 g (assuming a density of 1.00 g/mL). The change in temperature is 7.7 °C (25.5 °C - 17.8 °C). Assuming the specific heat capacity of the solution is the same as that of water (4.18 J/g·°C), we can calculate the heat produced by the reaction:
q = 99.2 g * 4.18 J/g·°C * 7.7 °C = 3221.85 J
To convert joules to kilojoules, we divide by 1000:
3221.85 J / 1000 = 3.22 kJ
Now we need to convert this value to the enthalpy change per mole of HCl:
Since the reaction uses equal moles of HCl and NaOH, the enthalpy change for the reaction is the same as the enthalpy change for 1 mole of HCl. Therefore, the enthalpy change is:
ΔH = 3.22 kJ / 0.0500 mol = 64.4 kJ/mol