To determine the enthalpy change [tex]\((\Delta H)\)[/tex] for the dissociation of [tex]\(19.64 \, \text{g}\)[/tex] of [tex]\( \text{H}_2\text{SO}_4 \)[/tex], follow these steps:
1. Calculate the Molar Mass of [tex]\(\text{H}_2\text{SO}_4\)[/tex]:
The molar mass of [tex]\(\text{H}_2\text{SO}_4\)[/tex] is calculated by summing the atomic masses of its components:
[tex]\[
\text{Molar mass of } \text{H}_2\text{SO}_4 = 2(1.01) + 32.07 + 4(16.00) \, \text{g/mol} = 98.09 \, \text{g/mol}
\][/tex]
2. Convert Grams to Moles:
Using the mass of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
[tex]\[
\text{Moles of } \text{H}_2\text{SO}_4 = \frac{19.64 \, \text{g}}{98.09 \, \text{g/mol}} \approx 0.2002 \, \text{mol}
\][/tex]
3. Enthalpy Change Calculation:
Given the heat of reaction (ΔH) for the dissociation process is [tex]\(-14300 \, \text{J}\)[/tex]. First, convert this to kilojoules:
[tex]\[
\Delta H = -14300 \, \text{J} \times \frac{1 \, \text{kJ}}{1000 \, \text{J}} = -14.30 \, \text{kJ}
\][/tex]
4. Calculate ΔH in kJ per mole:
Use the moles calculated in step 2 to find [tex]\(\Delta H\)[/tex] per mole of [tex]\( \text{H}_2\text{SO}_4 \)[/tex]:
[tex]\[
\Delta H \text{ (kJ/mol)} = \frac{-14.30 \, \text{kJ}}{0.2002 \, \text{mol}} \approx -71.42 \, \text{kJ/mol}
\][/tex]
Final Answer:
[tex]\(\Delta H\)[/tex] for the dissociation process of [tex]\(\text{H}_2\text{SO}_4\)[/tex] is [tex]\(-71.42 \, \text{kJ/mol}\)[/tex].
