madey21
Answered

[tex]$19.64 \, \text{g} \, \text{H}_2\text{SO}_4$[/tex] dissociating resulted in a heat of reaction equal to [tex]$-14,300 \, \text{J}$[/tex]. What is the enthalpy [tex]$(\Delta H, \, \text{kJ/mol})$[/tex] for the dissociation process?
[tex]\[
\begin{array}{c}
\text{H}_2\text{SO}_4 \rightarrow \text{H}^+ + \text{HSO}_4^- \\
\Delta H = [?] \, \text{kJ/mol}
\end{array}
\][/tex]

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Answer :

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].