Certainly! Let's go through the problem step-by-step to address each part of the question:
### Step 1: Determine the Nature of the Reaction
The reaction given is:
[tex]\[2 \, NO_2(g) \rightarrow N_2O_4(g) \quad \Delta H = -55.3 \, \text{kJ}\][/tex]
The enthalpy change ([tex]\(\Delta H\)[/tex]) for this reaction is negative, which indicates that the reaction releases heat. Therefore, the reaction is exothermic.
### Answer:
This reaction is... [tex]\(\boxed{\text{exothermic}}\)[/tex].
### Step 2: Determine if Heat is Released or Absorbed
Since the reaction is exothermic, heat will be released during the reaction.
### Answer:
Will any heat be released or absorbed? [tex]\(\boxed{\text{Yes, released.}}\)[/tex]
### Step 3: Calculate the Amount of Heat Released
#### Given Information:
- Molar mass of [tex]\(NO_2 = 46.0055 \, \text{g/mol}\)[/tex]
- Mass of [tex]\(NO_2\)[/tex] reacting = 53.6 g
- [tex]\(\Delta H = -55.3 \, \text{kJ}\)[/tex] for 2 moles of [tex]\(NO_2\)[/tex]
#### Step-by-Step Calculation:
1. Calculate the moles of [tex]\(NO_2\)[/tex] reacting:
[tex]\[
\text{Moles of } NO_2 = \frac{\text{Mass of } NO_2}{\text{Molar mass of } NO_2} = \frac{53.6 \, \text{g}}{46.0055 \, \text{g/mol}} = 1.1650780884894198 \, \text{mol}
\][/tex]
2. Calculate the energy change per mole of [tex]\(NO_2\)[/tex]:
Since [tex]\(\Delta H = -55.3 \, \text{kJ}\)[/tex] is for 2 moles of [tex]\(NO_2\)[/tex],
[tex]\[
\text{Energy change per mole of } NO_2 = \frac{-55.3 \, \text{kJ}}{2} = -27.65 \, \text{kJ/mol}
\][/tex]
3. Calculate the total heat released for 53.6 g of [tex]\(NO_2\)[/tex]:
[tex]\[
\text{Heat released} = \text{Energy change per mole of } NO_2 \times \text{Moles of } NO_2 = -27.65 \, \text{kJ/mol} \times 1.1650780884894198 \, \text{mol} = -32.214 \, \text{kJ}
\][/tex]
4. Round the answer to 3 significant digits:
[tex]\[
\text{Heat released} = -32.214 \, \text{kJ} \approx -32.2 \, \text{kJ}
\][/tex]
### Answer:
The amount of heat released: [tex]\(\boxed{32.2 \, \text{kJ}}\)[/tex]
In summary:
1. The reaction is exothermic.
2. Yes, heat will be released.
3. The amount of heat released when 53.6 g of [tex]\(NO_2\)[/tex] react is 32.2 kJ.
