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The image shows four problems related to thermodynamics and chemistry. I'll break them down and provide help on each problem step-by-step.

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**1. Work done by gas expansion**

The question asks to calculate the work done in joules when nitrogen gas expands under different conditions:

- Initial volume: 1.6 L
- Final volume: 5.4 L
- (a) Expansion against vacuum (no external pressure): \( P = 0 \, \text{atm} \)
- (b) Constant external pressure of 0.80 atm
- (c) Constant pressure of 3.7 atm

The formula for work done by gas expansion is:

\[
W = - P \Delta V = - P (V_f - V_i)
\]

Where:
- \( W \) is the work,
- \( P \) is the external pressure,
- \( V_f \) and \( V_i \) are the final and initial volumes.

You'll need to convert the pressure from atm to joules using \( 1 \, \text{L·atm} = 101.325 \, \text{J} \).

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**2. Work done in dissolution reaction**

For the dissolution of 50.0 g of tin:

\[
\text{Sn}(s) + 2\text{H}^+ (aq) \rightarrow \text{Sn}^{2+} (aq) + \text{H}_2 (g)
\]

You need to calculate the work done when hydrogen gas is produced at 1.00 atm and 25°C. 

Use the ideal gas law:

\[
PV = nRT
\]

To find the number of moles of gas produced and apply it to calculate the work done.

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**3. Standard enthalpy of formation of acetylene**

You are given the formation reaction:

\[
2\text{C}(graphite) + \text{H}_2(g) \rightarrow \text{C}_2\text{H}_2(g)
\]

The enthalpy changes for the steps are provided:

(a) \( \Delta H_f = -393.5 \, \text{kJ/mol} \) for \( \text{C}(graphite) + O_2 \rightarrow CO_2(g) \)  
(b) \( \Delta H_f = -285.8 \, \text{kJ/mol} \) for \( H_2(g) + \frac{1}{2}O_2 \rightarrow H_2O(l) \)  
(c) \( \Delta H_f = -2598.8 \, \text{kJ/mol} \) for \( 2C_2H_2(g) + 5O_2 \rightarrow 4CO_2(g) + 2H_2O(g) \)

You'll need to use Hess's law to calculate the enthalpy of formation for acetylene.

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**4. Thermite reaction**

For the thermite reaction involving aluminum and iron(III) oxide:

\[
2\text{Al}(s) + \text{Fe}_2O_3(s) \rightarrow \text{Al}_2O_3(s) + 2\text{Fe}(l)
\]

You need to calculate the heat released per gram of aluminum reacted, given \( \Delta H_f \) for \( \text{Fe}(l) \) is 12.40 kJ/mol.

Use stoichiometry and the given data to find the heat released.

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Would you like detailed solutions for any or all of these problems? 

Here are five related questions that expand on this information:
1. How does changing pressure affect the work done in gas expansion?
2. What assumptions are made in using the ideal gas law for gas-phase reactions?
3. How do you apply Hess's law to calculate enthalpy changes in multi-step reactions?
4. What are the applications of the thermite reaction in real-world industries?
5. How does heat of formation differ from heat of reaction?

**Tip:** Always remember to check the units when converting between atmospheres, joules, and liters to avoid calculation errors.

The image shows four problems related to thermodynamics and chemistry.

Solve problems related to the work done by gas expansion, the enthalpy of formation, and the heat released in reactions. Includes the application of gas laws and Hess's Law, suitable for advanced high school or college-level chemistry.

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