https://file.aiquickdraw.com/mathbot/file/1726547729298fqn7idm6.jpg

To solve the problem shown in the image, we need to calculate the amount of heat absorbed when 45.00 g of carbon (C) reacts according to the given chemical equation:

\[ 5C(s) + 2SO_2(g) \rightarrow CS_2(l) + 4CO(g) \]

The enthalpy change (\( \Delta H^\circ \)) is provided as \( 239.9 \, \text{kJ} \). This value represents the heat absorbed or released when the amount of reactants shown in the balanced equation reacts completely.

### Steps to solve:

1. **Find the molar mass of carbon (C)**:
   - The molar mass of carbon \( C \) is \( 12.01 \, \text{g/mol} \).

2. **Calculate the moles of carbon in 45.00 g**:
   \[
   \text{Moles of } C = \frac{45.00 \, \text{g}}{12.01 \, \text{g/mol}} = 3.747 \, \text{mol}
   \]

3. **Relate the moles of carbon to the enthalpy change**:
   - According to the balanced chemical equation, 5 moles of carbon correspond to an enthalpy change (\( \Delta H \)) of \( 239.9 \, \text{kJ} \).

4. **Calculate the heat absorbed for 3.747 moles of carbon**:
   - The ratio of heat absorbed to moles of carbon is:
   \[
   \text{Heat absorbed per mole of } C = \frac{239.9 \, \text{kJ}}{5 \, \text{mol}} = 47.98 \, \text{kJ/mol}
   \]

   - Now, multiply by the number of moles of carbon (3.747 mol):
   \[
   \text{Heat absorbed} = 3.747 \, \text{mol} \times 47.98 \, \text{kJ/mol} = 179.78 \, \text{kJ}
   \]

Thus, the heat absorbed when 45.00 g of carbon reacts is **179.78 kJ**.

Would you like further details or have any questions? Here are some related questions to explore:

1. What is the significance of \( \Delta H^\circ \) in chemical reactions?
2. How would the heat absorbed change if a different amount of carbon was used?
3. Can you calculate the heat released if the reaction were exothermic?
4. How does the number of moles of reactants affect the overall heat absorbed or released?
5. How is the molar ratio used to calculate enthalpy changes?

**Tip:** Always make sure your units are consistent when calculating energy changes in chemical reactions, especially when converting between grams and moles.

How much heat is absorbed when 45.00 g of C(s) reacts in the presence of excess SO2(g) to produce CS2(l) and CO(g) according to the given chemical equation: 5C(s) + 2SO2(g) → CS2(l) + 4CO(g), with ΔH° = 239.9 kJ?

This example calculates the heat absorbed when 45.00 g of carbon reacts with sulfur dioxide in a thermochemical process. By using stoichiometry and the enthalpy change (ΔH° = 239.9 kJ), we determine the heat absorbed as 179.78 kJ. Suitable for Grades 10-12.

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