Question

1. using the following reactions, calculate the heat of formation, \\( \delta h_{f} \\), of \\( cs_{2} \\) using hess law. show all your work.

i. \\( c(s)+o_{2}(g) \
ightarrow co_{2}(g) \\) \\( \delta h=-393.3 \mathrm{~kj} \\)
ii. \\( s(s)+o_{2}(g) \
ightarrow so_{2}(g) \\) \\( \delta h=-293.72 \mathrm{~kj} \\)
iii. \\( cs_{2}(\ell)+3 o_{2}(g) \
ightarrow co_{2}(g)+2 so_{2}(g) \\) \\( \delta h=-1108.76 \mathrm{~kj} \\)

Explanation:

Step1: Reverse reaction iii

$$\text{CO}_2(\text{g}) + 2\text{SO}_2(\text{g})\to\text{CS}_2(\ell)+3\text{O}_2(\text{g})\quad\Delta H = + 1108.76\ \text{kJ}$$

Step2: Use reaction i as is

$$\text{C}(\text{s})+\text{O}_2(\text{g})\to\text{CO}_2(\text{g})\quad\Delta H=-393.3\ \text{kJ}$$

Step3: Multiply reaction ii by 2

$$2\text{S}(\text{s}) + 2\text{O}_2(\text{g})\to2\text{SO}_2(\text{g})\quad\Delta H = 2\times(- 293.72\ \text{kJ})=-587.44\ \text{kJ}$$

Step4: Add the three adjusted reactions

$$\begin{align*} &\text{CO}_2(\text{g}) + 2\text{SO}_2(\text{g})\to\text{CS}_2(\ell)+3\text{O}_2(\text{g})\quad\Delta H = + 1108.76\ \text{kJ}\\ &\text{C}(\text{s})+\text{O}_2(\text{g})\to\text{CO}_2(\text{g})\quad\Delta H=-393.3\ \text{kJ}\\ &2\text{S}(\text{s}) + 2\text{O}_2(\text{g})\to2\text{SO}_2(\text{g})\quad\Delta H=-587.44\ \text{kJ}\\ \hline &\text{C}(\text{s})+2\text{S}(\text{s})\to\text{CS}_2(\ell) \end{align*}$$

Sum the $\Delta H$ values:
$$\Delta H=(1108.76-393.3 - 587.44)\ \text{kJ}$$
$$\Delta H = 128.02\ \text{kJ}$$

Answer:

The heat of formation of $\text{CS}_2$, $\Delta H_f = 128.02\ \text{kJ}$