Question

The powerful chlorinating agent sulfuryl dichloride $\left({\mathrm{SO}}_2{\mathrm{Cl}}_2\right)$can be prepared by the following two-step sequence:

${\mathbf{H}}_{\mathbf{2}}\mathbf{S}\left(g\right)\mathbf{+}{\mathbf{O}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(g\right)\mathbf{+}{\mathbf{SO}}_{\mathbf{2}}\left(g\right)$

${\mathbf{SO}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{Cl}}_{\mathbf{2}}\left(g\right)\mathbf{\to }{\mathbf{SO}}_{\mathbf{2}}{\mathbf{Cl}}_{\mathbf{2}}\left(g\right)$

1. Balance each step, and write the overall equation.
2. Show that the overall${\mathbf{Q}}_{\mathbf{c}}$equals the product of the${\mathbf{Q}}_{\mathbf{c}}$'s for the individual steps.

Short answer

1. The equation is $2{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_2\left(\mathrm{g}\right)+2{\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right)$.
2. The product of the individual${\mathrm{Q}}_{\mathrm{c}}$ is equal to the${\mathrm{Q}}_{\mathrm{c}}$ of the overall reaction.

Step-by-step solution

Definition of Concept

Reactions: A balanced chemical reaction equation shows the mole relationships of reactants and products, while a chemical reaction equation gives the reactants and products. The amount of energy involved in the reaction is frequently stated. Reaction stoichiometry is the study of the quantitative aspects of chemical reactions.

Write the overall equation

(a)

Considering the given information:

$$\begin{gathered} {\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_2\left(\mathrm{g}\right) \\ {\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right) \end{gathered}$$

Write the overall equation after balancing each step.

Prior to moving on to step 1, make sure you have a good oxygen balance.

${\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+\frac{3}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\to {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_2\left(\mathrm{g}\right)$

After that, divide everything in half.

$2{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+2{\mathrm{SO}}_2\left(\mathrm{g}\right)$

Step 2 is already in a good place. Begin by composing the overall equation.

$$\begin{gathered} 2{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+2{\mathrm{SO}}_2\left(\mathrm{g}\right) \\ {\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right) \\ 2{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2\left(\mathrm{g}\right)+2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right) \end{gathered}$$

Show that the overall Qc equals the product of the  Qc's for the individual steps

(b)

Considering the given information:

Write the${\mathrm{Q}}_{\mathrm{c}}$ of each step first.

For the first step:

$2{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+2{\mathrm{SO}}_2\left(\mathrm{g}\right)$

Write the${\mathrm{Q}}_{\mathrm{c}1}$ for step (1).

$$\begin{gathered} {\mathrm{Q}}_{\mathrm{c}1}=\frac{\left[\mathrm{product}\right]}{\left[\mathrm{reactant}\right]} \\ {\mathrm{Q}}_{\mathrm{c}1}=\frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2{\left[{\mathrm{SO}}_2\right]}^2}{{\left[{\mathrm{H}}_2\mathrm{S}\right]}^2{\left[{\mathrm{O}}_2\right]}^3} \end{gathered}$$

Step two is as follows:

${\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to {\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right)$

Write the${\mathrm{Q}}_{\mathrm{c}2}$ for step (2):

$$\begin{gathered} {\mathrm{Q}}_{\mathrm{c}2}=\frac{\left[\mathrm{product}\right]}{\left[\mathrm{reactant}\right]} \\ {\mathrm{Q}}_{\mathrm{c}2}=\frac{\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]}{\left[{\mathrm{SO}}_2\right]\left[{\mathrm{Cl}}_2\right]} \end{gathered}$$

For the overall reaction:

$2{\mathrm{H}}_2\mathrm{S}\left(\mathrm{g}\right)+3{\mathrm{O}}_2\left(\mathrm{g}\right)+{\mathrm{Cl}}_2\left(\mathrm{g}\right)\to 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)+{\mathrm{SO}}_2\left(\mathrm{g}\right)+{\mathrm{SO}}_2{\mathrm{Cl}}_2\left(\mathrm{g}\right)$

For the overall reaction, write the${\mathrm{Q}}_{\mathrm{c}}$ .

$$\begin{gathered} {\mathrm{Q}}_{\mathrm{c}}=\frac{\left[\mathrm{product}\right]}{\left[\mathrm{reactant}\right]} \\ {\mathrm{Q}}_{\mathrm{c}}=\frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2\left[{\mathrm{SO}}_2\right]\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]}{{\left[{\mathrm{H}}_2\mathrm{S}\right]}^2{\left[{\mathrm{O}}_2\right]}^3\left[{\mathrm{Cl}}_2\right]} \end{gathered}$$

Show that ${\mathrm{Q}}_{\mathrm{c}}={\mathrm{Q}}_{\mathrm{c}1}\times {\mathrm{Q}}_{\mathrm{c}2}$.

$$\begin{gathered} {\mathrm{Q}}_{\mathrm{c}}={\mathrm{Q}}_{\mathrm{c}1}\times {\mathrm{Q}}_{\mathrm{c}2} \\ \frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2\left[{\mathrm{SO}}_2\right]\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]}{{\left[{\mathrm{H}}_2\mathrm{S}\right]}^2{\left[{\mathrm{O}}_2\right]}^3\left[{\mathrm{Cl}}_2\right]}=\frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2{\left[{\mathrm{SO}}_2\right]}^2}{{\left[{\mathrm{H}}_2\mathrm{S}\right]}^2{\left[{\mathrm{O}}_2\right]}^3}\times \frac{\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]}{\left[{\mathrm{Cl}}_2\right]{\left[{\mathrm{SO}}_2\right]}^2} \\ \frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2\left[{\mathrm{SO}}_2\right]\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]}{{\left[{\mathrm{H}}_2\mathrm{S}\right]}^2{\left[{\mathrm{O}}_2\right]}^3\left[{\mathrm{Cl}}_2\right]}=\frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^2\left[{\mathrm{SO}}_2\right]\left[{\mathrm{SO}}_2{\mathrm{Cl}}_2\right]}{{\left[{\mathrm{H}}_2\mathrm{S}\right]}^2{\left[{\mathrm{O}}_2\right]}^3\left[{\mathrm{Cl}}_2\right]} \end{gathered}$$

Therefore, the product of the individual${\mathrm{Q}}_{\mathrm{c}}$ is equal to the${\mathrm{Q}}_{\mathrm{c}}$ of the overall reaction.