Q20P - Chemistry: Molecular Nature Of Matter And Change

Question

Question: Balance each of the following examples of heterogeneous

equilibria and write its reaction quotient, Qc:

$$\begin{gathered} \left(a\right)\mathbf{ }{\mathbf{NaHCO}}_{\mathbf{3}}\mathbf{ }\left(s\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{֏}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{Na}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}\left(s\right)\mathbf{+}{\mathbf{CO}}_{\mathbf{2}}\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{+}\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(g\right) \\ \left(b\right)\mathbf{ }{\mathbf{SNO}}_{\mathbf{2}}\left(s\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{ }{\mathbf{H}}_{\mathbf{2}}\mathbf{ }\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{֏}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{Sn}\left(s\right)\mathbf{+}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\left(g\right) \\ \left(c\right)\mathbf{ }{\mathbf{H}}_{\mathbf{2}}{\mathbf{SO}}_{\mathbf{4}}\left(I\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{+}\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{SO}}_{\mathbf{3}}\left(g\right)\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{֏}\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }{\mathbf{H}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}\left(I\right) \end{gathered}$$

Step-by-Step Solution

Answer

A reaction quotient $\left({\mathrm{Q}}_{\mathrm{c}}\right)$ can create from a balanced chemical equation. Products and reactants are written in numerator and denominator with their coefficients as power and they are multiplied.

     $$\begin{gathered} a) 2{\mathrm{NaHCO}}_3\left(\mathrm{s}\right) \mathrm{֏} {\mathrm{Na}}_2{\mathrm{CO}}_3\left(\mathrm{s}\right) +{\mathrm{CO}}_2\left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O} \\ {\mathrm{Q}}_{\mathrm{c}}=\frac{{\left[{\mathrm{Na}}_2{\mathrm{CO}}_3\right]}^8\left[{\mathrm{CO}}_2\right]\left[{\mathrm{H}}_2\mathrm{O}\right]}{\left[{\mathrm{NaHCO}}_3\right]} \end{gathered}$$

     $$\begin{gathered} \mathrm{b}) {\mathrm{SnO}}_2\left(\mathrm{s}\right) + {\mathrm{H}}_2\left(\mathrm{g}\right) \mathrm{֏} \mathrm{Sn}\left(\mathrm{s}\right) + {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right) \\ {\mathrm{Q}}_{\mathrm{c}}=\frac{\left[\mathrm{Sn}\right]\left[{\mathrm{H}}_2\mathrm{O}\right]}{\left[{\mathrm{SnO}}_2\right]\left[{\mathrm{H}}_2\right]} \end{gathered}$$

     $$\begin{gathered} \mathrm{c}) 2{\mathrm{H}}_2{\mathrm{SO}}_4\left(\mathrm{I}\right) + 2{\mathrm{SO}}_3\left(\mathrm{g}\right) \mathrm{֏} 2{\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_7\left(\mathrm{I}\right) \\ {\mathrm{Q}}_{\mathrm{c}}=\frac{{\left[{\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_7\right]}^2}{{\left[{\mathrm{H}}_2{\mathrm{SO}}_4\right]}^2{\left[{\mathrm{SO}}_3\right]}^2} \end{gathered}$$

Step 1: Reaction quotient ( Q c ) of ( a )

$$\begin{gathered} 2{\mathrm{NaHCO}}_3\left(\mathrm{s}\right) \mathrm{֏} {\mathrm{Na}}_2{\mathrm{CO}}_3\left(\mathrm{s}\right) + {\mathrm{CO}}_2\left(\mathrm{g}\right) + {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right) \\ {\mathbf{Q}}_{\mathbf{c}}\mathbf{=}\frac{{\mathbf{\left[}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}\mathbf{\right]}}^{\mathbf{8}}\mathbf{\left[}{\mathbf{CO}}_{\mathbf{2}}\mathbf{\right]}\mathbf{\left[}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\right]}}{{\mathbf{\left[}{\mathbf{NaHCO}}_{\mathbf{3}}\mathbf{\right]}}^{\mathbf{2}}} \end{gathered}$$  

Step 2: Reaction quotient ( Q c ) of (b)

$$\begin{gathered} {\mathrm{SnO}}_2\left(\mathrm{s}\right)+ {\mathrm{H}}_2\left(\mathrm{g}\right) \mathrm{֏} + \mathrm{Sn}\left(\mathrm{s}\right) + {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right) \\ {\mathbf{Q}}_{\mathbf{c}}\mathbf{=}\frac{\mathbf{\left[}\mathbf{Sn}\mathbf{\right]}\mathbf{\left[}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}\mathbf{\right]}}{{\mathbf{\left[}{\mathbf{SnO}}_2\mathbf{\right]}}^{\mathbf{2}}\left[H_2\right]} \end{gathered}$$

Step 3: Reaction quotient ( Q c ) of (c)

$$\begin{gathered} 2{\mathrm{H}}_2{\mathrm{SO}}_4\left(\mathrm{I}\right)+ 2{\mathrm{SO}}_3\left(\mathrm{g}\right) \mathrm{֏} 2{\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_7\left(\mathrm{I}\right) \\ {\mathbf{Q}}_{\mathbf{c}}\mathbf{=}\frac{{\mathbf{\left[}{\mathbf{H}}_{\mathbf{2}}{\mathbf{S}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{7}}\mathbf{\right]}}^{\mathbf{2}}}{{\mathbf{\left[}{\mathbf{H}}_{\mathbf{2}}{\mathbf{SO}}_4\mathbf{\right]}}^{\mathbf{2}}\mathbf{\left[}{\mathbf{SO}}_{\mathbf{3}}\mathbf{\right]}} \end{gathered}$$