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Chapter 21: Problem 30

Some baking powders contain the solids \(\mathrm{NaHCO}_{3}\) and \(\mathrm{NaAl}\left(\mathrm{SO}_{4}\right)_{2} .\) When water is added to this mixture of compounds, \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{Al}(\mathrm{OH})_{3}(\mathrm{s})\) are two of the products. Write plausible net ionic equations for the formation of these two products.

Short Answer

Expert verified
The net ionic equations for the formation of \(CO_2(g)\) and \(Al(OH)_3(s)\) when \(NaHCO_3\) and \(NaAl(SO_4)_2\) are dissolved in water are:1. \(HCO_3^- (aqueous) + H_2O (l) \rightarrow OH^- (aqueous) + CO_2 (g)\)2. \(Al^{3+} (aqueous) + 3H_2O (l) \rightarrow Al(OH)_3 (s)\

Step by step solution

01

Identify the Reaction of NaHCO3 with Water

When sodium bicarbonate (\(NaHCO_3\)) dissolves in water, it breaks down into its constituent ions, \(Na^+\) and \(HCO_3^-\). This bicarbonate ion reacts with water to form hydroxide ion, \(OH^-\), and carbon dioxide gas, \(CO_2\). This can be written as follows:\(HCO_3^- (aqueous) + H_2O (l) \rightarrow OH^- (aqueous) + CO_2 (g)\)Ensure this equation is balanced.
02

Identify the Reaction of NaAl(SO4)2 with Water

When sodium alum (\(NaAl(SO_4)_2\)) dissolves in water, it dissociates into it's constituent ions: \(Na^+\), \(Al^{3+}\), and \(SO_4^{2-}\). The \(Al^{3+}\) ions react with water to form \(Al(OH)_3\). This reaction can be written as:\(Al^{3+} (aqueous) + 3H_2O (l) \rightarrow Al(OH)_3 (s)\)Ensure this equation is balanced.
03

Construct Net Ionic Equations

Now we can construct the net ionic equations by eliminating the spectator ions. As a reminder, net ionic equations don't include ions that don’t participate in the reaction (spectator ions). In these reactions, the \(Na^+\) ions and \(SO_4^{2-}\) ions in the second reaction are the spectator ions.Net Ionic Equation 1:\(HCO_3^- (aqueous) + H_2O (l) \rightarrow OH^- (aqueous) + CO_2 (g)\)Net Ionic Equation 2:\(Al^{3+} (aqueous) + 3H_2O (l) \rightarrow Al(OH)_3 (s)\)

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The Gibbs energies of formation, \(\Delta G_{\mathrm{f}}^{\circ},\) for \(\mathrm{Na}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) are \(-379.09 \mathrm{kJ} \mathrm{mol}^{-1}\) and \(-449.63 \mathrm{kJ} \mathrm{mol}^{-1}\) respectively, at 298 K. Calculate the equilibrium constant for the reaction below at \(298 \mathrm{K} .\) Is \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) thermodynamically stable with respect to \(\mathrm{Na}_{2} \mathrm{O}(\mathrm{s})\) and \(\mathrm{O}_{2}(\mathrm{g})\) at \(298 \mathrm{K} ?\) $$ \mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s}) \longrightarrow \mathrm{Na}_{2} \mathrm{O}(\mathrm{s})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{g}) $$
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