Q127CP - Chemistry: Molecular Nature Of Matter And Change

Question

A typical formulation for window glass is 75% SiO₂, 15% Na₂O, and 10.% CaO by mass. What masses of sand (SiO₂), sodium carbonate, and calcium carbonate must be combined to produce 1.00 kg of glass after carbon dioxide is driven off by thermal decomposition of the carbonates?

Step-by-Step Solution

Answer

The mass of sand, sodium carbonate and calcium carbonate is 0.75 kg, 0.26 kg, and 0.18 kg, respectively.

Step 1: Determination of mass of sand (SiO 2 )

The reaction for the decomposition of sodium carbonate is,

 ${\mathbf{Na}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}\left(s\right)\mathbf{\to }{\mathbf{Na}}_{\mathbf{2}}\mathbf{O}\left(s\right)\mathbf{+}{\mathbf{CO}}_{\mathbf{2}}\left(g\right)\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathbf{1}\mathbf{\right)}$

 

The reaction for the decomposition of calcium carbonate is,

 ${\mathbf{CaCO}}_{\mathbf{3}}\left(s\right)\mathbf{\to }\mathbf{CaO}\left(s\right)\mathbf{+}{\mathbf{CO}}_{\mathbf{2}}\left(g\right)\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{.}\mathbf{\left(}\mathbf{2}\mathbf{\right)}$

 

The percentage of SiO₂ in glass is 75%.

The mass of SiO₂ in 1.00 kg of glass is,

 $$\begin{gathered} \mathbf{=}\frac{\mathbf{75}}{\mathbf{100}}{\mathbf{SiO}}_{\mathbf{2}}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{kg}\mathbf{\times }\frac{\mathbf{1000}\mathbf{g}}{\mathbf{1}\mathbf{kg}} \\ \mathbf{=}\mathbf{750}\mathbf{g} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{75}\mathbf{kg}\mathbf{ }{\mathbf{SiO}}_{\mathbf{2}} \end{gathered}$$

Hence, the mass of the sand is 0.75 kg.

Step 2: Determination of mass of sodium carbonate

The percentage of Na₂O in glass is 15%.

The mass of Na₂O in 1.00 kg of glass is,

$$\begin{gathered} \mathbf{=}\frac{\mathbf{15}}{\mathbf{100}}{\mathbf{Na}}_{\mathbf{2}}\mathbf{O}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{kg}\mathbf{\times }\frac{\mathbf{1000}\mathbf{g}}{\mathbf{1}\mathbf{kg}} \\ \mathbf{=}\mathbf{150}\mathbf{g} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{15}{\mathbf{kgNa}}_{\mathbf{2}}\mathbf{O} \end{gathered}$$

 

From equation (1), it can be concluded that 1 mol of sodium carbonate produces 1 mol of Na₂O. 

So, the mass of sodium carbonate is,

 $$\begin{gathered} \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{15}\mathbf{kg}\mathbf{\times }\frac{\mathbf{1000}\mathbf{g}}{\mathbf{1}\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}{\mathbf{molNa}}_{\mathbf{2}}\mathbf{O}}{\mathbf{61}\mathbf{.}\mathbf{98}{\mathbf{gNa}}_{\mathbf{2}}\mathbf{O}}\mathbf{\times }\frac{\mathbf{1}{\mathbf{molNa}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}}{\mathbf{1}{\mathbf{molNa}}_{\mathbf{2}}\mathbf{O}}\mathbf{\times }\frac{\mathbf{105}\mathbf{.}\mathbf{99}{\mathbf{Na}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}}{\mathbf{1}{\mathbf{molNa}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1000}\mathbf{g}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{26}{\mathbf{kgNa}}_{\mathbf{2}}{\mathbf{CO}}_{\mathbf{3}} \end{gathered}$$

 

Hence, the mass of sodium carbonate is 0.26 kg.

Step 3: Determination of mass of calcium carbonate

The percentage of CaO in glass is 10%.

The mass of Na₂O in 1.00 kg of glass is,

 $$\begin{gathered} \mathbf{=}\frac{\mathbf{10}}{\mathbf{100}}\mathit{C}\mathit{a}\mathit{O}\mathbf{\times }\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{kg}\mathbf{\times }\frac{\mathbf{1000}\mathbf{g}}{\mathbf{1}\mathbf{kg}} \\ \mathbf{=}\mathbf{100}\mathbf{g} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{kgCaO} \end{gathered}$$

 

From equation (1), it can be concluded that 1 mol of calcium carbonate produces 1 mol of CaO. 

So, the mass of calcium carbonate is,

 $$\begin{gathered} \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{kg}\mathbf{\times }\frac{\mathbf{1000}\mathbf{g}}{\mathbf{1}\mathbf{kg}}\mathbf{\times }\frac{\mathbf{1}{\mathbf{molNa}}_{\mathbf{2}}\mathbf{O}}{\mathbf{56}\mathbf{.}\mathbf{08}\mathbf{gCaO}}\mathbf{\times }\frac{\mathbf{1}{\mathbf{molCaCO}}_{\mathbf{3}}}{\mathbf{1}\mathbf{molCaO}}\mathbf{\times }\frac{\mathbf{100}\mathbf{.}\mathbf{09}\mathit{C}\mathit{a}{\mathbf{CO}}_{\mathbf{3}}}{\mathbf{1}\mathbf{mol}\mathit{C}\mathit{a}{\mathbf{CO}}_{\mathbf{3}}}\mathbf{\times }\frac{\mathbf{1}\mathbf{kg}}{\mathbf{1000}\mathbf{g}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{18}{\mathbf{kgCaCO}}_{\mathbf{3}} \end{gathered}$$

 

Hence, the mass of calcium carbonate is 0.18 kg.