Question

Disilane $\left({\mathbf{Si}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}\right)$ gas that react with oxygen to give silica $\left({\mathbf{SiO}}_{\mathbf{2}}\right)$and water. Calculate the mass to silica that would form it 25.0cm³ disilane (with a density of $\mathbf{2}\mathbf{.}\mathbf{76}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{3}}{\mathbf{cm}}^{\mathbf{-}\mathbf{3}}$) reacted with excess oxygen.

Short answer

The mass of silica formed in the reaction is 0.314g.

Step-by-step solution

Calculating mass of Disilane

• Density of disilane =$2.78\times {10}^{-3}g/c{m}^3$
• Volume of disilane = $25.0c{m}^3$.

The relation between the density (d), volume (v), and mass(m) is

$\mathbf{Mass}\mathbf{=}\mathbf{density}\mathbf{\times }\mathbf{volume}$

$$\begin{gathered} =2.78\times {10}^{-3}g/c{m}^3\times 25.0c{m}^3 \\ =0.0695g \end{gathered}$$

Calculating the molar mass of disilane and silica

From the given equation, we get the balanced equation:

$\mathbf{2}{\mathbf{Si}}_{\mathbf{2}}{\mathbf{H}}_{\mathbf{6}}\mathbf{+}\mathbf{7}{\mathbf{O}}_{\mathbf{2}}\to \mathbf{4}{\mathbf{SiO}}_{\mathbf{2}}\mathbf{+}\mathbf{6}{\mathbf{H}}_{\mathbf{2}}\mathbf{O}$

$ThemolarmassesofSi,H,Oisare28,06g,1.0079g,and16.00grespectively.$

$$\begin{gathered} {\text{The molar mass of Si}}_{\text{2}}{\text{H}}_{\text{6}}\text{=}\left(\text{2}\times \text{28.09 + 6}\times \text{1.0079}\right)\text{g/mol} \\ \text{= 62.23g/mol} \end{gathered}$$

$$\begin{gathered} {\text{The molar mass of SiO}}_{\text{2}}\text{=}\left(\text{1}\times \text{28.09 + 2}\times \text{16.00}\right)\text{g/mol} \\ \text{= 60.09g/mol} \end{gathered}$$

Calculating the mass of silica

Balance equation is: $2S{i}_2{H}_6+7O_2\to 4Si{O}_2+6H_{2}O$

2 moles of $S{i}_2{H}_6$=4$Si{O}_2$

0.0695g of $S{i}_2{H}_6$= ?

$\text{Mass = 0.0695g.} {\text{Si}}_{\text{2}}{\text{H}}_{\text{6}}$$\times \frac{{\text{1mol.Si}}_{\text{2}}{\text{H}}_{\text{6}}}{{\text{62.23g.Si}}_{\text{2}}{\text{H}}_{\text{6}}}\times$$\frac{{\text{2mol.SiO}}_{\text{2}}}{{\text{1mol.SiO}}_{\text{2}}}\times$$\frac{{\text{60.09g.SiO}}_{\text{2}}}{{\text{1mol.SiO}}_{\text{2}}}$

${\text{= 0.314g.SiO}}_{\text{2}}$

Therefore, the mass of silica formed in the reaction is 0.314g.