15. determine the percent - composition by mass of zn in zn(oh)₂.\n16. given the equation: si + ga →…

Explanation:

Step1: Calculate molar mass of (Zn(OH)_2)

The molar mass of (Zn = 65.38\ g/mol), (O=16\ g/mol), (H = 1.01\ g/mol). For (Zn(OH)_2), (M = 65.38+2\times(16 + 1.01)=65.38+2\times17.01=65.38 + 34.02=99.4\ g/mol).

Step2: Calculate percent - mass of (Zn) in (Zn(OH)_2)

The percent - mass of (Zn) is (\frac{65.38}{99.4}\times100%). [ \begin{align*} \frac{65.38}{99.4}\times100%&=\frac{6538}{99.4}%\ &\approx65.8% \end{align*} ]

Step3: Balance the reaction (Si+Ga\rightarrow Ga_5Si_3)

The balanced equation is (3Si + 5Ga\rightarrow Ga_5Si_3).

Step4: Calculate moles of (Si)

The molar mass of (Si) is (M_{Si}=28.09\ g/mol). The number of moles of (Si), (n_{Si}=\frac{m}{M}=\frac{96\ g}{28.09\ g/mol}\approx3.42\ mol).

Step5: Calculate moles of (Ga_5Si_3) formed

From the balanced equation, the mole - ratio of (Si) to (Ga_5Si_3) is (3:1). So the number of moles of (Ga_5Si_3) formed, (n_{Ga_5Si_3}=\frac{3.42\ mol}{3}=1.14\ mol).

Step6: Calculate molar mass of (Ga_5Si_3)

The molar mass of (Ga = 69.72\ g/mol), (Si = 28.09\ g/mol). (M_{Ga_5Si_3}=5\times69.72+3\times28.09=348.6+84.27 = 432.87\ g/mol).

Step7: Calculate mass of (Ga_5Si_3) formed

(m_{Ga_5Si_3}=n_{Ga_5Si_3}\times M_{Ga_5Si_3}=1.14\ mol\times432.87\ g/mol\approx493\ g).

Answer:

The percent - composition by mass of (Zn) in (Zn(OH)_2) is approximately (65.8%). The mass of (Ga_5Si_3) formed when 96 grams of (Si) reacts is approximately (493\ g).