Question

use the following equation to solve the problems below:
3 sio₂ + 4 al → 3 si + 2 al₂o₃
a. if 6.0 moles of sio₂ react, how many moles of:
i. al react?
ii. si are produced?
iii. al₂o₃ are produced?

Explanation:

Step1: Analyze the mole ratio from the balanced equation

From the balanced equation \(3SiO_{2}+4Al
ightarrow3Si + 2Al_{2}O_{3}\), the mole ratio of \(SiO_{2}\) to \(Al\) is \(3:4\), \(SiO_{2}\) to \(Si\) is \(3:3 = 1:1\), and \(SiO_{2}\) to \(Al_{2}O_{3}\) is \(3:2\).

Step2: Calculate moles of \(Al\)

Given \(n(SiO_{2})=6.0\space mol\). Using the mole ratio \(\frac{n(Al)}{n(SiO_{2})}=\frac{4}{3}\), so \(n(Al)=\frac{4}{3}\times n(SiO_{2})\).
Substitute \(n(SiO_{2}) = 6.0\space mol\) into the formula: \(n(Al)=\frac{4}{3}\times6.0\space mol = 8.0\space mol\).

Step3: Calculate moles of \(Si\)

Using the mole ratio \(\frac{n(Si)}{n(SiO_{2})}=1\), so \(n(Si)=n(SiO_{2})\).
Substitute \(n(SiO_{2}) = 6.0\space mol\) into the formula: \(n(Si)=6.0\space mol\).

Step4: Calculate moles of \(Al_{2}O_{3}\)

Using the mole ratio \(\frac{n(Al_{2}O_{3})}{n(SiO_{2})}=\frac{2}{3}\), so \(n(Al_{2}O_{3})=\frac{2}{3}\times n(SiO_{2})\).
Substitute \(n(SiO_{2}) = 6.0\space mol\) into the formula: \(n(Al_{2}O_{3})=\frac{2}{3}\times6.0\space mol = 4.0\space mol\).

Answer:

i. \(8.0\space mol\)
ii. \(6.0\space mol\)
iii. \(4.0\space mol\)