To determine the number of moles of silicon in the sample, we need to use the stoichiometric relationship between magnesium (Mg) and silicon (Si) in the chemical formula for talc, \( \text{Mg}_3(\text{Si}_2\text{O}_5)_2(\text{OH})_2 \).
The formula indicates that 3 moles of magnesium (\( \text{Mg} \)) are associated with 4 moles of silicon (\( \text{Si} \)) because:
\[ \text{Mg}_3(\text{Si}_2\text{O}_5)_2(\text{OH})_2 \]
shows \( \text{Mg}_3 \) (3 moles of Mg) and \( \text{Si}_2 \) twice (which makes \( 2 \times 2 = 4 \) moles of Si in the entire formula unit).
Given:
\[ \text{Moles of magnesium (Mg)} = 0.0725 \, \text{moles} \]
Using the stoichiometric ratio, we find the moles of silicon (\( \text{Si} \)):
\[ \frac{4 \, \text{moles of Si}}{3 \, \text{moles of Mg}} = x \, \text{moles of Si} \]
where \( x \) represents the moles of silicon (Si) in our sample based on the number of moles of magnesium (Mg) given.
Setting up the proportion, we get:
\[ x = 0.0725 \, \text{moles of Mg} \times \frac{4 \, \text{moles of Si}}{3 \, \text{moles of Mg}} \]
Calculating \( x \):
\[ x = 0.0725 \, \text{moles} \times \frac{4}{3} \]
\[ x = 0.0725 \times 1.3333 \ldots \] (repeating 3)
Perform the multiplication:
\[ x \approx 0.09667 \]
Considering significant figures, the number 0.0725 has three significant figures. Therefore, our result should also be expressed with three significant figures:
\[ x \approx 0.0967 \, \text{moles of Si} \]
Thus, the number of moles of silicon in the sample is \( 0.0967 \) moles.
This is the chemical formula for talc
Mg3(Si2O5)2(OH)2
An analytical chemist has determined by measurements that there are 0.0725 moles of magnesium in a sample of talc. How many moles of silicon are in the sample?
Be sure your answer has the correct number of significant digits.
1 answer