Question

this is the chemical formula for talc (the main ingredient in talcum powder):

mg₃(si₂o₅)₂(oh)₂

an analytical chemist has determined by measurements that there are 6.90 moles of silicon in a sample of talc. how many moles of hydrogen are in the sample?

round your answer to 3 significant digits.

mol

Explanation:

Step1: Find the ratio of silicon to hydrogen

In the formula \(Mg_3(Si_2O_5)_2(OH)_2\), the number of silicon (\(Si\)) atoms is \(2\times2 = 4\) (from \((Si_2O_5)_2\)), and the number of hydrogen (\(H\)) atoms is \(2\times1= 2\) (from \((OH)_2\)). So the ratio of \(Si:H\) is \(4:2 = 2:1\).

Step2: Calculate the moles of hydrogen

Let \(n_{Si}=6.90\) mol. Using the ratio \(\frac{n_{Si}}{n_{H}}=\frac{2}{1}\). Then \(n_{H}=\frac{n_{Si}}{2}\). Substitute \(n_{Si} = 6.90\) mol into the formula: \(n_{H}=\frac{6.90}{2}\) mol.

Answer:

\(3.45\) mol