How many moles of hydrogen fluoride will react with #5.90# moles of silicon dioxide to produce silicon tetrafluoride?

The key to this problem is the balanced chemical equation for this reaction.

Hydrogen fluoride, #"HF"#, will react with silicon dioxide, #"SiO"_2#, to produce silicon tetrachloride, #"SiF"_4#, and liquid water according to the following chemical equation

#color(red)(4)"HF"_text((g]) + "SiO"_text(2(s]) -> "SiF"_text(4(g]) + 2"H"_2"O"_text((l])#

Notice that you have a #color(red)(4):1# mole ratio between hydrogen fluoride and silicon dioxide.

This tells you that regardless of how many moles of silicon dioxide take part in the reaction, the reaction will always consume #color(red)(4)# times more moles of hydrogen fluoride.

In your case, you need to know how many moles of hydrogen fluoride will be needed to react completely with #5.90# moles of silicon dioxide.

To react completely simply means that all the moles of silicon dioxide must be consumed in the reaction.

So, use the aforementioned mole ratio to get

#5.90color(red)(cancel(color(black)("moles SiO"_2))) * (color(red)(4)" moles HF")/(1color(red)(cancel(color(black)("mole SiO"_2)))) = color(green)("23.6 moles HF")#