How many grams of carbon are needed to react completely with 75.2 g #SiO_2# according to the equation: #SiO_2(s) + 2C(s) -> Si(s) + 2CO(g)#?

The balanced chemical equation given to you tells you the mole ratio that must exist between the two reactants, silicon dioxide, #"SiO"_2#, and carbon, #"C"#

#"SiO"_ (2(s)) + color(red)(2)"C"_ ((s)) -> "Si" _ ((s)) + 2"CO"_ ((g))#

You know by examining this chemical equation that #1# mole of silicon dioxide requires #color(red)(2)# moles of carbon in order to react completely.

The problem provides you with grams of silicon dioxide and asks you to find the number of grams of carbon required to ensure that all the mass of silicon dioxide reacts.

The first thing to do here is use the molar mass of silicon dioxide to convert the mass to moles

#75.2 color(red)(cancel(color(black)("g"))) * "1 mole SiO"_2/(60.08color(red)(cancel(color(black)("g")))) = "1.252 moles SiO"_2#

You can now use the aforementioned mole ratio to find the number of moles of carbon needed

#1.252 color(red)(cancel(color(black)("moles SiO"_2))) * (color(red)(2)color(white)(a) "C")/(1 color(red)(cancel(color(black)("mole SiO"_2)))) = "2.504 moles C"#

Finally, use the molar mass of elemental carbon to see how many grams would contain this many moles

#2.504 color(red)(cancel(color(black)("moles C"))) * "12.011 g"/(1color(red)(cancel(color(black)("mole C")))) = color(green)(|bar(ul(color(white)(a/a)color(black)("30.1 g")color(white)(a/a)|)))#

The answer is rounded to three sig figs.