# Question 8d737

Mar 30, 2015

This reaction will consume $\text{1.01 g}$ of carbon.

Start with the balanced chemical equation for this reaction (this is a carbothermic reaction)

$N {a}_{2} S {O}_{4 \left(s\right)} + \textcolor{red}{2} {C}_{\left(s\right)} \to N {a}_{2} {S}_{\left(s\right)} + 2 C {O}_{2 \left(g\right)}$

Notice that you have a $1 : \textcolor{red}{2}$ mole ratio between sodium sulfate and carbon, which means that every mole of sodium sulfate that reacts needs twice as many moles of carbon.

In other words, regardless of how many moles of sodium sulfate react, you'll always need two times more moles of carbon for the reaction to take place.

Use sodium sulfate's molar mass to determine how many moles you have in 6.00 g

6.00cancel("g") * "1 mole"/(142.04cancel("g")) = "0.04224 moles" $N {a}_{2} S {O}_{4}$

According to the mole ratio, you'll need

0.04224cancel("moles "Na_2SO_4) * "2 moles C"/(cancel("1 mole "Na_2SO_4)) = "0.08448 moles C"

Now use carbon's molar mass to see how many grams you'd need

0.08448cancel("moles C") * "12.011 g"/cancel("1 mole C") = "1.0147 g C"#

Rounded to three sig figs, the answer will be

${m}_{\text{C") = color(green)("1.01 g}}$