Question

Pure carbon was burned in an excess of oxygen. The gaseous products were

$\begin{array}{l}{\mathbf{\text{CO}}}_{\mathbf{\text{2}}}\mathbf{72}\mathbf{.0}\mathbf{\text{\hspace{0.17em}mol}}\mathbf{\%}\\ \mathbf{\text{CO\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}}\mathbf{16}\mathbf{.0}\mathbf{\text{\hspace{0.17em}mol\%}}\\ {\mathbf{\text{O}}}_{\mathbf{2}}\mathbf{\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}}\mathbf{12}\mathbf{.0}\mathbf{\text{\hspace{0.17em}mol\%}}\end{array}$

How many moles of${\mathbf{\text{O}}}_{\mathbf{2}}$ were present in the initial reaction mixture for every mole of carbon?

Short answer

$1.5$moles of ${\text{O}}_2$were present in the initial reaction mixture for every mole of carbon

Step-by-step solution

Definition of mole

$6.02214076\times {10}^{23}$of some chemical unit, like atoms molecules ions or others is defined as mole

Find the ratio of the reaction

The reaction here is$3C\left(s\right)+3O_2\left(g\right)\to C{O}_2\left(g\right)+2CO\left(g\right)+O_2\left(g\right)$

$\begin{array}{l}n\left(C\right):n\left(O_2\right)=3:3\\ =1:1\end{array}$

Calculation of the moles of C and O

If there are 100 moles of products, then calculate the moles of $C$and $O$in every molecules, that is

data-custom-editor="chemistry" $72.0\text{mol}+16\text{mol}=88\text{\hspace{0.17em}moles\hspace{0.17em}of\hspace{0.17em}C}$and

data-custom-editor="chemistry" $2\times 72.0mol+16.0\text{mol}+2\times 12\text{mol}=184\text{\hspace{0.17em}moles\hspace{0.17em}of\hspace{0.17em}O}$

The ratio is

data-custom-editor="chemistry" $\begin{array}{l}n\left(0\right):n\left(C\right)=184\text{mol\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}:88\text{mol}\\ =2.09\text{mol}:1\text{mol}\end{array}$

So,

data-custom-editor="chemistry" $\begin{array}{c}n\left(O_2\right):n\left(C\right)=\frac{184\text{mol}}{2}:88\text{mol}\\ =1.45\text{mol}:1\text{mol}\end{array}$

data-custom-editor="chemistry" $1.5$moles ofdata-custom-editor="chemistry" ${\text{O}}_2$ were present in the initial reaction mixture for every mole of carbon