Question

how many moles of iron(iii) oxide are required to completely react with 1.40 x 10^22 atoms of carbon in the following reaction? fe2o3 + 3c → 2fe + 3co 0.00775 mol 0.0697 mol 0.0232 mol 4.67 x 10^21 mol

Explanation:

Step1: Calculate moles of carbon

Use Avogadro's number ($N_A = 6.022\times 10^{23}\text{ atoms/mol}$). Moles of carbon $n_C=\frac{N_C}{N_A}$, where $N_C = 1.40\times 10^{22}$ atoms. So $n_C=\frac{1.40\times 10^{22}\text{ atoms}}{6.022\times 10^{23}\text{ atoms/mol}}\approx0.02325\text{ mol}$.

Step2: Determine mole - ratio from balanced equation

From the balanced equation $\text{Fe}_2\text{O}_3 + 3\text{C}\longrightarrow2\text{Fe}+3\text{CO}$, the mole - ratio of $\text{Fe}_2\text{O}_3$ to $\text{C}$ is $\frac{n_{\text{Fe}_2\text{O}_3}}{n_C}=\frac{1}{3}$.

Step3: Calculate moles of $\text{Fe}_2\text{O}_3$

$n_{\text{Fe}_2\text{O}_3}=\frac{1}{3}n_C$. Substitute $n_C = 0.02325\text{ mol}$ into the equation, $n_{\text{Fe}_2\text{O}_3}=\frac{1}{3}\times0.02325\text{ mol}= 0.00775\text{ mol}$.

Answer:

0.00775 mol