Q. 7.62 - An Introduction to General, Organic, and Biological Chemistry

Question

Iron(III) oxide reacts with carbon to give iron and carbon monoxide.

$F{e}_2{O}_3\left(s\right)+3C\left(s\right)\to 2Fe\left(s\right)+3CO\left(g\right)$

a. How many grams of $C$ are required to react with $16.5 \mathrm{g}$ of $F{e}_2{O}_3?$

b. How many grams of $CO$ are produced when$36.0 \mathrm{g}$ of $C$reacts ?

c. How many grams of Fe can be produced when $6.00 \mathrm{g}$of $F{e}_2{O}_3$ reacts?

Step-by-Step Solution

Answer

(a) The$3.6 \mathrm{g} \mathrm{C}$ grams are required to react with $16.5 \mathrm{g}$of $F{e}_2{O}_{3.}$

(b) The $84 \mathrm{g} \mathrm{CO}$ produced when $36.0 \mathrm{g}$of $C$ reacts

(c) The $4.254 \mathrm{g} \mathrm{Fe}$can be produced when $6.00 \mathrm{g}$of $F{e}_2{O}_3$ reacts.

Part(a) Step 1: Given information

We have to find out the how many grams of $C$required to react with $16.5 \mathrm{g}$of $F{e}_2{O}_3$.

Part(a) Step 2: Explanation

Now, we find the solution of this questions,

$165 \mathrm{g} {\mathrm{Fe}}_2{\mathrm{O}}_3$ reacts with $36 \mathrm{g} \mathrm{C}$,

$1 \mathrm{g} {\mathrm{Fe}}_2{\mathrm{O}}_3$ reacts with $\frac{36 \cancel{\mathrm{g}}}{165 \cancel{\mathrm{g}}} \mathrm{C}$,

So, $16.5 \mathrm{g} {\mathrm{Fe}}_2{\mathrm{O}}_3$ reacts with $\frac{36 \cancel{\mathrm{g} }\times 16.5 \mathrm{g}}{165 \cancel{\mathrm{g}}} \mathrm{C}$,

$=3.6 \mathrm{g} \mathrm{C}$

Part(b) Step 1: Given information

We have to find out the how many grams of $CO$are produced when $36.0 \mathrm{g}$of $C$reacts.

Part(b) Step 2: Explanation

Now, we solve this question,

$F{e}_2{O}_3\left(s\right)+3C\left(s\right)\to 2Fe\left(s\right)+3CO\left(g\right)$,

$1 \mathrm{mol} \mathrm{C}=12 \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.$,

$3 \mathrm{mol} \mathrm{C}=12 \frac{\mathrm{g}}{\cancel{\mathrm{mol}}} \times 3 \cancel{\mathrm{mol}}=36 \mathrm{g}$,

So, $36 \mathrm{g} \mathrm{C}$produced $84 \mathrm{g} \mathrm{CO}$.

Part(c) Step 1: Given information

We have to find out the how many grams of $Fe$can be produced when $6.00 \mathrm{g}$of ${\mathrm{Fe}}_2{\mathrm{O}}_3$ reacts.

Part(c) Step 2: Explanation

We know that

$165 \mathrm{g} {\mathrm{Fe}}_2{\mathrm{O}}_3$ produces $117 \mathrm{g} \mathrm{Fe}$,

$1 \mathrm{g} {\mathrm{Fe}}_2{\mathrm{O}}_3$ produces $\frac{175 \cancel{\mathrm{g}}}{165 \cancel{\mathrm{g}}} \mathrm{Fe}$,

$\therefore 6 \mathrm{g} {\mathrm{Fe}}_2{\mathrm{O}}_3$ produces $\frac{117 \cancel{\mathrm{g} }\times 6 \mathrm{g}}{165 \cancel{\mathrm{g}}} \mathrm{Fe}$,

$=4.254 \mathrm{g} \mathrm{Fe}$.