Q. 7.54 - An Introduction to General, Organic, and Biological Chemistry

Question

Write all of the mole-mole factors for each of the following chemical equations:

a. $2\mathrm{Al}\left(\mathrm{s}\right) + 3{\mathrm{Cl}}_2\left(\mathrm{g}\right) \to 2{\mathrm{AICI}}_3\left(\mathrm{s}\right)$

b.$4\mathrm{HCI}\left(\mathrm{g}\right) + {\mathrm{O}}_2\left(\mathrm{g}\right)\to 2{\mathrm{Cl}}_2\left(\mathrm{g}\right) + 2{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

Step-by-Step Solution

Answer

(a) The mole-mole factors are$\frac{2 \mathrm{mole} \mathrm{Al}}{3 \mathrm{mole} {\mathrm{Cl}}_2},\frac{3 mole C{l}_2}{2 mole AlC{l}_3}and \frac{2 mole AlC{l}_3}{2 mole Al}$.

(b) The mole-mole factors are$\frac{4 \mathrm{mole} \mathrm{HCl}}{1 \mathrm{mole} {\mathrm{O}}_2},\frac{1 mole O_2}{2 mole C{l}_2}and \frac{2 mole C{l}_2}{4 mole HCl}$.

Part (a) Step 1: Given Information

We are given the equation and we have to find the mole-mole factors.

Part (a) Step 2: Explanation

In the given equation, there are ways to find mole factors by considering two compounds every time.

Consider,$Al and C{l}_2$

$2$mole Al=data-custom-editor="chemistry" $3$ mole data-custom-editor="chemistry" ${\mathrm{Cl}}_2$

which gives the data-custom-editor="chemistry" $\frac{2 \mathrm{mole} \mathrm{Al}}{3 \mathrm{mole} {\mathrm{Cl}}_2}$mole-mole factor.

Now considerdata-custom-editor="chemistry" ${\mathrm{Cl}}_2 \mathrm{and} {\mathrm{AlCl}}_3$

$3$ mole$C{l}_2=2$  mole data-custom-editor="chemistry" ${\mathrm{AlCl}}_3$

which gives the data-custom-editor="chemistry" $\frac{3 \mathrm{mole} {\mathrm{Cl}}_2}{2 \mathrm{mole} {\mathrm{AlCl}}_3}$mole-mole factor.

Again, consider data-custom-editor="chemistry" $\mathrm{Al} \mathrm{and} {\mathrm{AlCl}}_3$

data-custom-editor="chemistry" $2$ mole Al=data-custom-editor="chemistry" $2$ mole data-custom-editor="chemistry" ${\mathrm{AlCl}}_3$

which gives the data-custom-editor="chemistry" $\frac{2 \mathrm{mole} {\mathrm{AlCl}}_3}{2 \mathrm{mole} \mathrm{Al}}$mole-mole factor.

Hence, these are the mole-mole factors.

Part (b) Step 1: Given Information

We are given the equation and we have to find the mole-mole factors.

Part (b) Step 2: Explanation

In the given equation, there are ways to find mole factors by considering two compounds every time.

Consider  HCl and ${\mathrm{O}}_2$

$4$mole HCl = $1$mole ${\mathrm{O}}_2$

which gives the$\frac{4 \mathrm{mole} \mathrm{HCl}}{1 \mathrm{mole} {\mathrm{O}}_2}$ mole-mole factor.

Now consider, ${\mathrm{O}}_{2 }\mathrm{and} {\mathrm{Cl}}_2$

$1$mole${\mathrm{O}}_2=2$ mole ${\mathrm{Cl}}_2$

which gives the$\frac{1 \mathrm{mole} {\mathrm{O}}_2}{2 \mathrm{mole} {\mathrm{Cl}}_2}$ mole-mole factor.

Again, consider HCl and ${\mathrm{Cl}}_2$

 $4$mole HCl= $2$mole ${\mathrm{Cl}}_2$

which gives the$\frac{2 \mathrm{mole} {\mathrm{Cl}}_2}{4 \mathrm{mole} \mathrm{HCl}}$ mole-mole factor.

Hence, these are the mole-mole factors.