Chapter 4, Problem 4.80PAE

4.80 The reaction shown below is used to destroy Freon-12 (CF₂Cl₂), preventing its release into the atmosphere. What mass of NaF will be formed if 250.0 kg of CF₂Cl₂ and 400.0 kg of Na₂C₂O₄ are heated and allowed to react to completion?

   ${\text{CF}}_{\text{2}}{\text{Cl}}_{\text{2}}+{\text{ 2 Na}}_{\text{2}}{\text{C}}_{\text{2}}{\text{O}}_{\text{4}}\to \text{ 2 NaF }+\text{ 2 NaCl }+\text{ C }+{\text{ 4CO}}_{\text{2}}$

Interpretation Introduction

Interpretation:

To calculate the mass of sodium fluoride required for the process.

Concept introduction:

• Use the stoichiometric ratios in order to verify the total amount of moles
• Use molar masses to calculate mass and moles.

Answer to Problem 4.80PAE

Solution:

$125.31kg$

Given:

$\begin{array}{l} m=250.0kgofC{F}_{2}C{l}_2\hfill \\ m=400.0kgofN{a}_2{C}_2{O}_4\hfill \end{array}$

Explanation of Solution

Use stoichiometry to relate the amounts of moles of $C{F}_{2}C{l}_2$ and phosphoric acid. Then use molar masses to calculate the mass of each material.

Verify the limiting reactant, and base the final calculation of sodium fluoride with the given species.

1^st step. Calculate moles of each species

$\begin{array}{l}molC{F}_{2}C{l}_2=\frac{mass}{molarmass}=\frac{\left(250.0kg\right)}{120.91kg/kmol}=2.067kmol\hfill \\ molN{a}_2{C}_2{O}_4=\frac{mass}{molarmass}=\frac{\left(\mathrm{400.0.0}kg\right)}{134.0kg/kmol}=2.985kmol\hfill \end{array}$

2^nd step. Verify ratio of species

$\begin{array}{l} 2molofN{a}_2{C}_2{O}_4=1molofC{F}_{2}C{l}_2 \hfill \\ 2.985kmolofN{a}_2{C}_2{O}_4=1.4925kmolofC{F}_{2}C{l}_2\hfill \\ Clearly,N{a}_2{C}_2{O}_{4}islimitingthereaction,C{F}_{2}C{l}_{2}isinexcess\hfill \end{array}$

$$

3^rd step: Calculate moles of NaF required .

$\begin{array}{l}2molofN{a}_2{C}_2{O}_4=2molofNaF\hfill \\ 2.985kmolofN{a}_2{C}_2{O}_4=2.985kmolofNaF\hfill \end{array}$

4^th step: Calculate mass of NaF

$\begin{array}{l}Mass=mol\text{ x (Molar}Mass)\hfill \\ Mass=(2.985 kmolofNaF)\text{x}\left(41.98g/mol\right)\hfill \\ Mass=125.31kg\hfill \end{array}$

Conclusion

The total mass of NaF produced to for this process is $125.31kg$