Chapter 22, Problem 22.56QP

Interpretation Introduction

Interpretation:

Balanced equation for the reaction of phosphorus pentoxide with nitric acid and theoretical yield of dinitrogen pentoxide has to be calculated.

Concept introduction:

Balanced equation

The overall mass of starting materials should be equal to the overall mass of the products.  This is governed by the law of conservation of mass.

Theoretical yield

The yield obtained on a paper by the calculation of reactant amounts taken for that balanced chemical reaction is known as theoretical yield.

Answer to Problem 22.56QP

• Balanced equation for the reaction of phosphorus pentoxide with nitric acid

${\text{4HNO}}_{\text{3}}{}_{\left(\text{aq}\right)}\text{+}{\text{P}}_{\text{4}}{\text{O}}_{\text{10}}{}_{\left(\text{s}\right)}\to {\text{2N}}_{\text{2}}{\text{O}}_{\text{5}}{}_{\left(\text{s}\right)}\text{+}{\text{4HPO}}_{\text{3}}{}_{\left(\text{l}\right)}$

• The theoretical yield of dinitrogen pentoxide produced from $\text{79}\text{.4}\text{g}$ of phosphorus pentoxide with nitric acid is $\text{60}\text{.41}\text{g}\text{of}{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}$

Explanation of Solution

To give: The balanced equation for the reaction of phosphorus pentoxide with nitric acid.

Reaction of phosphorus pentoxide with nitric acid

${\text{4HNO}}_{\text{3}}{}_{\left(\text{aq}\right)}\text{+}{\text{P}}_{\text{4}}{\text{O}}_{\text{10}}{}_{\left(\text{s}\right)}\to {\text{2N}}_{\text{2}}{\text{O}}_{\text{5}}{}_{\left(\text{s}\right)}\text{+}{\text{4HPO}}_{\text{3}}{}_{\left(\text{l}\right)}$

Dinitrogen pentoxide is produced from the reaction of phosphorus pentoxide with nitric acid.  The overall mass of the reactants is equal to the overall mass the products.

To calculate: The theoretical yield of dinitrogen pentoxide produced from $\text{79}\text{.4}\text{g}$ of phosphorus pentoxide with nitric acid.

The amount of phosphorus pentoxide reacted with nitric acid is $\text{79}\text{.4}\text{g}$.

$\begin{array}{l}\text{Theoretical}\text{yield}\\ \text{=}\text{reactant}\text{amount(g)}\text{×}\left(\frac{\text{1mol}\text{of}\text{reatant}}{\text{molar}\text{mass}\text{of}\text{reatant}}\right)\text{×}\left(\text{mole}\text{ratio}\frac{\text{product}}{\text{reactant}}\right)\text{×}\left(\frac{\text{molar}\text{mass}\text{of}\text{product}}{\text{1}\text{mole}\text{of}\text{product}}\right)\end{array}$

Molar mass of phosphorus pentoxide $\left({\text{P}}_{\text{4}}{\text{O}}_{\text{10}}\right)$ is $\text{283}\text{.9}\text{g}$

Molar mass of dinitrogen pentoxide $\left({\text{N}}_{\text{2}}{\text{O}}_{\text{5}}\right)$ is $\text{108}\text{g}$

Substitute these values into the theoretical yield calculation formula

$\begin{array}{l}{\text{Theoretical yield of N}}_{\text{2}}{\text{O}}_{\text{5}}\text{=}\text{79}\text{.4}\text{g}\left(\frac{\text{1}\text{mole}\text{of}{\text{P}}_{\text{4}}{\text{O}}_{\text{10}}}{\text{283}\text{.9}\text{g}}\right)\text{×}\left(\frac{\text{2}\text{mole}\text{of}{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}}{\text{1}\text{mole}\text{of}{\text{P}}_{\text{4}}{\text{O}}_{\text{10}}}\right)\text{×}\left(\frac{\text{108}\text{g}\text{of}{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}}{\text{1}\text{mole}\text{of}{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}}\right)\\ \text{=}\left(\text{79}\text{.4}\text{×}\left(\frac{\text{2}\text{×}\text{108}}{\text{283}\text{.9}}\right)\right)\text{grams}\\ \text{=}\left(\text{79}\text{.4}\text{×}\text{0}\text{.7608}\right)\text{grams}\\ \text{=}\text{60}\text{.41}\text{grams}\end{array}$

The theoretical yield of dinitrogen pentoxide produced from $\text{79}\text{.4}\text{g}$ of phosphorus pentoxide with nitric acid is $\text{60}\text{.41}\text{g}\text{of}{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}$

By using molar mass of the reactants and products the theoretical yield of dinitrogen pentoxide produced from the reaction of $\text{79}\text{.4}\text{g}$ of phosphorus pentoxide with nitric acid was found as $\text{60}\text{.41}\text{g}\text{of}{\text{N}}_{\text{2}}{\text{O}}_{\text{5}}$

Conclusion

Balanced equation for the reaction of phosphorus pentoxide with nitric acid and theoretical yield of dinitrogen pentoxide was calculated.