Q3.65P - Chemistry: Molecular Nature Of Matter And Change

Question

Potassium nitrate decomposes on heating, producing potassium oxide and gaseous nitrogen and oxygen: 

$\mathbf{4}\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}\left(s\right)\mathbf{\to }\mathbf{2}{\mathit{K}}_{\mathbf{2}}\mathit{O}\left(s\right)\mathbf{+}\mathbf{2}{\mathit{N}}_{\mathbf{2}}\left(g\right)\mathbf{+}{\mathbf{50}}_{\mathbf{2}}\left(g\right)$

To produce 56.6 kg of oxygen, how many 

(a) Moles of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$ must be heated?

(b) Grams of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$ must be heated?

Step-by-Step Solution

Answer

Answer

1. The number of moles of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$ is $\mathbf{1}\mathbf{.}\mathbf{41}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}\mathbf{.}$

2. The mass of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$ is $\mathbf{1}\mathbf{.}\mathbf{43}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathit{g}\mathbf{.}$

Step 1: Relation between the number of moles of K N O 3 and O 2

In the given reaction, 5 mol of ${\mathit{O}}_{\mathbf{2}}$ are formed from 4 mol of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}$

Thus,

$$\begin{gathered} \mathbf{5}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }{\mathit{O}}_{\mathbf{2}}\mathbf{=}\mathbf{4}\mathit{m}\mathit{o}\mathit{l}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}} \\ \mathbf{1}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }{\mathit{O}}_{\mathbf{2}}\mathbf{=}\frac{\mathbf{4}\mathbf{ }\mathbf{mol}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{KNO}}_{\mathbf{3}}}{\mathbf{5}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{8}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}} \end{gathered}$$

Therefore,1mol of ${\mathit{O}}_{\mathbf{2}}$ is formed by 0.8 mol of $\mathit{K}\mathit{N}{\mathit{O}}_{\mathbf{3}}\mathbf{.}$

Step 2: Relation between mass and number of moles

The number of moles is calculated by the mass and Molar mass. The relationship between the number of moles, mass, and molar mass is given below.

$\mathit{N}\mathit{u}\mathit{m}\mathit{b}\mathit{e}\mathit{r}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}\mathit{e}\mathit{s}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}}{\mathbf{M}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{ }\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}}$

Step 2: Calculate the number of moles of O 2

The mass of ${\mathit{O}}_{\mathbf{2}}$ = 56.6kg = 56600 g.

The molar mass of ${\mathit{O}}_{\mathbf{2}}$ =31.999 g/mol

Thus, the number of moles of ${\mathit{O}}_{\mathbf{2}}$ is:

$\overline{)\begin{array}{ccc}\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{moles}\mathbf{ }\mathbf{of}\mathbf{ }{\mathbf{O}}_{\mathbf{2}}& \mathbf{=}& \frac{\mathbf{mass}}{\mathbf{Molar}\mathbf{ }\mathbf{mass}}\\ & \mathbf{=}& \frac{\mathbf{56600}\mathbf{ }\mathbf{g}}{\mathbf{31}\mathbf{.}\mathbf{999}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{mol}}\\ & \mathbf{=}& \mathbf{1768}\mathbf{.}\mathbf{80528}\mathbf{ }\mathbf{mol}\\ & \mathbf{;}& \mathbf{1768}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{1}\mathbf{mol}\end{array}}$

Step 4: Calculate the number of moles of K N O 3

The number of $KN{O}_3$is:

$\begin{array}{ccc}\mathbf{1}\mathbf{ }\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }{\mathbf{O}}_{\mathbf{2}}& \mathbf{=}& \mathbf{0}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{K}\mathbf{N}{\mathbf{O}}_{\mathbf{3}}\\ \mathbf{1768}\mathbf{.}\mathbf{81}\mathbf{ }\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }{\mathbf{O}}_{\mathbf{2}}& \mathbf{=}& \mathbf{1768}\mathbf{.}\mathbf{81}\mathbf{\times }\mathbf{0}\mathbf{.}\mathbf{8}\mathbf{ }\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{K}\mathbf{N}{\mathbf{O}}_{\mathbf{3}}\\ & \mathbf{=}& \mathbf{1415}\mathbf{.}\mathbf{048}\mathbf{.}\mathbf{048}\mathbf{ }\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{K}\mathbf{N}{\mathbf{O}}_{\mathbf{3}}\end{array}$

Therefore, the number of moles of $KN{O}_3$is approximately $\mathbf{1}\mathbf{.}\mathbf{41}\mathbf{\times }{\mathbf{10}}^{\mathbf{3}}\mathbf{ }\mathit{m}\mathit{o}\mathit{l}\mathbf{.}$

Step 4: Calculate the mass of K N O 3

The mass of $KN{O}_3$is:

$\begin{array}{ccc}\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{s}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{K}\mathbf{N}{\mathbf{O}}_{\mathbf{3}}& \mathbf{=}& \mathbf{m}\mathbf{o}\mathbf{l}\mathbf{e}\mathbf{s}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{K}\mathbf{N}{\mathbf{O}}_{\mathbf{3}}\mathbf{\times }\mathbf{M}\mathbf{o}\mathbf{l}\mathbf{a}\mathbf{r}\mathbf{ }\mathbf{m}\mathbf{a}\mathbf{s}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{K}\mathbf{N}{\mathbf{O}}_{\mathbf{3}}\\ & \mathbf{=}& \mathbf{1415}\mathbf{.}\mathbf{048}\mathbf{ }\mathbf{m}\mathbf{o}\mathbf{l}\mathbf{\times }\mathbf{101}\mathbf{.}\mathbf{1032}\mathbf{ }\mathbf{g}\mathbf{/}\mathbf{m}\mathbf{o}\mathbf{l}\\ & \mathbf{=}& \mathbf{143065}\mathbf{.}\mathbf{881}\mathbf{g}\end{array}$

Therefore, the mass of $KN{O}_3$ is approximately $\mathbf{1}\mathbf{.}\mathbf{43}\mathbf{\times }{\mathbf{10}}^{\mathbf{5}}\mathbf{ }\mathit{g}$