Respuesta :
Answer:
[tex]\boxed{\text{(a) 2.85 mol; (b) 21.7 g; (c) 712 g}}[/tex]
Explanation:
We will need a balanced chemical equation with molar masses, volumes, and concentrations, so, let's gather all the information in one place.
M_r: 65.01 28.01
2NaN₃(s) ⟶ 2Na(s) + 3N₂(g)
n/mol: 1.90
m/g: 14.0
(a) Moles of N₂
The molar ratio is 3 mol N₂ = 2 mol NaN₃
[tex]\text{Moles of N}_{2} = \text{1.90 mol NaN$_{3}$}\times \dfrac{\text{3 mol N}_{2}}{\text{2 mol NaN$_{3}$}}= \textbf{2.85 mol N}_{2}\\\\\text{The reaction produces $\boxed{\textbf{2.85 mol N}_{2}}$}[/tex]
(b) Mass of NaN₃
(i) Moles of N₂
[tex]\text{Moles of N}_{2} = \text{14.0 g N}_{2} \times \dfrac{\text{1 mol N}_{2}}{\text{ 28.01 g N}_{2}} = \text{0.4998 mol N}_{2}[/tex]
(ii) Moles of NaN₃
[tex]\text{Moles of NaN}_{3} =\text{0.4998 mol N}_{2} \times \dfrac{\text{2 mol NaN}_{3}}{\text{3 mol N}_{2}} = \text{0.3332 mol NaN}_{3}[/tex]
(iii) Mass of NaN₃
[tex]\text{Mass of NaN}_{3} = \text{0.3332 mol NaN}_{3} \times \dfrac{\text{65.01 g NaN}_{3}}{\text{1 mol NaN}_{3}} =\textbf{21.7 g NaN}_{3}\\\\\text{You must use }\boxed{\textbf{21.7 g NaN}_{3}}[/tex]
(c)Mass of NaN₃
(i) Volume of N₂
[tex]V = \text{13.0 ft}^{3} \times \dfrac{\text{28.32 L}}{\text{1 ft}^{3}} = \text{368.2 L}[/tex]
(ii) Mass of N₂
[tex]\text{Mass of N}_{2} = \text{368.2 L N}_{2} \times \dfrac{\text{1.25 g N}_{2}}{\text{1 L N}_{2}} = \text{460.2 g N}_{2}[/tex]
(iii) Moles of N₂
[tex]\text{Moles of N}_{2} = \text{460.2 g N}_{2} \times \dfrac{\text{1 mol N}_{2}}{\text{ 28.01 g N}_{2}} = \text{16.43 mol N}_{2}[/tex]
(iv) Moles of NaN₃
[tex]\text{Moles of NaN}_{3} =\text{16.43 mol N}_{2} \times \dfrac{\text{2 mol NaN}_{3}}{\text{3 mol N}_{2}} = \text{10.95 mol NaN}_{3}[/tex]
(v) Mass of NaN₃
[tex]\text{Mass of NaN}_{3} = \text{10.95 mol NaN}_{3} \times \dfrac{\text{65.01 g NaN}_{3}}{\text{1 mol NaN}_{3}} =\textbf{712 g NaN}_{3}\\\\\text{You must use }\boxed{\textbf{712 g NaN}_{3}}[/tex]
The moles of nitrogen gas produced is 2.85 moles.
21.6 grams of sodium azide will be required.
709 grams of sodium azide will be required.
Given:
An automotive airbag inflates when sodium azide decomposes.
The decomposition reaction:
[tex]2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)[/tex]
To find:
(a) The moles of [tex]N_2[/tex] produced by the decomposition of 1.90 mol of [tex]NaN_3[/tex].
(b) Grams of [tex]NaN_3[/tex] are required to form 14.0 grams of nitrogen gas
(c) Grams of [tex]NaN_3[/tex] are required to produce [tex]13.0 ft^3[/tex] of nitrogen gas if the gas has a density of 1.25 g/L.
Solution:
(a)
[tex]2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)[/tex]
Moles of sodium azide = 1.90 mol
According to reaction, 2 moles of sodium azide gives 3 moles of nitrogen gas, then 1.90 moles of sodium azide will give:
[tex]=\frac{3}{2}\times 1.90 mol=\text{2.85 mol of }N_2[/tex]
The moles of nitrogen gas produced is 2.85 moles.
(b)
[tex]2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)[/tex]
Mass of nitrogen gas = 14.0 g
Moles of nitrogen gas = [tex]\frac{14.0 g}{28.0134 g/mol}=0.500 mol[/tex]
According to the reaction, 3 moles of nitrogen gas are obtained from 2 moles of sodium azide, then 0.500 moles of nitrogen gas will be obtained from:
[tex]=\frac{2}{3}\times 0.500 mol=0.333\text{ mol of }NaN_3[/tex]
Mass of 0.333 moles of sodium azide:
[tex]=0.333 mol\times 65.0099 g/mol=21.6 g[/tex]
21.6 grams of sodium azide will be required.
(c)
[tex]2NaN_3(s)\rightarrow 2Na(s)+3N_2(g)[/tex]
The volume of nitrogen gas = V = [tex]13.0 ft^3[/tex]
[tex]1 ft^3=28.317 L\\V=13.0ft^3=13.0\times 28.317 L=368L[/tex]
The density of the nitrogen gas = d = 1.25 g/L
The mass of nitrogen gas = m
[tex]d=\frac{m}{v}\\1.25 g/L=\frac{m}{368 L}\\m=1.25 g/L\times 368 =460g[/tex]
Mass of nitrogen gas = 460 g
Moles of nitrogen gas =[tex]\frac{460g}{28.0134 g/mol}=16.4mol[/tex]
According to the reaction, 3 moles of nitrogen gas are obtained from 2 moles of sodium azide, then 16.4 moles of nitrogen gas will be obtained from:
[tex]=\frac{2}{3}\times 16.4mol=10.9\text{ mol of }NaN_3[/tex]
Mass of 10.9 moles of sodium azide:
[tex]=10.9mol\times 65.0099 g/mol=708.60g\approx 709g[/tex]
709 grams of sodium azide will be required.
Learn more about the unitary method here:
brainly.com/question/2499283?referrer=searchResults
brainly.com/question/2500793?referrer=searchResults
