Q147CP - Chemistry: Molecular Nature Of Matter And Change

Question

Various nitrogen oxides, as well as sulfur oxides, contribute to acidic rainfall through complex reaction sequences. Nitrogen and oxygen combine during high-temperature combustion of fuels in air to form nitrogen monoxide gas, which reacts with more oxygen to form nitrogen dioxide gas. In contact with water vapor, nitrogen dioxide forms aqueous nitric acid and more nitrogen monoxide. (a) Write balanced equations for these reactions. (b) Use the equations to write one overall balanced equation that does not include nitrogen monoxide and nitrogen dioxide. (c) How many metric tons (t) of nitric acid form when 1350 t of atmospheric nitrogen is consumed (1 t = 1000 kg)?

Step-by-Step Solution

Answer

1. The balanced equations are:
   $$\begin{gathered} \left(i\right) N_2\left(g\right)+O_2\left(g\right)\to 2NO\left(g\right) \\ \left(ii\right) 2NO\left(g\right)+O_2\left(g\right)\to 2N{O}_2\left(g\right) \\ \left(iii\right) 2N{O}_2\left(g\right)+H_{2}0\left(I\right)\to 2HN{O}_3\left(g\right)+NO\left(g\right) \end{gathered}$$
   
2. The overall balanced equation is $2N_2\left(g\right)+5O_2\left(g\right)+2H_{2}O\left(I\right)\to 4HN{O}_3\left(g\right)$
3. The mass of HNO₃ is approximately 6072 metric tons.

Step 1: Determine the balanced chemical equation for the formation of nitrogen monoxide gas

When oxygen (O₂) is combined with nitrogen (N₂) at a high temperature, they undergo a combustion reaction and form nitrogen monoxide gas (NO). The balanced chemical equation is:

${\mathit{N}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{+}{\mathit{O}}_{\mathbf{2}}\mathbf{\left(}\mathit{g}\mathbf{\right)}\mathbf{\to }\mathbf{2}\mathit{N}\mathit{O}\mathbf{\left(}\mathit{g}\mathbf{\right)}$

Step 2: Determine the balanced chemical equation for the formation of nitrogen dioxide gas

When nitrogen monoxide gas (NO) is further heated in presence of oxygen (O₂) it forms nitrogen dioxide gas (NO₂) The balanced chemical equation is:

$2NO\left(g\right)+O_2\left(g\right)\to 2N{O}_2\left(g\right)$

Step 3: Determine the balanced chemical equation for the formation of nitric acid

When nitrogen dioxide gas (NO₂) is further reacted with water vapor, nitric acid (HNO₃) is formed. The balanced chemical equation is:

$3N{O}_2\left(g\right)+H_{2}O\left(l\right)\to 2HN{O}_3\left(g\right)+NO\left(g\right)$

Step 4: Write the balanced chemical equation of the overall reaction

The balanced chemical equation of the overall reaction does not include NO and NO₂ is written by reacting nitrogen (N₂) and oxygen (O₂) in presence of water vapor.  Thus, the overall chemical equation is:

$2N_2\left(g\right)+5O_2\left(g\right)+2H_{2}O\left(I\right)\to 4HN{O}_2\left(g\right)$

Step 5: 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.

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

Step 6: Conversion of metric tons into gram

The mass of N₂ = 1350 metric tons.

Since 1 metric ton = 1000 kg

So, 

$\begin{array}{rcl}1metricton& =& 1000\\ 1350metrictons& =& 1350\times 1000\\ & =& 1350\times 1000\times 1000g\end{array}$

Step 7: Calculate the number of moles of N 2

The mass of N₂ = $1350\times {10}^{6}g$

The molar mass of N₂ = 28.02 g/mol

Thus, the number of moles N₂ is:

$\begin{array}{rcl}Number of moles of N_2& =& \frac{mass of N_2}{Molar massof N_2}\\ & =& \frac{1350\times {10}^{6}g}{28.02g/mol}\\ & =& 48.18\times {10}^{6}mol\end{array}$

Step 8: Calculate the number of moles of nitric acid HNO 3

In the reaction, 2 mol of N₂ formed 4 mol of HNO₃Thus,

$\begin{array}{rcl}2mol of N_2& =& 4mol of HN{O}_3\\ 48.18\times {10}^{6}mol of N_2& =& 48.18\times {10}^6\times \frac{4}{2}mol of HN{O}_3\\ & =& 96.36\times {10}^{6}mol of HN{O}_3\end{array}$

Step 9: Calculate the mass of HNO 3

The molar mass of HNO₃  = 63.01 g/mol

Thus, the mass of HNO₃ is:

$\begin{array}{rcl}mass of HN{O}_3& =& mole of HN{O}_3\times molar mass of HN{O}_3\\ & =& 48.18\times {10}^{6}mol\times 63.01g/mol\\ & =& 6071.6436\times {10}^{6}g\end{array}$

Step 10: Conversion of a gram into a metric ton

Since 1 metric ton = 1000 kg

So, 

$\begin{array}{rcl}{10}^{6}g& =& 1metriicto\\ 6071.6436\times {10}^{6}g& =& 6071.6436\times {10}^6\times \frac{1}{{10}^6}metrictons\\ & =& 6071.6436metrictons\end{array}$

Therefore, the mass of HNO₃ is approximately 6072 metric tons.