Question

Various nitrogen oxides, as well as sulfur oxides, contribute to acidic rainfall through complex reaction sequences. Nitrogen and oxygen combine during the 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 \(1350 \mathrm{t}\) of atmospheric nitrogen is consumed \((1 \mathrm{t}=1000 \mathrm{~kg}) ?\)

Short answer

6065 metric tons of HNO_3 forms when 1350 metric tons of N_2 are consumed.

Step-by-step solution

Write the Combustion Reaction Equation

When nitrogen (N_2) and oxygen (O_2) react at high temperatures, nitrogen monoxide (NO) is formed. The balanced chemical equation for this reaction is: \(N_2(g) + O_2(g) \rightarrow 2NO(g)\)

Write the Reaction of NO with Oxygen

Nitrogen monoxide (NO) further reacts with oxygen (O_2) to form nitrogen dioxide (NO_2). The balanced chemical equation for this reaction is: \(2NO(g) + O_2(g) \rightarrow 2NO_2(g)\)

Write the Reaction of NO_2 with Water Vapor

Nitrogen dioxide (NO_2) reacts with water vapor (H_2O) to form nitric acid (HNO_3) and nitrogen monoxide (NO). The balanced chemical equation for this reaction is: \(3NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g)\)

Write the Overall Balanced Equation

We need to eliminate the intermediates NO and NO_2 to get the overall reaction. Adding the equations from previous steps:\(N_2(g) + O_2(g) \rightarrow 2NO(g)\)\(2NO(g) + O_2(g) \rightarrow 2NO_2(g)\)\(3NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g)\)We see that NO and NO_2 cancel out:\(N_2 + 2O_2 + H_2O \rightarrow 2HNO_3\)

Calculate the Mass of HNO_3 Formed

Calculate the molar mass of nitrogen (N_2) and nitric acid (HNO_3):\(M_{N_2} = 28.02 \mathrm{g/mol}\)\(M_{HNO_3} = 63.02 \mathrm{g/mol}\)From the balanced equation, 1 mole of N_2 produces 2 moles of HNO_3. Convert 1350 t of N_2 to kilograms, then find the number of moles:\(1350 \mathrm{t} \times 1000 = 1350000 \mathrm{kg}\)\(n_{N_2} = \frac{1350000}{28.02} \approx 48107 \mathrm{mol}\)Calculate moles of HNO_3:\(n_{HNO_3} = 2 \times 48107 \mathrm{mol} = 96214 \mathrm{mol}\)Convert moles of HNO_3 to mass in kg:\(m_{HNO_3} = 96214 \times 63.02 \approx 6065051 \mathrm{kg}\)Convert kg to metric tons:\(6065051 \mathrm{kg} \div 1000 \approx 6065 \mathrm{t}\)

Key concepts

Nitrogen Oxides

Nitrogen oxides are a group of gases that are primarily formed during high-temperature combustion. The main nitrogen oxides in the atmosphere are nitrogen monoxide (NO) and nitrogen dioxide (NO₂). These gases play a significant role in the formation of acid rain.

In combustion processes like those in car engines or power plants, nitrogen and oxygen from the air combine to form NO. The balanced equation for this reaction is: \( N_2(g) + O_2(g) \rightarrow 2NO(g) \). NO can further react with more oxygen to produce NO₂: \( 2NO(g) + O_2(g) \rightarrow 2NO_2(g) \). Understanding these reactions helps us comprehend the broader impact of these gases, such as in forming acid rain and affecting air quality.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products. They are represented by chemical equations that show which substances react and what they produce. For instance, the reactions of NO with O₂ and NO₂ with H₂O are typical chemical processes in atmospheric chemistry.

These reactions can often be complex and occur in sequences. Take the formation of nitric acid (HNO₃) from nitrogen oxides, for example. NO₂ reacts with water vapour to produce HNO₃ and NO: \( 3NO_2(g) + H_2O(l) \rightarrow 2HNO_3(aq) + NO(g) \). Understanding chemical reactions allows us to predict the products formed and their impacts.

Balancing Equations

Balancing chemical equations is crucial to accurately describing chemical reactions. Each side of the equation must represent the same quantity of each element, ensuring the law of conservation of mass is respected.

For the reaction where nitrogen and oxygen form nitrogen monoxide: \( N_2(g) + O_2(g) \rightarrow 2NO(g) \), we see that one nitrogen molecule reacts with one oxygen molecule to produce two molecules of NO. Similarly, for the reaction where NO forms NO₂: \( 2NO(g) + O_2(g) \rightarrow 2NO_2(g) \), the amounts of reactants and products must balance out. This ensures we're correctly representing the chemical phenomena.

Stoichiometry

Stoichiometry helps us understand the quantitative relationships between reactants and products in a chemical reaction. It’s essential for calculations like in step 5 of the exercise, where we determine the amount of HNO₃ formed from N₂.

Using stoichiometry, we know one mole of N₂ produces two moles of HNO₃. Therefore, converting metric tons of N₂ to moles using its molar mass, and then using that to find the moles of HNO₃, illustrates these relationships. This allows us to accurately determine the mass of products formed from a given amount of reactants.

Molar Mass Calculation

Molar mass calculation is essential for converting between mass and moles of a substance. Molar mass is the mass of one mole of a substance, typically measured in grams per mole (g/mol).

For example, the molar masses of nitrogen (N₂) and nitric acid (HNO₃) are 28.02 g/mol and 63.02 g/mol, respectively. Given the mass of N₂, we convert to moles by dividing by its molar mass: \( n_{N_2} = \frac{mass}{molar \text{ mass}} \). These moles can then be used to find the moles of HNO₃ produced, illustrating the importance of molar mass in chemical calculations.