Question

Assume that coal can be represented by the chemical formula \(\mathrm{C}_{135} \mathrm{H}_{96} \mathrm{O}_{9} \mathrm{NS}\). a. What is the percent of nitrogen by mass in coal? b. If 3 tons of coal is burned, what mass of nitrogen in the form of NO is produced? Assume that all of the nitrogen in the coal is converted to NO. c. Actually more NO is produced than you just calculated. Explain.

Short answer

a. 0.66% nitrogen by mass. b. 38,483.13 g NO produced. c. More NO can be produced from atmospheric nitrogen reactions.

Step-by-step solution

Calculate Molar Mass of Coal

First, we need to determine the molar mass of coal, represented by its chemical formula \(\mathrm{C}_{135}\mathrm{H}_{96}\mathrm{O}_{9}\mathrm{NS}\). Calculate the molar mass by adding the atomic masses of each element: \(135(12.01) + 96(1.01) + 9(16.00) + 14.01 + 32.07 = 2123.29\,\text{g/mol}\).

Determine Mass Percent of Nitrogen

Using the molar mass of coal, calculate the percent of nitrogen by mass. The molar mass contribution of nitrogen is \(14.01\,\text{g/mol}\). Thus, the percent of nitrogen in coal is \(\frac{14.01}{2123.29} \times 100\% = 0.66\%\).

Convert Tons of Coal to Grams

3 tons of coal must be converted to grams for the calculation. Since 1 ton is approximately 907,185 grams, 3 tons are \(3 \times 907,185 = 2,721,555\,\text{g}\).

Calculate Mass of Nitrogen in Coal

Using the percent of nitrogen and total mass of coal burned, calculate the mass of nitrogen: \(0.66\% \times 2,721,555\,\text{g} = 17,973.84\,\text{g}\).

Calculate Mass of NO Produced

Assuming all nitrogen converts to NO, calculate the mass of NO produced using the molar ratios. Nitrogen's atomic mass is 14.01 and NO's molar mass is \(14.01 + 16.00 = 30.01\,\text{g/mol}\). Thus, \(17,973.84\,\text{g}\, \text{N} \times \frac{30.01}{14.01} = 38,483.13\,\text{g NO}\).

Explain Additional NO Production

The actual amount of NO produced can often be higher than theoretical calculations due to additional reactions at high combustion temperatures. Not all nitrogen comes from coal; atmospheric nitrogen can also form NO when burning.

Key concepts

Percent Composition

Percent composition helps us understand how much of a specific element is in a compound. In chemistry, it's important to find out what portion of a substance by mass comes from each component. For example, to find the percent composition of nitrogen in coal, you first calculate the molar mass of coal. This involves adding up the atomic masses of all the atoms in the chemical formula. Then, using the mass of nitrogen, you divide it by the total molar mass and multiply by 100 to get the percentage.

• Molar mass of coal = sum of all elements' atomic masses.
• Mass of nitrogen = atomic mass of nitrogen from the formula.
• Percent nitrogen = (mass of nitrogen / molar mass of coal) × 100%

This way, you can see how nitrogen contributes to the total weight of coal.

Combustion Reaction

During a combustion reaction, substances burn in the presence of oxygen, releasing energy. When coal burns, a specific type of combustion reaction happens, often involving complex components and high temperatures. Coal is mainly carbon-based, but it can also include hydrogen, oxygen, nitrogen, and sulfur.

• Combustion of carbon produces carbon dioxide.
• Combustion of hydrogen forms water.
• Nitrogen in coal, when burned, can transform into nitrogen oxides like NO.

The specifics of these reactions include the release of heat and can influence how pollutants form.

Pollutant Formation

Pollutant formation during combustion is a critical aspect as it affects air quality and health. When burning coal, pollutants like nitrogen oxides (NOx) can be produced. These pollutants form when nitrogen present in coal reacts with oxygen during combustion. Factors influencing pollutant formation:

• Temperature: High temperatures can cause more NOx formation.
• Presence of atmospheric nitrogen: Besides coal nitrogen, air nitrogen contributes to NOx.
• Chemical conditions: Varying conditions can result in different types and quantities of pollutants.

Understanding these factors can help in reducing emissions and improving combustion processes.

Chemical Stoichiometry

Chemical stoichiometry involves using balanced chemical equations to understand the relationships between reactants and products in a reaction. This concept helps calculate the quantities of substances involved in chemical reactions. In our coal example, stoichiometry is used to determine how much nitrogen turns into nitric oxide (NO) during combustion.

• Start with the chemical formula to find molar masses.
• Use molar ratios to relate the amounts of reactants and products.
• Calculate using the initial amount of coal to find out the mass of NO produced.

Stoichiometry ensures precise calculations, vital for predicting and measuring reactions in chemical processes.