Question

Spark-ignition engine exhaust gases contain several air pollutants including the oxides of nitrogen, \(\mathrm{NO}\) and \(\mathrm{NO}_{2}\), collectively known as \(\mathrm{NO}_{x}\). Additionally, the exhaust gases may contain carbon monoxide (CO) and unburned or partially burned hydrocarbons (HC). (a) The pollutant amounts actually present depend on engine design and operating conditions, and typically differ significantly from values calculated on the basis of chemical equilibrium. Discuss both the reasons for these discrepancies and possible mechanisms by which such pollutants are formed in an actual engine. (b) For spark-ignition engines, the average production of pollutants upstream of the catalyst, in g per mile of vehicle travel, are nitric oxides, \(1.5\); hydrocarbons, 2 ; and carbon monoxide, 20 . For a city in your locale having a population of 100,000 or more, estimate the annual amount, in \(\mathrm{kg}\), of each pollutant that would be discharged if automobiles had no emission control devices. Repeat if the vehicles adhere to current U.S. government emissions standards.

Short answer

Without control: NOx = 900,000 kg/year, HC = 1,200,000 kg/year, CO = 12,000,000 kg/year. With standards: NOx = 24,000 kg/year, HC = 30,000 kg/year, CO = 2,040,000 kg/year.

Step-by-step solution

Title - Understanding pollutant formation

Discuss why the pollutant amounts from engines differ significantly from values calculated on the basis of chemical equilibrium. Consider factors like engine design, operating conditions, fuel composition, and combustion efficiency. Explain the possible mechanisms through which these pollutants are formed, such as high temperatures leading to NOx formation, incomplete combustion causing CO, and unburned hydrocarbons.

Title - Gathering data

Identify and gather the given data from the problem. The pollutants produced upstream of the catalyst are: nitric oxides (NOx) = 1.5 g/mile, hydrocarbons (HC) = 2 g/mile, carbon monoxide (CO) = 20 g/mile. The population of the city is 100,000 or more.

Title - Estimating annual vehicle travel

Assume an average vehicle travels a certain number of miles per year. Use an estimated figure such as 12,000 miles/year per vehicle for calculation purposes.

Title - Calculating total vehicle travel in city

Estimate the number of vehicles in the city. For simplicity, assume 1 vehicle per 2 people. Therefore, for a city with a population of 100,000, there would be 50,000 vehicles. Multiply this number by the average miles traveled per year: 50,000 vehicles * 12,000 miles/year = 600,000,000 miles/year.

Title - Calculating annual emissions without control devices

Multiply the total miles traveled annually by the pollutant production rates. For nitric oxides: 600,000,000 miles/year * 1.5 g/mile = 900,000,000 g/year. For hydrocarbons: 600,000,000 miles/year * 2 g/mile = 1,200,000,000 g/year. For carbon monoxide: 600,000,000 miles/year * 20 g/mile = 12,000,000,000 g/year. Convert grams to kilograms by dividing by 1,000.

Title - Calculating emissions with current standards

Use the current U.S. government emissions standards for spark-ignition engines, which are significantly lower. For instance, standards might be: NOx = 0.04 g/mile, HC = 0.05 g/mile, CO = 3.4 g/mile. Repeat the calculation with these new figures.

Title - Total annual emissions with standards

Multiply the total miles traveled annually by the new pollutant production rates. For nitric oxides: 600,000,000 miles/year * 0.04 g/mile = 24,000,000 g/year. For hydrocarbons: 600,000,000 miles/year * 0.05 g/mile = 30,000,000 g/year. For carbon monoxide: 600,000,000 miles/year * 3.4 g/mile = 2,040,000,000 g/year. Convert grams to kilograms by dividing by 1,000.

Final Calculations

Without emission control devices: NOx: 900,000,000 g/year = 900,000 kg/year HC: 1,200,000,000 g/year = 1,200,000 kg/year CO: 12,000,000,000 g/year = 12,000,000 kg/year With current emission standards: NOx: 24,000,000 g/year = 24,000 kg/year HC: 30,000,000 g/year = 30,000 kg/year CO: 2,040,000,000 g/year = 2,040,000 kg/year

Key concepts

Pollutant Formation Mechanisms

When discussing how pollutants form in engines, it’s important to consider several factors. Pollutants like nitrogen oxides (NOx), carbon monoxide (CO), and hydrocarbons (HC) are often products of complex chemical and physical processes occurring in the engine. For example, NOx formation is predominantly due to high combustion temperatures. The heat causes nitrogen and oxygen in the air to react.
CO forms mainly because of incomplete combustion. If there isn't enough oxygen to burn all the fuel, or if the air-fuel mixture is rich, CO will result. Hydrocarbons (HC) are remaining unburned or partially burned fuel molecules. This can occur due to flame quenching or uneven mixing of air and fuel.
Overall, engine design, operating conditions, fuel type, and combustion efficiency play crucial roles in the types and amounts of pollutants produced.

Chemical Equilibrium Discrepancies

In ideal conditions, the pollutants produced by an engine would strictly follow chemical equilibrium laws. However, real-world engines seldom achieve this. Discrepancies arise because engines operate under a range of dynamic conditions. Fluctuations in temperature, pressure, and fuel-air mixing levels mean that reactions do not always proceed to completion or as expected.
Specifically, in the high-temperature environment of an engine, reactions can become extremely fast and create transient conditions where equilibrium isn't reached. The spatial and temporal variability within the combustion chamber also means that local non-equilibrium states can exist. For instance, while some regions might have excess oxygen, others might suffer from a deficit, leading to different reaction pathways and incomplete combustion.
This is one of the reasons why the actual output of pollutants in an engine doesn't match calculated values based on equilibrium alone.

Engine Emission Calculations

Accurate emission calculations help estimate the environmental impact of vehicles. To start, gather the average production rates for different pollutants. For instance, a typical spark-ignition engine produces 1.5 g/mile of NOx, 2 g/mile of HC, and 20 g/mile of CO.
Next, estimate the annual travel for all vehicles in a city. If each vehicle travels around 12,000 miles a year and the city has 50,000 vehicles, the total miles traveled is 600,000,000 miles per year.
Now, multiply the pollutant production rate by the total miles traveled. For NOx: 1.5 g/mile * 600,000,000 miles/year = 900,000,000 g/year or 900,000 kg/year.
Similarly, for HC: 2 g/mile * 600,000,000 miles/year = 1,200,000,000 g/year or 1,200,000 kg/year, and for CO: 20 g/mile * 600,000,000 miles/year = 12,000,000,000 g/year or 12,000,000 kg/year.
These calculations show the sheer scale of pollutants emitted without control devices.

U.S. Emission Standards

The U.S. government has set stringent emission standards to curb the environmental impact of vehicles. These regulations limit the permissible amounts of pollutants that can be emitted by cars and trucks. For spark-ignition engines, the current standards are much lower compared to vehicles without emission control.
For instance, the standards may dictate NOx emissions at a maximum of 0.04 g/mile, HC at 0.05 g/mile, and CO at 3.4 g/mile. Using the same 600,000,000 miles/year for total miles traveled, the calculations would be significantly different.
For NOx: 0.04 g/mile * 600,000,000 miles/year = 24,000,000 g/year or 24,000 kg/year.
For HC: 0.05 g/mile * 600,000,000 miles/year = 30,000,000 g/year or 30,000 kg/year.
For CO: 3.4 g/mile * 600,000,000 miles/year = 2,040,000,000 g/year or 2,040,000 kg/year.
These reductions highlight the effectiveness of emission standards in significantly lowering the environmental footprint of automotive travel.