Question

A typical car driven \(20,000 \mathrm{km}\) a year emits to the atmosphere about 11 kg per year of \(\mathrm{NO}_{\mathrm{x}}\) (nitrogen oxides) which cause smog in major population areas. Natural gas burned in the furnace emits about \(4.3 \mathrm{g}\) of \(\mathrm{NO}_{x}\) per therm (1 therm \(=105,500 \mathrm{kJ}\) ), and the electric power plants emit about \(7.1 \mathrm{g}\) of \(\mathrm{NO}_{x}\) per \(\mathrm{kWh}\) of electricity produced. Consider a household that has two cars and consumes \(9000 \mathrm{kWh}\) of electricity and 1200 therms of natural gas. Determine the amount of \(\mathrm{NO}_{x}\) emission to the atmosphere per year for which this household is responsible.

Short answer

The total amount of NOx emissions for which the household is responsible per year is 91.06 kg.

Step-by-step solution

Calculate the emission from cars

Each car emits 11 kg of \(\mathrm{NO}_{x}\) per year, and there are two cars in the household. So, the emission from cars annually is: \(2 \times 11 \mathrm{kg}\) of \(\mathrm{NO}_{x}\) per year.

Calculate the emission from electricity consumption

The household consumes 9000 kWh of electricity per year and for each kWh, 7.1 grams of \(\mathrm{NO}_{x}\) is emitted. Therefore, the total emission from electricity consumption is: \(9000\,\mathrm{kWh} \times 7.1\,\mathrm{g}\,\mathrm{NO}_{x}/\mathrm{kWh}\).

Calculate the emission from the natural gas consumption

The household uses 1200 therms of natural gas per year and for each therm, 4.3 grams of \(\mathrm{NO}_{x}\) is emitted. So the total emission from natural gas consumption is: \(1200\,\mathrm{therms} \times 4.3\,\mathrm{g}\,\mathrm{NO}_{x}/\mathrm{therm}\).

Calculate the total emission

Now, we add the emissions from cars, electricity consumption, and natural gas consumption to find the total emission: $$2\times11\,\mathrm{kg/year} + 9000\times7.1\,\mathrm{g/year} + 1200\times4.3\,\mathrm{g/year}$$ $$=22\,\mathrm{kg/year} + 63900\,\mathrm{g/year} + 5160\,\mathrm{g/year}$$

Convert the total emission to kilograms

The total emission is obtained by adding all the emissions in grams to the emissions in kilograms. Convert the grams to kilograms by dividing by 1000: $$22\,\mathrm{kg/year} + \frac{63900\,\mathrm{g/year} + 5160\,\mathrm{g/year}}{1000}$$ $$=22\,\mathrm{kg/year} + 69.06\,\mathrm{kg/year}$$

Find the final result

The total amount of \(\mathrm{NO}_{x}\) emissions for which the household is responsible per year is: $$22\,\mathrm{kg/year} + 69.06\,\mathrm{kg/year} = 91.06\,\mathrm{kg/year}$$