Question

It is estimated that \(3 \times 10^{5}\) tons of sulfur dioxide, \(\mathrm{SO}_{2}\), enters the atmosphere daily owing to the burning of coal and petroleum products. Assuming an even distribution of the sulfur dioxide throughout the earth's atmosphere (which is not the case), calculate in parts per million by weight the concentration of \(\mathrm{SO}_{2}\) added daily to the atmosphere. The weight of the atmosphere is \(4.5 \times 10^{15}\) tons. (On the average, about 40 days are required for the removal of the \(\mathrm{SO}_{2}\) by rain \() .\)

Short answer

The concentration of sulfur dioxide (SO₂) added daily to the Earth's atmosphere is approximately \(6.6667 \times 10^{-5}\) parts per million (ppm) by weight.

Step-by-step solution

Analyze the given values

We are given the following values: - The daily amount of sulfur dioxide (SO₂) released: \(3 \times 10^5\) tons - The weight of the Earth's atmosphere: \(4.5 \times 10^{15}\) tons

Calculate the concentration ratio

Divide the amount of daily SO₂ released by the weight of the atmosphere to find the concentration ratio in tons: Concentration ratio = (Daily SO₂ amount) / (Weight of the atmosphere) = \(\frac{3 \times 10^5}{4.5 \times 10^{15}}\)

Simplify the fraction

We can simplify the fraction by cancelling out common factors: \(\frac{3 \times 10^5}{4.5 \times 10^{15}} = \frac{3}{4.5} \times \frac{10^5}{10^{15}}\) Divide \(3\) by \(4.5\) and subtract the exponents in the powers of ten: \(\frac{3}{4.5} = 0.66667\) \(\frac{10^5}{10^{15}} = 10^{-10}\) The simplified fraction becomes: \(0.66667 \times 10^{-10}\)

Convert the concentration ratio to parts per million (ppm)

To convert the concentration ratio to parts per million (ppm), we can multiply the ratio by \(10^6\): Concentration (ppm) = \(0.66667 \times 10^{-10} \times 10^6\)

Calculate the resulting concentration

Now, simplify the expression by multiplying numbers and adding exponents: Concentration (ppm) = \(0.66667 \times 10^{-4}\)

Express the concentration in a more convenient form

Since the concentration is very small, it's more convenient to express it as a decimal: Concentration (ppm) = \(6.6667 \times 10^{-5}\) ppm We have found that the concentration of sulfur dioxide (SO₂) added daily to the Earth's atmosphere is approximately \(6.6667 \times 10^{-5}\) parts per million (ppm) by weight.

Key concepts

Parts Per Million (ppm)

The term 'parts per million' or ppm is a unit of measurement used to describe very dilute concentrations of substances. It essentially indicates how many units of a substance are present in one million units of the total mixture. In environmental chemistry, it’s a crucial concept as it allows scientists and researchers to express very small concentrations which are often found in atmospheric conditions. For example, the calculation of the sulfur dioxide concentration in the Earth's atmosphere in ppm would help assess its potential impact on the environment and health.

When dealing with ppm, it’s important to remember that it is a unit-less measure; it describes the ratio of the number of parts of a substance to one million parts of the total. This can apply to weight, volume, or any other countable unit of measurement. This makes ppm an ideal unit for expressing concentrations in the atmosphere, where the substances are typically found in very low amounts. For instance, in our sulfur dioxide example, the calculation resulted in a concentration of approximately 0.000066667 ppm, which effectively communicates the very low level of this pollutant in such a vast atmosphere.

Earth's Atmosphere Composition

The composition of the Earth's atmosphere is a delicate balance of various gases that are essential for life. It consists primarily of nitrogen (about 78%) and oxygen (about 21%), with trace amounts of other gases like argon, carbon dioxide, and neon. The understanding of our atmosphere's makeup is crucial in environmental chemistry, as it affects everything from climate change patterns to pollution levels.

A detailed knowledge of what makes up our atmosphere is necessary when calculating concentrations of pollutants like sulfur dioxide. The weight of the atmosphere, around 4.5 x 10^15 tons, is an essential factor in determining how much of a certain pollutant the atmosphere can contain. It also plays a role in how pollutants disperse and react with other atmospheric components. Given the vast size of the atmosphere, even a small addition of a substance in tons can result in a negligible ppm concentration, which may still have significant environmental impacts.

Environmental Chemistry

Environmental chemistry is the branch of science that studies the chemical and biochemical phenomena occurring in the natural environment. It's a field that investigates the effects of chemicals and pollutants like sulfur dioxide on ecosystems and human health. It involves understanding how chemicals move through different environmental compartments (air, water, soil), and how they interact or degrade with time.

In environmental chemistry, calculating the concentration of pollutants such as sulfur dioxide is crucial for assessing their potential impact. By determining that there's approximately 0.000066667 ppm of sulfur dioxide being added daily to the atmosphere, scientists can start to evaluate whether this poses a threat to air quality and what measures could be taken to control the emission levels. Issues like acid rain, ozone depletion, and smog are all areas where environmental chemistry is applied to understand and help mitigate human impact on Earth's atmosphere. Using such knowledge, policies and regulations can be designed to prevent and control environmental damage.