Question

The total mass of carbon in living systems on Earth is estimated to be \(7.5 \times 10^{17} \mathrm{~g} ;\) the total mass of carbon in all forms on Earth is estimated as \(7.5 \times 10^{22} \mathrm{~g} .\) Calculate the concentration of organic carbon as a fraction of total carbon. Express your answer as percent and in parts per million (ppm).

Short answer

The organic carbon is 0.001% or 10 ppm of the total carbon.

Step-by-step solution

Understand the Problem

We have the total mass of organic carbon in living systems and the total mass of carbon on Earth. We need to find out how much of the total carbon is organic by comparing these two masses.

Calculate the Fraction of Organic Carbon

To find the fraction of organic carbon in terms of total carbon, divide the mass of organic carbon by the mass of total carbon. This is done using the formula: \( \text{Fraction of Organic Carbon} = \frac{\text{Mass of Organic Carbon}}{\text{Total Mass of Carbon}} \)Plug in the given values: \( \frac{7.5 \times 10^{17} \, \text{g}}{7.5 \times 10^{22} \, \text{g}} \).

Simplify the Fraction

Simplify the fraction by canceling out the common factor: \( \frac{7.5}{7.5} = 1 \), and subtracting the exponents for like bases: \( \frac{10^{17}}{10^{22}} = 10^{-5} \).Thus, the fraction simplifies to \( 10^{-5} \).

Convert Fraction to Percentage

To convert the fraction into a percentage, multiply by 100: \( 10^{-5} \times 100 = 10^{-3} \)%.So, the organic carbon represents \(0.001\%\) of the total carbon.

Convert Fraction to Parts Per Million

To express the fraction in parts per million, multiply by 1,000,000:\( 10^{-5} \times 1,000,000 = 10 \) ppm.Thus, the concentration of organic carbon is \(10\) ppm.

Key concepts

Carbon Cycle

The carbon cycle is a natural process involving the movement of carbon between the earth's biosphere, geosphere, hydrosphere, and atmosphere. This cycle is crucial for maintaining a balance of carbon on earth, which is vital for life.

• In the carbon cycle, carbon moves through living organisms, leftover biological matter, and the environment.
• Plants play a critical role, as they absorb carbon dioxide (CO\(_2\)) from the atmosphere to produce oxygen and organic compounds during photosynthesis.
• Animals then ingest these compounds, releasing carbon back into the atmosphere through respiration.

Overall, the carbon cycle ensures the continuous transformation and exchange of carbon, balancing its levels across different systems.

Concentration Calculations

Concentration calculations help us understand the proportion of one substance in a mixture or solution. When performing these calculations with large numbers, such as in environmental measurements, we often use exponential notation for simplicity.

• The concentration of organic carbon in the total carbon can be calculated as a fraction or ratio, determining how much of the total carbon is in organic form.
• The process involves dividing the mass of organic carbon by the mass of total carbon: \[\text{Fraction} = \frac{\text{Mass of Organic Carbon}}{\text{Total Mass of Carbon}}.\]
• It's important to express the concentration in different units such as percentage or parts per million (ppm) to provide a clearer understanding of the relative concentration.

For example, in our original exercise, using the masses provided, the concentration was calculated to be 0.001% or 10 ppm, showcasing the small fraction of organic carbon relative to the total carbon on Earth.

Environmental Chemistry

Environmental chemistry focuses on the chemical processes occurring in the environment and how they are affected by human activity. A key area of study is understanding how chemicals like carbon interact with the environment and influence ecosystems.

• Key chemical processes in environmental chemistry include the decomposition of organic materials, emissions of CO\(_2\), and the chemical reactions within different natural reservoirs.
• Understanding how carbon behaves in the environment helps in addressing issues like climate change, as carbon acts as a major greenhouse gas.
• Researchers and environmentalists analyze the concentration of substances, such as organic carbon, to assess their impact on the health of ecosystems and the broader environment.

By calculating the organic carbon concentration within different ecosystems, scientists can better understand the ecological balance and how changes might affect biodiversity and environmental stability.