Question

Bioremediation is the process by which bacteria repair their environment in response, for example, to an oil spill. The efficiency of bacteria for "eating" hydrocarbons depends on the amount of oxygen in the system, pH, temperature, and many other factors. In a certain oil spill, hydrocarbons from the oil disappeared with a first-order rate constant of \(2 \times 10^{-6} \mathrm{s}^{-1} .\) At that rate, how many days would it take for the hydrocarbons to decrease to 10\(\%\) of their initial value?

Short answer

It would take approximately 13.34 days for the hydrocarbons to decrease to 10% of their initial value at the given first-order rate constant of \(2 \times 10^{-6} \mathrm{s}^{-1}\).

Step-by-step solution

Set up the first-order reaction equation

Apply the first-order reaction equation using the given information: \[ln \frac{[A]_0}{[A]} = kt\] Since we want the hydrocarbons to decrease to 10% of their initial value, \([A] = 0.1[A]_0\). Substitute this into the equation: \[ln \frac{[A]_0}{0.1[A]_0} = kt\]

Solve for time t

Now, we can simplify the equation and solve for \(t\): \[ln(1/0.1) = kt\] \[ln(10) = kt\] Now, substitute the given first-order rate constant \(k = 2 \times 10^{-6} \mathrm{s}^{-1}\): \[t = \frac{ln(10)}{2 \times 10^{-6} \mathrm{s}^{-1}}\]

Calculate the time t

Use a calculator to find the value of \(t\): \[t \approx \frac{2.303}{2 \times 10^{-6} \mathrm{s}^{-1}} \approx 1.1515 \times 10^6 \mathrm{s}\]

Convert the time to days

To convert the time from seconds to days, divide by the number of seconds in a day (86,400 seconds): \[t \approx \frac{1.1515 \times 10^6 \mathrm{s}}{86400 \frac{\mathrm{s}}{\mathrm{day}}} \approx 13.34 \mathrm{days}\] Therefore, it would take approximately 13.34 days for the hydrocarbons to decrease to 10% of their initial value.

Key concepts

First-Order Rate Constant

In the context of environmental chemistry, particularly in bioremediation, a **first-order rate constant** is essential to understanding how quickly a substance decreases over time. A first-order reaction means that the rate of degradation depends linearly on the concentration of the substance. In simpler terms, the more there is of the substance, the faster it gets consumed.

**Key points of first-order reactions:**

• The rate at which the concentration of a substance decreases is proportional to its current concentration.
• Mathematically, this can be described by the equation: \[ - \frac{d[A]}{dt} = k[A] \] where \( [A] \) is the concentration of the substance, and \( k \) is the first-order rate constant.
• The solution to this differential equation can be rearranged into the form: \[ ln \frac{[A]_0}{[A]} = kt \] where \( [A]_0 \) is the initial concentration.

Understanding the first-order rate constant helps us predict how long it will take for a particular material, such as hydrocarbons in an oil spill, to degrade naturally with the aid of microbial action.

Hydrocarbon Degradation

**Hydrocarbon degradation** is a fundamental process in bioremediation, particularly in the cleanup of oil spills. Hydrocarbons, which are compounds made of hydrogen and carbon, are a common component of oils. When an oil spill occurs, the presence of hydrocarbons in the environment can lead to pollution, affecting both terrestrial and aquatic ecosystems.

The degradation process, often aided by microorganisms, involves breaking down these hydrocarbons into less harmful substances. This is where bioremediation comes into play. Microorganisms such as bacteria have the ability to "eat" or metabolize hydrocarbons, ultimately reducing environmental pollutants.

**Factors influencing hydrocarbon degradation:**

• **Oxygen availability** – Essential for aerobic bacteria which are more efficient in breaking down hydrocarbons.
• **Temperature** – Warmer temperatures generally speed up the degradation process as they boost microbial activity.
• **pH** – Extremes in pH can inhibit microbial activity; most bacteria prefer a neutral pH.
• **Nutrient availability** – Microorganisms require nutrients such as nitrogen and phosphorus to grow and effectively decompose hydrocarbons.

By understanding these processes and factors, we can better predict and enhance the rates of hydrocarbon degradation in polluted environments.

Environmental Chemistry

Environmental chemistry plays a crucial role in understanding the **interactions between chemical compounds and the natural world**. It's the study of chemical processes occurring in the environment and their effects on human health and ecosystems. When we look at bioremediation through the lens of environmental chemistry, it helps us comprehend the chemistry behind the cleanup processes.

Environmental chemistry involves:

• **Identifying pollutants** and understanding their sources and pathways in the environment.
• **Assessing environmental risks** posed by these chemicals, considering both immediate and long-term effects.
• **Developing strategies for pollution control** and remediation, including bioremediation techniques.

In the context of an oil spill, chemical analysis helps determine what needs to be cleaned up and assesses the effectiveness of different remediation strategies. It also involves evaluating how these pollutants interact with oxygen, water, and other environmental factors. Understanding environmental chemistry is critical for developing sustainable solutions to pollution and for assessing the impact human activities have on the planet's ecosystems.