Problem 82 - Chemistry: The Central Science

Question

An experiment was designed to determine whether an aquatic plant absorbed iodide ion from water. Iodine-131 \(\left(t_{1 / 2}=8.02\right.\) days) was added as a tracer, in the form of iodide ion, to a tank containing the plants. The initial activity of a \(1.00-\mu \mathrm{L}\) sample of the water was 214 counts per minutc. After 30 days the level of activity in a \(1.00-\mu \mathrm{I}\). sample was \(15.7\) counts per minute. Did the plants absorb iodide from the water?

Step-by-Step Solution

Answer

The number of half-lives that elapsed in 30 days can be calculated as: \( \text{Number of half-lives} = \frac{30}{8.02} \approx 3.74 \) Assuming no plant absorption, the remaining activity after 30 days is: \( \text{Remaining activity} = 214 \times (\frac{1}{2})^{3.74} \approx 22.8 \) The expected activity of 22.8 counts per minute without plant absorption is higher than the observed activity of 15.7 counts per minute. Therefore, we can conclude that the plants absorbed iodide from the water.

Step 1: Determine the number of half-lives that elapsed in 30 days

To find the number of half-lives that transpired within the given time frame, we can use the following formula: Number of half-lives = Time elapsed (days) ÷ Half-life (days/half-life) Let's calculate this value: \( \text{Number of half-lives} = \frac{30}{8.02} \)

Step 2: Calculate the expected activity after 30 days with no plant absorption

Assuming no plant absorption, the iodium-131 would just decay at its normal rate. In this situation, the remaining activity can be calculated by the following formula: Remaining activity (counts per minute) = Initial activity (counts per minute) × \((\frac{1}{2})\)^{number\:of\:half-lives} Solving for the remaining activity after 30 days: \( \text{Remaining activity} = 214 \times (\frac{1}{2})^{\frac{30}{8.02}} \)

Step 3: Compare the expected and observed activity after 30 days

Evaluate the expected activity obtained in Step 2 and compare it with the observed activity of 15.7 counts per minute. If the expected activity is higher than the observed activity, this suggests that the plants absorbed iodide from the water.

Step 4: Determine whether the plants absorbed iodide

Based on the comparison between the expected and observed activity of iodine-131 in Step 3, make a conclusion about the absorption of iodide by the aquatic plants.

Key Concepts

Understanding Half-Life Calculation

Half-life is a concept used to describe the time it takes for half of a given amount of a radioactive substance to decay. To determine how much of a substance remains after a certain period, you can use the number of half-lives passed. Typically, you calculate this with the formula: \[\text{Number of half-lives} = \frac{\text{Time elapsed (days)}}{\text{Half-life (days/half-life)}}\] For Iodine-131, with a half-life of 8.02 days, you can calculate the number of half-lives over 30 days with the formula: \[\frac{30}{8.02} \] This gives a clear picture of the decay progression. It helps you predict the remaining activity, crucial to understanding whether additional processes, like plant absorption, affect the system.

Exploring Radioactive Decay

Radioactive decay is a random process in which unstable nuclei release energy by emitting radiation. This natural process follows an exponential decay pattern. When you add a radioactive isotope, like iodine-131, into an environment, it decays over time in a predictable manner. The decay can be calculated using: \[\text{Remaining activity (counts per minute)} = \text{Initial activity (counts per minute)} \times \left(\frac{1}{2}\right)^{\text{number of half-lives}}\] This formula reflects how the initial quantity decreases exponentially. Inferring from changes between expected and observed decay levels, like in our experiment, can help indicate other influences, such as plant absorption, altering expected outcomes.

Designing a Chemistry Experiment

The design of an experiment in chemistry is crucial for obtaining accurate and reliable results. When investigating the absorption of iodide by aquatic plants, careful planning is essential. Here are the key elements for a successful experimental design: - **Objective:** Clearly define what you're testing—here, whether plants absorb iodide. - **Controlled Variables:** Keep the conditions consistent to ensure that any observed changes are due to the independent variable. - **Use of Tracers:** Radioactive tracers like iodine-131 provide a quantifiable way to track substance movement and transformations. - **Data Collection:** Use precise measurements, like counts per minute, to quantify results over time. - **Comparison:** Compare expected decay with actual observations to determine if absorption occurred. This methodical approach allows for determining the effects of aquatic plants on iodide levels, ensuring conclusions are valid and based on solid data.