Question

Fish need at least 4 ppm dissolved \(\mathrm{O}_{2}\) for survival. (a) What is this concentration in mol/L? (b) What partial pressure of \(\mathrm{O}_{2}\) above the water is needed to obtain this concentration at \(10{ }^{\circ} \mathrm{C}\) ? (The Henry's law constant for \(\mathrm{O}_{2}\) at this temperature is \(\left.1.71 \times 10^{-3} \mathrm{~mol} / \mathrm{L}-\mathrm{atm} .\right)\)

Short answer

(a) To convert the concentration from ppm to mol/L, we use the molar mass of O₂ (32 g/mol) and the given concentration of 4 ppm: \(Moles\, per\, Liter = \frac{4}{32 \times 10^6}\) (b) To calculate the partial pressure of O₂, we use Henry's Law formula: \(P = \frac{ gas\, concentration}{k}\) Using the concentration from part (a) and the given Henry's law constant (\(1.71 \times 10^{-3} \,\frac{mol}{L \cdot atm}\)): \( P = \frac{\frac{4}{32 \times 10^6}}{1.71 \times 10^{-3}}\) Calculate the partial pressure, P, to find the required pressure for the given concentration at \(10{ }^{\circ}C\).

Step-by-step solution

a) Convert concentration to mol/L

To convert the concentration from ppm to moles per liter (mol/L), we first need to know the molar mass of oxygen. The molar mass of O₂ is 32 g/mol. The concentration given is 4 ppm, which means there are 4 grams of O₂ in a million (10^6) grams of water. We can use the molar mass of O₂ to convert the concentration from g/L to mol/L. Mol/L = (grams of O₂) / (molar mass of O₂) To compute this, just substitute the values: \( Moles\, per\, Liter = \frac{4}{32 \times 10^6} \)

b) Calculate partial pressure of O₂

Now that we have the concentration of O₂ in mol/L, we can use Henry's Law to find the partial pressure of O₂ above the water. Henry's Law formula is: \( C=gas\, concentration = k \times P \) Where C is the concentration (mol/L), k is the Henry's law constant (\(1.71 \times 10^{-3} \,\frac{mol}{L \cdot atm}\)), and P is the partial pressure (atm). Rearrange the formula to solve for P: \(P = \frac{ gas\, concentration}{k}\) Substitute the given values in the formula: \( P = \frac{\frac{4}{32 \times 10^6}}{1.71 \times 10^{-3}}\) Now, calculate the partial pressure, P.

Key concepts

Dissolved Oxygen

Dissolved oxygen refers to the amount of oxygen gas (O₂) that is found dissolved in water. It is a crucial parameter in assessing water quality and is vital for aquatic life. Fish and other marine organisms rely on dissolved oxygen to survive, much like terrestrial animals breathe air. To measure dissolved oxygen, scientists often express it in parts per million (ppm) or milligrams per liter (mg/L).
While small concentrations are sufficient for some aquatic organisms, fish typically require a minimum of 4 ppm to thrive. When dissolved oxygen levels fall below this threshold, it can lead to dire consequences, such as fish kills, where large numbers of fish die suddenly. Monitoring and managing dissolved oxygen levels are thus essential to preserving aquatic ecosystems.

Partial Pressure

Partial pressure is the pressure exerted by a single gas in a mixture of gases, like air. When studying dissolved gases, partial pressure refers to the pressure exerted by the gas dissolved in a liquid, such as oxygen in water. According to Henry’s Law, the concentration of a gas in a liquid is directly proportional to the partial pressure of that gas above the liquid. This relationship helps determine how much gas will dissolve in the liquid under specific conditions.
This concept is particularly significant in aquatic environments, where gases from the atmosphere, like oxygen, dissolve into water. The partial pressure of oxygen must be sufficient to maintain necessary dissolved oxygen concentrations to support aquatic life. Without adequate partial pressures, oxygen may not dissolve in enough quantity, impacting aquatic organisms negatively. Thus, understanding and calculating partial pressures is key for environmental scientists and water chemists.

PPM to Mol/L Conversion

Converting ppm to mol/L is essential in certain chemistry calculations, especially in environmental science. PPM stands for 'parts per million', which is a way of expressing very dilute concentrations. For water-based solutions, 1 ppm is often considered equivalent to 1 mg/L, assuming the density of water is approximately 1 g/mL.
To convert ppm to mol/L, you need the molar mass of the substance you're dealing with. In the case of oxygen, the molar mass is 32 g/mol. Given a concentration of 4 ppm of dissolved oxygen, converting to mol/L involves the equation: \[ \text{Moles per Liter} = \frac{\text{grams of O}_2}{\text{molar mass of O}_2} \]
The typical calculation would involve dividing the ppm value by 10^6 to convert parts per million to a gram-based measure, and then using the molar mass to convert grams to moles, providing the final concentration in mol/L.

Water Chemistry

Water chemistry examines the chemical components and properties of water. It plays a vital role in understanding aquatic ecosystems, influencing everything from fish health to water quality. One of its fundamental aspects is analyzing the solubility and concentration of different gases and compounds in water.
Practices in water chemistry involve the study of pH levels, hardness, dissolved gases like oxygen and carbon dioxide, and other chemical interactions. Understanding these components helps in maintaining healthy aquatic environments. It ensures that the water bodies support a diversity of life forms.

• Maintaining balanced levels of dissolved gases.
• Understanding impacts of pollutants.
• Ensuring compatibility with native marine life.

Knowledge of these chemical interactions helps in addressing environmental challenges and in the development of sustainable practices for water conservation and treatment.