Most fish need at least 4 ppm dissolved O 2 in water for survival. (a) What is this concentration in mol/L?

Hi everyone for this problem. It reads the maximum allowable amount of nitrate measured as nitrogen and drinking water is 10 parts per million by mass, calculate the corresponding polarity of the nitrate ion. So our goal here is to calculate the malaria t of the nitrate ion. So let's just recall what is malaria T, malaria T is moles over leader. And so our goal is to go from our 10 parts per million. Two moles per liter. Okay? And let's translate what tens parts per million means first. So 10 parts per million of nitrogen. Because it's telling us it's measured as nitrogen. This is equal to 10 g of nitrogen over one times 10 to the six g of water. So this is our starting point. So we want to go from this two moles of nitrate ion per liter of water. And we're going to need the density of water to convert from massive water to volume of water. Okay? And so the density of water is one g per middle leader. Okay, so let's go ahead and get started. So we have 10 g of nitrogen per one times 10 to the 6th g of water. Let's go ahead and convert our grams of water. Two liters of water. Okay? So and Using the density we know that in one gram of water We have one millim of water. So here our grams of water cancel. And we're in milliliters of water. But we want to go to leaders because Armel arat E. Is in the unit of leaders. And so and one mil a liter of water. There's 10 to the negative three leaders of water. Okay. So now are milliliters of water cancel. And we're left with leaders. Which is what we want for our denominator of Armel Arat E. Okay. So now we're going to go from grams of nitrogen. Two moles of nitrate ion. So to go from grams of nitrogen, two moles of nitrogen, we need the molar mass of nitrogen. Okay. And so in one mole of nitrogen using our periodic table to find the mass there's 14.1 g of nitrogen. Okay so our grams of nitrogen here cancels with our grams of nitrogen here and now we need to use a multiple ratio between nitrogen and nitrate to get our molds of nitrate and one more. The ratio is 1 to 1. So for every one mole of nitrogen there's one more of nitrate ion. Okay, So let's go ahead and plug that into our table. So one mole of nitrogen for every one mole of nitrogen there's one more of nitrate. Okay. And so here our molds of nitrogen cancel. And we're left with mold of nitrate ion in the numerator. So now we have our desired units and we can do our calculation and solve. And so when we do that we're going to get a final answer of 7. Times 10 to the -4 moller which is most per liter of our nitrate ion. We can write out actual nitrate ion here. Okay. so this is our malaria T and this is our final answer. That's the end of this problem. I hope this was helpful.

Ch.13 - Properties of Solutions

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Brown 14th Edition

Ch.13 - Properties of Solutions

Problem 93a

Chapter 13, Problem 93a

Most fish need at least 4 ppm dissolved O₂ in water for survival. (a) What is this concentration in mol/L?

Verified step by step guidance

Step 1: Understand that ppm stands for parts per million. This means that for every million parts of a solution, there are 4 parts of O₂.

Step 2: Convert the given concentration from ppm to g/L. Since 1 ppm is equivalent to 1 mg/L, 4 ppm of O₂ is equivalent to 4 mg/L.

Step 3: Convert the mass in mg to g. Remember that 1 g = 1000 mg, so 4 mg = 0.004 g.

Step 4: Calculate the molar mass of O₂. The atomic mass of oxygen is approximately 16 g/mol, so the molar mass of O₂ (which consists of two oxygen atoms) is 32 g/mol.

Step 5: Use the formula for molarity, which is moles of solute divided by liters of solution. In this case, the solute is O₂ and the solution is water. Convert the mass of O₂ in g to moles by dividing by the molar mass, and then divide by the volume of the solution in liters to find the molarity in mol/L.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Dissolved Oxygen Concentration

Dissolved oxygen (DO) refers to the amount of oxygen that is present in water, which is crucial for aquatic life. The concentration of DO is typically measured in parts per million (ppm) or milligrams per liter (mg/L). For fish, a minimum concentration of 4 ppm is necessary for survival, indicating the importance of oxygen availability in aquatic ecosystems.

Molarity (mol/L)

Molarity is a way to express concentration, defined as the number of moles of solute per liter of solution (mol/L). It is a fundamental concept in chemistry that allows for the quantification of substances in a solution. To convert ppm to molarity, one must consider the molar mass of the solute and the density of the solution, as ppm is a mass-based measurement.

Conversion between ppm and molarity

To convert a concentration from ppm to molarity, the formula used is: molarity (mol/L) = (ppm / molar mass of solute) × (1/1000). This conversion is essential for understanding how mass-based concentrations relate to the number of moles in a given volume, which is critical for chemical calculations and understanding biological needs in aquatic environments.

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Most fish need at least 4 ppm dissolved O₂ in water for survival. (b) What partial pressure of O₂ above water is needed to obtain 4 ppm O₂ in water at 10 °C? (The Henry's law constant for O₂ at this temperature is 1.71⨉10^-3 mol/L-atm.)

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Most fish need at least 4 ppm dissolved O2 in water for survival. (a) What is this concentration in mol/L?

Verified video answer for a similar problem:

Key Concepts

Dissolved Oxygen Concentration

Molarity (mol/L)

Conversion between ppm and molarity

Most fish need at least 4 ppm dissolved O₂ in water for survival. (a) What is this concentration in mol/L?