Most fish need at least 4 ppm dissolved O 2 in water for survival. (b) What partial pressure of O 2 above water is needed to obtain 4 ppm O 2 in water at 10 °C? (The Henry's law constant for O 2 at this temperature is 1.71⨉10 -3 mol/L-atm.)

Hello everyone today. We have the following problem. A concentration of as low as 0.5 parts per million of dissolved ammonia and water can already cause damage to the gills of the fish, calculate the partial pressure of ammonia in tour when it reaches a concentration of 0.5 parts per million at 25 degrees Celsius, ammonia has Henry's law constant of 59.8 moles Over L per atmospheres. Assume that the density of the solution is one grand per middle leader. So to calculate that we're gonna take the gas and equal it to this, Henry's constant times our partial pressure of the gas. So in malaria T This is going to be equal to 0.05 parts per million. Equal To our 0. milligram of ammonia divided by our kilogram of solution. Next, what we're gonna do to further calculate that Is we're gonna take what we just saw it for our 0. mg of ammonia per kilogram solution. We're gonna multiply by several different factors. First. We're gonna get rid of milligrams in that. We're gonna use a conversion factor that one mg is equal to 10 to the negative three g. We're gonna multiply by the molar mass of ammonium which states That one mole is equal to 17.03 g. And this is from the periodic table. We're then gonna get rid of grams with the conversion factor that one kg is equal to 10 to the third grams. We're then going to convert our grams to leaders. And in doing that, we're gonna say that one g is equal to one male leader. Given the density and then we're gonna multiply that by one, middle year is equal to one leader. And this is gonna give us our 2.9 times 10 to the power of negative six moles per liter. This is gonna be our polarity. So from our earlier formula, if we rearranged it to get the partial pressure of our gas equal that Polarity of the gas over Henry's constant, it's gonna be our 2.9 times 10 to the negative six moles per liter Divided by Henry's Continent 59.8 moles per liter of times atmosphere. And this is going to give us a value of 4.9 times 10 to the - atmospheres. However, the answer recall wants us to have it in tour. So we're gonna use the conversion factor that one atmosphere is equal to 760 tour. When are units of atmospheric cancels out? We're left with a final partial pressure of 3.73 times to the negative fifth tour. And with that, we have solved the problem overall, I hope this helped hand until next time

Ch.13 - Properties of Solutions

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Brown 14th Edition

Ch.13 - Properties of Solutions

Problem 93b

Chapter 13, Problem 93b

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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Understand that ppm (parts per million) is a way to express concentration. For gases dissolved in water, 4 ppm means 4 mg of O_2 per liter of water.

Convert the concentration from ppm to molarity (mol/L). Use the molar mass of O_2, which is approximately 32.00 g/mol, to convert mg/L to mol/L.

Apply Henry's Law, which states that the concentration of a gas in a liquid is directly proportional to the partial pressure of the gas above the liquid. The formula is C = kP, where C is the concentration of the gas, k is the Henry's law constant, and P is the partial pressure.

Rearrange the formula to solve for the partial pressure: P = C/k.

Substitute the values for C (from step 2) and k (given as 1.71⨉10^-3 mol/L-atm) into the equation to find the partial pressure of O_2 needed.

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Key Concepts

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

Henry's Law

Henry's Law states that the amount of a gas that dissolves in a liquid at a given temperature is directly proportional to the partial pressure of that gas above the liquid. This relationship can be expressed mathematically as C = kH * P, where C is the concentration of the gas in the liquid, kH is the Henry's law constant, and P is the partial pressure of the gas.

Dissolved Oxygen Concentration

Dissolved oxygen concentration refers to the amount of oxygen that is present in water, typically measured in parts per million (ppm) or milligrams per liter (mg/L). For aquatic life, maintaining a certain level of dissolved oxygen is crucial for survival, as it is essential for respiration in fish and other organisms.

Temperature Effects on Gas Solubility

The solubility of gases in liquids is influenced by temperature; generally, as temperature increases, the solubility of gases decreases. This is important in aquatic environments, as warmer water holds less dissolved oxygen, which can affect fish survival and ecosystem health.

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A supersaturated solution of sucrose (C₁₂H₂₂O₁₁) is made by dissolving sucrose in hot water and slowly letting the solution cool to room temperature. After a long time, the excess sucrose crystallizes out of the solution. Indicate whether each of the following statements is true or false: (b) After the excess sucrose has crystallized out, the system is now unstable and is not in equilibrium.

Textbook Question

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

Textbook Question

The presence of the radioactive gas radon (Rn) in well water presents a possible health hazard in parts of the United States. (a) Assuming that the solubility of radon in water with 1 atm pressure of the gas over the water at 30 °C is 7.27⨉10^-3 M, what is the Henry's law constant for radon in water at this temperature?

Textbook Question

The presence of the radioactive gas radon (Rn) in well water presents a possible health hazard in parts of the United States. (b) A sample consisting of various gases contains 3.5 × 10^-6 mole fraction of radon. This gas at a total pressure of 32 atm is shaken with water at 30 °C. Calculate the molar concentration of radon in the water.

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.)

Verified video answer for a similar problem:

Key Concepts

Henry's Law

Dissolved Oxygen Concentration

Temperature Effects on Gas Solubility

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.)