The vapor pressure of water at 100.0ºC is 0.720 atm. Determine the mass percent of iron (II) chloride, FeCl 2 , needed to reduce its vapor pressure to 0.655 atm. (MW of FeCl 2 is 126.756 g/mol)

The vapor pressure of water at a 100 degrees Celsius is 0.720 atmospheres. Determine the mass percent of iron 2 chloride needed to reduce its vapor pressure to 0.655 atmospheres. Here, we're given the molecular weight of iron 2 chloride as 126 0.756 grams per mole. Alright. So we need to determine the mass percent of iron 2 chloride. Here, since we're dealing with vapor pressure, we say pressure of our solution equals mole fraction of our solvent times the pressure of our pure solvent. Here, pressure of our solution, remember, is always lower because adding solute decreases my vapor pressure. And then this is x solvent, and then pressure of my pure solvent is 0.720 atmospheres. Divide both sides now by 0.720 atmospheres, and we'll have the mole fraction of my solvent. So mole fraction of solvent equals 0.9097. And that's the majority of the information given to us, but we need to realize here is that this piece of information is saying a lot, we just have to expand it out. Remember, mole fraction of my solvent, so we're going to have it up here to help us remember, is our moles of solvent divided by I times my moles of solute plus my moles of solvent. So if I were to expand this out, what it's really telling me is I have 0.9097 moles of solvent, so moles of water, divided by 1 mole of solution, because remember, mole fraction also means moles of of, in this case, a solvent divided by the total moles of solution. From this one mole of solution, we can expand it into 0.9097 moles of water divided by still 0.9097 moles of water. Remember we need I. Iron 2 chloride is ionic, it breaks up into 1 iron 2 ion plus 2 chloride ions. So that's 3 total ions. So here I is 3, and we don't know what the moles of iron 2chloride is, so that's x. Now guess what? We know that the total value on the bottom for mole fraction is equal to 1, so that means that this equals 1 because they're the same bottom. I just expanded it outwards. So make them equal to each other and help us to solve for x. So 3 x+.9097 equals 1. Subtract 0.9097 from both sides. So 3 x equals 0.0903. Divide both sides by 3. So x here, which equals my moles of iron 2 chloride, is 0.0301. So guess what? We have the moles of iron 2 chloride, and we have the moles of water. With this information, I can find the mass percent of iron 2 chloride. So mass percent equals the grams of iron 2. Alright? So here I would just change these moles, so 1 mole of iron 2 chloride on the bottom, and we're told the mass is 126.756 grams. When we work that out, that comes out to 3.8154 grams of iron 2 chloride, and then for mass percent, we need the grams of solution on the bottom, which would be the grams of our solute again, plus the grams of our solvent. Water is 0.9097 moles. So let's change that into grams. So here, remember, for water, 1 mole of water is 18.016 grams. Moles cancel out and we have here 16.3892 grams of water, and then we multiply this by 100. Doing that gives me my mass percent which would come out to 18 0.9%, which would give me option b as my correct answer. So just realize that although not a lot of information is given to us within this question, it does help us find the moles of our solvent. Just from that piece of information, I can expand it outwards and from it I can determine the moles of both my solvent water and my solute of iron 2 chloride. Once you know their moles, change them into grams, and you can find the mass percent of iron chloride.

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14. Solutions

Vapor Pressure Lowering (Raoult's Law)

General Chemistry

14. Solutions

Vapor Pressure Lowering (Raoult's Law)

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Multiple Choice

The vapor pressure of water at 100.0ºC is 0.720 atm. Determine the mass percent of iron (II) chloride, FeCl₂, needed to reduce its vapor pressure to 0.655 atm. (MW of FeCl₂ is 126.756 g/mol)

67.7%

18.9%

22.5%

58.3%

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Verified step by step guidance

Understand that the problem involves a colligative property, specifically vapor pressure lowering, which is described by Raoult's Law.

Raoult's Law states that the vapor pressure of a solvent above a solution (P_solution) is equal to the vapor pressure of the pure solvent (P_solvent) times the mole fraction of the solvent (X_solvent): P_solution = P_solvent * X_solvent.

Calculate the mole fraction of water (X_water) using the given vapor pressures: X_water = P_solution / P_solvent = 0.655 atm / 0.720 atm.

Determine the mole fraction of FeCl2 (X_FeCl2) using the relationship: X_water + X_FeCl2 = 1.

Convert the mole fraction of FeCl2 to mass percent. First, calculate the moles of FeCl2 using its molar mass (126.756 g/mol), then find the mass of FeCl2 and water, and finally calculate the mass percent: (mass of FeCl2 / (mass of FeCl2 + mass of water)) * 100%.