The vapor pressure of CCl 3 F at 300 K is 856 torr. If 11.5 g of CCl 3 F is enclosed in a 1.0-L container, will any liquid be present? If so, what mass of liquid?

Hey everyone, we're told that a three liter close vessel contains 2.75 g of acetone with a vapor pressure of 282 mm of mercury at 30°C determine if there will be any liquid present in the vessel. If so, calculate the mass of the liquid. To answer this question, we need to use our ideal gas law equation in order to determine the number of moles of acetone. So this is going to be our pressure times are volume, which is equal to the number of moles times, r gas constant times our temperature. Now, since we want to determine the number of moles of acetone, we have to rearrange this equation into the number of moles is equal to our pressure times are volume divided by our gas constant times our temperature. So let's go ahead and write out our values. So we have a pressure of 282 mm of mercury. Now we want to convert this into atmospheric pressure. Using dimensional analysis, we know that we have 760 of mercury per one atmospheric pressure. Now, when we calculate this out, we end up with the pressure of 0.3711 atmospheric pressure. Now for our volume, we were told that we had 3.00 l And our temperature is said to be 30°C. Now we want to convert this into Kelvin and we can do so by adding 273. And this will get us to 303.15 Kelvin. So now let's go ahead and solve for the number of moles of our acetone in its gas phase. So plugging in our values, we have a pressure of 0.3711 atmospheric pressure And we're going to multiply this buyer volume of 3.00 leaders. This will all be divided by our ideal gas constant which is 0.08-06 leaders times atmospheric pressure divided by Mole Times Kelvin. And we're going to multiply this value by our temperature of 303.15 Kelvin. Now, when we calculate this out and cancel out all of our units, We end up with a value of 0.0448 mol. Now let's go ahead and solve for the mass of acetone in our gas phase. To solve for the mass of our acetone In its gas phase, we're going to take the value we just calculated which was 0.0448 mol. And we're going to convert this into grams by using dimensional analysis Using acetone Mueller mass. We know that we have 58.79 g of acetone per one mole of acetone. This will get us to a mass of 2. g. Now we want to determine the mass of our acetone in its liquid phase and we can do so by taking our total mass and subtracting the mass of our acetone in its gas phase. So, plugging in these values, we have 2.75g -2.6019g, and this will get us to A value of 0.148 g, which is going to be our final answer. So to answer our question Yes, there is 0.148g of liquid acetone present in our vessel. Now, I hope this made sense and let us know if you have any questions.

Ch.11 - Liquids, Solids & Intermolecular Forces

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Tro 4th Edition

Ch.11 - Liquids, Solids & Intermolecular Forces

Problem 86

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Chapter 11, Problem 86

The vapor pressure of CCl₃F at 300 K is 856 torr. If 11.5 g of CCl₃F is enclosed in a 1.0-L container, will any liquid be present? If so, what mass of liquid?

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Calculate the number of moles of CCl_3F using its molar mass.

Use the ideal gas law, PV = nRT, to calculate the pressure exerted by the gas if all the CCl_3F were in the gaseous state.

Compare the calculated pressure with the given vapor pressure of CCl_3F at 300 K.

If the calculated pressure is greater than the vapor pressure, some liquid will be present. Calculate the moles of gas that would exert the vapor pressure using the ideal gas law.

Subtract the moles of gas from the total moles to find the moles of liquid, then convert this to mass using the molar mass.

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Key Concepts

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

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It indicates the tendency of a substance to evaporate; higher vapor pressure means a greater tendency to vaporize. In this context, the vapor pressure of CCl3F at 300 K is 856 torr, which serves as a critical threshold for determining whether liquid will remain in the container.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law helps in calculating the number of moles of CCl3F present in the container, which is essential for comparing it to the vapor pressure. Understanding this relationship allows us to determine if the conditions favor the presence of liquid or if all the substance will be in the gaseous state.

Phase Equilibrium

Phase equilibrium occurs when the rates of evaporation and condensation of a substance are equal, resulting in a stable mixture of liquid and vapor. In this scenario, if the number of moles of CCl3F exceeds what can exist as vapor at the given vapor pressure, some of it will remain as liquid. Analyzing the mass of CCl3F and its vapor pressure helps in assessing whether liquid will be present in the container.