. p-Dichlorobenzene, C6 H4 Cl2, can be one of the ingredients in mothballs. Its vapor pressure a

step 1 Let's list what we know. Okay, we know our pressure is 0 .4 millimeters of mercury. Let's change

. p-Dichlorobenzene, C6 H4 Cl2, can be one of the...

. $p$-Dichlorobenzene, $\mathrm{C}_6 \mathrm{H}_4 \mathrm{Cl}_2$, can be one of the ingredients in mothballs. Its vapor pressure at $20^{\circ} \mathrm{C}$ is 0.40 mm Hg . (a) How many milligrams of $\mathrm{C}_6 \mathrm{H}_4 \mathrm{Cl}_2$ will sublime into an evacuated $750-\mathrm{mL}$ flask at $20^{\circ} \mathrm{C}$ ? (b) If 5.0 mg of $p$-dichlorobenzene were put into an evacuated $750-\mathrm{mL}$ flask, how many milligrams would remain in the solid phase? (c) What is the final pressure in an evacuated $500-\mathrm{mL}$ flask at $20^{\circ} \mathrm{C}$ that contains 2.00 mg of $p$-dichlorobenzene? Will there be any solid in the flask?

. $p$-Dichlorobenzene, $\mathrm{C}_6 \mathrm{H}_4 \mathrm{Cl}_2$, can be one of the ingredients in mothballs. Its vapor pressure at $20^{\circ} \mathrm{C}$ is 0.40 mm Hg .
(a) How many milligrams of $\mathrm{C}_6 \mathrm{H}_4 \mathrm{Cl}_2$ will sublime into an evacuated $750-\mathrm{mL}$ flask at $20^{\circ} \mathrm{C}$ ?
(b) If 5.0 mg of $p$-dichlorobenzene were put into an evacuated $750-\mathrm{mL}$ flask, how many milligrams would remain in the solid phase?
(c) What is the final pressure in an evacuated $500-\mathrm{mL}$ flask at $20^{\circ} \mathrm{C}$ that contains 2.00 mg of $p$-dichlorobenzene? Will there be any solid in the flask?

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, number of moles, and temperature of a gas. It is a critical tool for converting pressures (such as vapor pressure) into the amount of substance in the gas phase, allowing calculation of mass after determining the number of moles from known pressure and container volume.

Mass-Mole Conversions

Mass-mole conversion is the process of converting the number of moles of a substance to its mass (or vice versa) using the substance’s molar mass. This conversion is essential in quantifying how much of a substance is present, especially when relating the gaseous number of moles determined by the ideal gas law to the mass measured in milligrams.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature. It is an intrinsic property of a substance and depends solely on temperature, and it determines the extent to which a substance will evaporate or sublime under specified conditions.

Sublimation and Phase Equilibrium

Sublimation is the process by which a solid turns directly into a gas without passing through a liquid phase. In a closed system, sublimation continues until the vapor pressure of the substance reaches its equilibrium value. At this phase equilibrium, the rates of sublimation and deposition are equal, dictating the dynamic balance between the solid and vapor phases.

Transcript

00:01 Let's list what we know.

00:03 Okay, we know our pressure is 0 .4 millimeters of mercury.

00:10 Let's change that to atm, since we're going to use the ideal gas law.

00:16 So 1 over 760.

00:20 So we'll have 5 .3 times 10 to the minus 4 atm.

00:27 Our temperature is 20 degrees celsius.

00:32 So we'll change that to kelvin by adding 273.

00:36 2 .93 kelvin, and our volume is 0 .750 liters.

00:46 Okay, so let's go ahead and calculate the moles that will fill that flask.

00:51 So moles is pv over rt.

00:55 So if our pressure is 5 .3 times 10 of the minus 4, and 0 .75, r is 0 .0821.

01:06 Temperature is 293 so the moles that can fill that flask are 1 .7 times 10 of the minus 5 moles let's go ahead and change moles to grams our molar mass is 147 so that will be 0 .0025 grams okay or 2 .5 milligrams so the most that you can fit in that flask of that is going to be our 2 .5 milligrams.

01:47 So the second question asks us how much solid remains if i add 5 milligrams, well, 5 minus 2 .5 milligrams is going to give us 2 .5 milligrams.

02:03 That's the amount of solid that remains in the flask.

02:09 What if i put 2 milligrams in a larger flask, i'm sorry, a smaller flask? so i'm putting less, but i'm putting it in a smaller flask.

02:18 So i'm going to need to check some math here.

02:22 So two milligrams.

02:24 Let's change milligrams to grams and grams to moles...

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