A sealed flask contains 0.55 g of water at 28^∘ C . The vapor pressure of water at this temperat

step 1 Okay, now, this will be problem number 94 from chapter 11. There's a sealed flask contains 0 .55

A sealed flask contains 0.55 g of water at 28^∘ C . The...

Key Concepts

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid (or solid) form at a given temperature. It represents the maximum possible pressure of the vapor in a closed system when the liquid is present, and is crucial in determining when phase transition between liquid and vapor will occur.

Ideal Gas Law

The ideal gas law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. It is used to calculate the volume needed to accommodate a given amount of gas at a specified pressure and temperature, which is important when ensuring that a substance exists solely in the gas phase.

Phase Equilibrium

Phase equilibrium refers to the state in which two phases (in this case, liquid and vapor) coexist at specific conditions like temperature and pressure. In problems like this, ensuring that only the vapor phase is present requires that the system's volume and conditions be such that the vapor pressure is not exceeded, preventing condensation of the liquid.

Transcript

00:15 Okay, now, this will be problem number 94 from chapter 11.

00:23 There's a sealed flask contains 0 .55 grams of water.

00:28 The vapor pressure of the water at this temperature is 28 .35 millimeters of mercury.

00:34 What is the minimum volume of the flask in order that no liquid water be present in the flask? okay, so well, what you know about water, because they gave you the vapor pressure, is that whenever you're at equilibrium, which is what we're going to assume you're going to be at.

00:56 The vapor pressure of the liquid is going to be equal to always, 28 .35 millimeters of mercury.

01:05 Okay.

01:07 So they also tell you that it's a sealed flask, first of all, so it can't escape into the atmosphere.

01:13 If it could, it would all vaporize eventually.

01:16 But what they also tell you is the vapor pressure, and they tell you the flask is sealed, and they tell you that there should be only vapor in there at equilibrium.

01:31 So what that should tell you is that when you have 0 .55 grams of water, it would all be vapor, all of it.

01:40 And they give you all the physical information here.

01:44 So we can easily calculate what the volume should be given that information.

01:50 So you might remember the ideal gas law.

01:53 So that.

01:57 So let's see if i'm going to right.

02:05 Oh, there you go.

02:08 So we start out with some details.

02:10 They give you 0 .55 grams of water.

02:17 And we can turn that into moles because we're going to use pv equals nrt.

02:21 I'll put this on the side here.

02:30 So 0 .55 grams of water.

02:33 And i'll let's give you the more mass of water.

02:36 18 .02 grams per mole.

02:39 And that would give you per mole of water implicitly.

02:49 So you would take 0 .55 grams divided by 18 .302 grams per mole.

03:03 And notice the units cancel here.

03:06 Grams here, grams there, those both go away and you end up with a number which is in moles, as you would hope.

03:14 So now that turns out to give you 0 .0352.

03:19 So let's just do this here.

03:21 0 .55 divided by 18 .0 .02.

03:28 I'm going to keep five, four digits, let's say.

03:31 0 .3052.

03:39 That is moles.

03:41 Okay.

03:42 So what we also have is equilibrium, the vapor pressure is 28 .35 millimeters age chief.

03:49 And i'm going to convert all these numbers here, pressure volume, and r and t.

03:56 We're going to use the standard units of kilograms, meters, and seconds to do this.

04:09 So that means we're going to use pressure is pascal's, and volume is cubic meters, and temperatures in kelvin's, also.

04:25 Those are the units we're going to use for this.

04:30 So now we're going to get the pressure in terms of pascal's.

04:36 So to convert the pressure from 28 .35 millimeters of mercury, you would use the conversion approximately 760 millimeters of mercury per atmosphere.

04:58 And it turns out that when you do that calculation, it is you find it here 20 .35 % percent of it should give you 3 ,779.

05:16 And i'm going to keep a few extra digits, 055 pascals.

05:25 Okay, so that's the pressure.

05:30 And now for the temperature, they gave us a temperature of 28 degrees celsius.

05:40 So to get 28 degrees celsius in terms of kelvin, we're just going to add.

05:44 Can add to 73 .15 to it, 28 kelvin's and that's going to be equal to 301 .15 kelvin.

06:06 So here's temperature, here's pressure, and here's the number of moles.

06:14 So that gives us, in the equation, the ideal gas law, we have, we've been given p, we've been given n, and we've been given t as well.

06:32 So we have all of those things.

06:34 The only thing we don't have is the volume, which we can solve for using pv equals nrt.

06:41 Okay, so now that we start plugging numbers in, you can get this equation, you'll end up with pv.

06:48 I'm going to write in pressure here, 3 ,0779 .055 pascal's times volume unknown.

07:04 Is equal to n and n we were given 0 .0352 and that is moles we'll squeeze this in here if i can n times r and for standard units that we've been using we'll use 8 .314 joules per mole kelvin so i'll use 8 .314 jules per mole kelvin and the last one is t temperature is 301 .15.

08:00 You can check the units to make sure everything comes out right by crossing out the stuff that disappears...

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