Which sample contains more molecules, 15.0 L of steam (gaseous H2 O ) at 123.0^∘ C and 0.93 atm

Which sample contains more molecules, 15.0 L of steam...

Key Concepts

Ideal Gas Law

The Ideal Gas Law (PV = nRT) relates the pressure, volume, and temperature of a gas to the number of moles present. This concept allows one to determine the number of gas molecules under various conditions by rearranging the equation to solve for n, thus connecting macroscopic measurements with molecular count.

Mole Concept and Avogadro's Number

The mole concept is a fundamental chemical concept used to count particles at the molecular scale. Avogadro's Number, which is approximately 6.02 x 10^23 particles per mole, bridges the gap between the macroscopic scale of measurable substances and the microscopic scale of atoms and molecules.

Mass-to-Mole Conversion Using Molar Mass

Converting a given mass of a substance to moles involves using its molar mass—the mass of one mole of that substance. This conversion is essential when determining the number of molecules in a sample of a substance in any state, by dividing the mass by the molar mass.

Phase and State Considerations

The state of a substance (gas, liquid, or solid) significantly influences its properties and the methods used to quantify its molecules. For gases, the Ideal Gas Law is employed, while for solids, direct conversion from mass to moles using molar mass is used. Understanding these differences is crucial for correctly comparing quantities of matter in different phases.

Transcript

00:03 So in this question, we're asked which of two samples contains more molecules? is it a steam? so it's gaseous water, 15 liters, 123 degrees celsius and 0 .93 atmospheres.

00:17 Or is it ice? so solid water at 10 .5 grams and negative 5 degrees celsius.

00:23 So first of all, i'm probably not going to calculate the number of molecules here because that's just going to be something that we have to convert from moles to molecules, the same way for both of them.

00:35 So it's an equivalent question to say which one has more moles of water.

00:41 So i'm going to actually calculate for moles, understanding that it's proportional to the number of molecules.

00:48 So let's do each of these one at a time, starting with the steam on the left to the gas.

00:54 So this is going to be an ideal gas law equation.

00:57 So we have pv equals n rt.

01:03 And we are looking for n in this case.

01:06 So n is equal to pv divided by rt.

01:13 P is going to be 0 .93 atmospheres times v, which is 15 liters, over rt.

01:32 R in this case is a consonant dependent on the unit that we're using.

01:38 For our pressure in atmospheres.

01:43 The value for r is 0 .0821.

01:50 And t is 123 degrees celsius, but we can't leave it in celsius.

01:56 We have to add 273, sorry, not 127, 123 celsius plus 273.

02:05 In order to convert it to kelvin, which is 396 kelvin.

02:10 So we put in 396 kelvin right here.

02:15 Gas laws, you always have to use kelvin because otherwise your formulas break down if you can use negative temperatures, for example.

02:25 So if we multiply all this out, so we do 0 .93 times 15 liters divide by 0 .0821 and then divide by 396, we get that there are, 0 .429, sorry, that's a 2, 0 .429 moles of water in the steam, 0 .429...

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