Manufacturers of headache remedies routinely claim that their own brands are more potent pain re

step 1 Let's consider the dosages of Tylenol and Advil. So as a rule of thumb, we know how strong the d

Manufacturers of headache remedies routinely claim that...

Key Concepts

Molecular Weight

The molecular weight (or molar mass) is the mass of one mole of a given substance, usually expressed in grams per mole (g/mol). It is calculated by summing the atomic weights of all the atoms in a molecule. This concept is essential for converting between the mass of a substance and the number of moles, which is further used to determine the number of individual molecules.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another, necessary in scientific calculations to ensure consistency and accuracy. An example is converting milligrams to grams before performing calculations involving molecular weight and mole conversions, as the standard unit for molecular weight is typically expressed in grams per mole.

Mole

A mole is a fundamental unit in chemistry that represents a specific number of particles, typically atoms or molecules. It provides a bridge between the atomic scale and the macroscopic scale, allowing chemists to count particles in measurable amounts of substances. One mole contains exactly 6.022 x 10^23 particles, a constant known as Avogadro's number.

Avogadro's Number

Avogadro's number is a constant that defines the quantity of entities (atoms, molecules, ions, etc.) in one mole of a substance. This number, approximately 6.022 x 10^23, is crucial when converting between the mass of a substance and the number of particles it contains, allowing for precise stoichiometric calculations.

Transcript

00:02 Let's consider the dosages of tylenol and advil.

00:15 So as a rule of thumb, we know how strong the dosage is based on how few molecules are needed in order to determine which one has the same effect per standard dosage given a certain amount of molecules.

00:34 So you have a small amount of molecules, you could say it's a more potent pain reliever.

00:41 Now, anyways, let's start with tylenol.

00:44 We're given that the average dose, let's go ahead and write given.

00:50 I find it's good etiquette for physics.

00:53 Standard dose is 325 milligram.

00:56 Tylenol, it's about 200 milligram for advil.

01:01 We know the chemical formula of tylenol is c -substcript 8, h -substcript 9, and, of chemical formula c13h18 o2 for advil so we need to find our molecules i'm not splitting it up strictly as amb because i think this seems like a logical sequence of events as is it was called tylenol t and advil a henceforth now if i were you i would go review a periodic table because you're going to go need these values i realize this tedious, but you always have access to these.

02:04 I have yet to find a chemistry teacher who is quite sadistic enough to force you to memorize these.

02:13 I did have one who i almost thought did, except he was just forgetful.

02:19 Very, very forgetful.

02:24 Oh, you need an equation for problem 16.

02:27 Oops, i forgot to give you that.

02:33 I actually liked that, professor.

02:34 Cool.

02:40 Okay.

02:41 So we also need to know avagadro's number, which is important.

02:45 And interpreting atomic mass units am u and avagatro's number is six times e to the 23rd not e to the 243rd that's just 10 to the 23rd just written shorthand okay so now we're going to go ahead and solve for tylenol go ahead and write t over here just so we can keep track what's going on so there are about eight molecules of carbon tylenol nine molecules of hydrogen excuse me there are eight eight atoms of carbon, nine atoms of hydrogen.

03:47 Running out of space on my page over here.

03:52 Ok, plus 14 .007.

03:55 You can probably get away with excluding a few of these digits, but i guess i'm in the habit of doing things this way.

04:07 All right.

04:08 So take all that and divide it by avagadro's number.

04:14 6 .02 times the 23rd.

04:21 Before we move on, i think i should review what these atomic mass units are.

04:26 So an atomic mass unit, by convention, the number of grams per 6 .02 times 10 to the 23rd molecules.

04:46 So the reason why the atomic mass unit of hydrogen is 1 .008 is because if you gather 6 .022 times 10 to the 23rd, atoms, you put them in a pile and then you weigh them.

05:04 It should weigh about 1 .008 grams.

05:07 I recall being told by my chemistry textbook in high school that this amounted to if this were in marbles, it would bury the earth several miles deep, this number of marbles.

05:20 Anyhow, once we take the atomic mass units and we divide it by 6 .023, i should have written atomic mass units.

05:37 That's sort of written atomic mass units.

05:38 Way it's 6 .022 times 10 to the 23rd atoms.

05:45 You know how many grams we have for any amount.

05:49 Actually, molecule.

05:52 We're talking molecules right now.

05:54 It can't be used for atoms.

05:56 When it's used for any given element of the periodic table, i guess an atom.

06:06 It's a rather strange looking okay.

06:27 So once we solve for all this, we're going to know how many grams we have for any given molecule of tylenol.

06:40 So it's just the weight of a tylenol molecule that we're solving for.

06:44 Now this is a bit of a, this is a bit of a nuisance to solve for.