(a) The molecular formula of acetylsalicylic acid (aspirin),...

(a) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$. How many moles of $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$ are in a 0.500 -g tablet of aspirin? (b) How many molecules of $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$ are in this tablet? (c) How many carbon atoms are in the tablet?

(a) The molecular formula of acetylsalicylic acid (aspirin), one of the most common pain relievers, is $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$. How many moles of $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$ are in a 0.500 -g tablet of aspirin?
(b) How many molecules of $\mathrm{C}_{9} \mathrm{H}_{8} \mathrm{O}_{4}$ are in this tablet?
(c) How many carbon atoms are in the tablet?

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, calculated by adding together the atomic masses of all the atoms present in its molecular formula. It is essential for converting a given mass of a compound into moles, allowing for further quantitative analysis in chemical reactions.

Mole Concept

The mole is a fundamental unit in chemistry that represents a specific number (Avogadro's number) of particles, whether they be atoms, molecules, or ions. This concept is crucial for linking the macroscopic mass of a sample to the number of microscopic entities it contains.

Avogadro's Number

Avogadro's number, approximately 6.022 × 10^23, is the constant that defines the number of constituent particles in one mole of a substance. It is a key factor in converting moles to the actual number of molecules or atoms in a sample.

Stoichiometry

Stoichiometry involves the calculations based on the quantitative relationships between substances in chemical reactions. It relies on molecular formulas and molar masses to relate masses of compounds to the number of moles, molecules, or atoms, enabling precise prediction and analysis of chemical quantities.

Transcript

00:01 Hi there.

00:03 This is problem number 88.

00:07 In problem number 88, we are working with aspirin or acetyosalic acid, and its formula is c9 h8 -04.

00:24 And we have a series of three questions here, all about this aspirin, where we're going to have to use molar mass to convert from grams to moles.

00:35 Then we're going to need to use avagalase.

00:37 Number to figure out number of molecules and then eventually number of atoms.

00:43 So let's go ahead and get started.

00:45 Our first part wants us to take 0 .50 grams and calculate the number of moles.

00:56 So we need the molar mass of the aspirin to do this.

01:00 We calculate the molar mass by using the periodic table and taking the atomic masses because the atomic mass in amus is the same numerically as the molar mass in grams.

01:13 We're going to add these all together.

01:15 So nine carbons, eight hydrogen, four oxygen, and we get 180 .16 grams per mole.

01:24 So i want to put those grams on the bottom in the denominator because i want grams to cancel.

01:39 That means that mole goes in the numerator.

01:47 And this one step will give me the answer of moles.

01:51 So i'm going to take 0 .5 divided by 180 .16 and rounded to three significant figures, since .5000 has three significant figures.

02:08 And that gives me .00278 moles of c9, h8, 0 .4.

02:19 And that is our answer for part a...