The molecular formula of aspartame, the artificial sweetener...

The molecular formula of aspartame, the artificial sweetener marketed as NutraSweet $^{\oplus}$, is $\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{5} .$ (a) What is the molar mass of aspartame? (b) How many moles of aspartame are present in $1.00 \mathrm{mg}$ of aspartame? (c) How many molecules of aspartame are present in $1.00 \mathrm{mg}$ of aspartame? (d) How many hydrogen atoms are present in $1.00 \mathrm{mg}$ of aspartame?

The molecular formula of aspartame, the artificial sweetener marketed as NutraSweet $^{\oplus}$, is $\mathrm{C}_{14} \mathrm{H}_{18} \mathrm{~N}_{2} \mathrm{O}_{5} .$ (a) What is the molar mass of aspartame? (b) How many moles of aspartame are present in $1.00 \mathrm{mg}$ of aspartame? (c) How many molecules of aspartame are present in $1.00 \mathrm{mg}$ of aspartame?
(d) How many hydrogen atoms are present in $1.00 \mathrm{mg}$ of aspartame?

Key Concepts

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions using the molecular formula, molar mass, and mole concept. It helps determine the precise numbers and ratios of atoms and molecules in chemical compounds and reactions, allowing conversion between mass, moles, and individual atoms or molecules.

Avogadro's Number

Avogadro's number, 6.022 x 10^23, is the number of particles in one mole of any substance. It is used to convert between the number of moles and the number of molecules (or atoms), permitting the calculation of the total count of entities in a given sample.

Mole (Amount of Substance)

A mole is a unit that quantifies the amount of substance, defined as containing exactly 6.022 x 10^23 elementary entities (such as atoms, molecules, or ions). This concept allows chemists to bridge the gap between the microscopic world of atoms and the macroscopic quantities we can measure.

Molar Mass

Molar mass is defined as the mass of one mole of a substance and is expressed in grams per mole. It is calculated by summing the atomic masses of all atoms present in the molecular formula, making it crucial for converting between the mass of a substance and the number of moles.

Molecular Formula

The molecular formula represents the types and numbers of atoms in a molecule. It provides essential information on the composition of the compound, which is used to calculate other properties such as molar mass and the number of specific atoms present in a given sample.

Transcript

00:02 Hi there.

00:03 Welcome to problem number 38.

00:06 In problem number 38, we are dealing with aspartame, whose formula is c -14, h -18, n2 -05.

00:21 Since that is kind of long in the interest of keeping this recording under an hour, i'm just kidding, but i am going to just abbreviate it asp, and i'm trying to write it out in these equations.

00:36 All right, so the first thing we need to do is find its molar mass.

00:41 So that means we need to take 14 times the molar mass of carbon, which is 12 .01 grams per mole.

00:52 And then we need to add that.

00:54 Since there are 18 hydrogens, i need to take 18 times the molar mass of hydrogen.

01:01 And all of these molar masses are coming from the periodic table.

01:06 And then there are two nitrogen.

01:10 Each nitrogen is 14 .01 grams per mole.

01:15 And finally, five oxygens at 16 grams per mole.

01:23 Grabbing our calculators, completing this calculation, we see that the molar mass of aspartame is 294 .30 grams per mole.

01:41 All right, so that is our answer for part a.

01:44 In part b, it says that we have 1 .00.

01:51 So three significant figures, milligrams of the aspartame.

01:58 So i'm going to start using my abbreviation rather than writing out the whole formula.

02:02 So i have one milligram of aspartame, and i want to know how many moles this is.

02:09 Well, i have the molar mass that is in grams per mole.

02:12 So i need to get to grams first.

02:15 So i'm going to convert.

02:16 There are 1 ,000 milligrams of aspartame in every gram.

02:24 All right, so this converts it to grams so that now i can use that molar mass.

02:34 In every mole of aspartame, there are 294 .30 grams.

02:41 That's what we just found out in part a.

02:45 That tells us how many grams there are per every mole.

02:47 I wanted to put grams of aspartame in the denominator and moles in the numerator because i want grams to cancel and i want moles left in my answer.

02:58 All right, now i'm ready to solve this.

03:00 I will take 1 and divide it by 1 ,000 and divide it by 294 .3.

03:06 And as you may predict, we get a very small number, 3 .40 times 10 to the negative 6th moles of aspartame...

Please give Ace some feedback