Carbohydrates are compounds containing carbon, hydrogen, and...

Carbohydrates are compounds containing carbon, hydrogen, and oxygen in which the hydrogen to oxygen ratio is $2: 1 .$ A certain carbohydrate contains 40.0 percent carbon by mass. Calculate the empirical and molecular formulas of the compound if the approximate molar mass is $178 \mathrm{~g}$

Key Concepts

Empirical Formula

The empirical formula represents the simplest whole-number ratio of the atoms of each element in a compound. It is derived by converting the percentage composition of elements to moles and then normalizing the values to the smallest whole numbers. This concept is fundamental in chemical analysis and is used as the basis for further molecular structure determination.

Molecular Formula

The molecular formula shows the exact number of atoms of each element in a single molecule of the compound. It is determined by comparing the empirical formula mass to the given molar mass of the compound. This concept connects the relative proportions provided by the empirical formula to the actual molecular structure.

Percent Composition

Percent composition refers to the percentage by mass of each element present in a compound. This concept is crucial for converting mass percentages into moles, which is the starting point for determining both the empirical and molecular formulas.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole. It is essential for relating the macroscopic mass of a substance to the number of moles, and it is used to scale the empirical formula up to the molecular formula when the actual molar mass of the compound is known.

Transcript

00:01 So for this problem, we're supposed to find the empirical and molecular formula of some carbohydrate, given that the molar mass of that carbohydrate is 178 grams per mole, and that the ratio of hydrogen to oxygen is 2 to 1.

00:21 So that's a ratio.

00:24 So the first thing that we want to do is we want to find the relative masses of each of these elements within the overall compound.

00:31 And another useful piece of information that we are given is that it is 40 % carbon by mass.

00:40 So let's hypothetically assume that the mass of the total carbohydrate is 100 grams.

00:51 From there, we then would know that the mass of the carbon would be 40 grams because it is 40 % carbon.

01:00 And we would know that the rest of the compound, which contains h and o, would be 60 grams.

01:10 So now that we have that, we can then convert it into moles of each.

01:15 So we know we have 40 grams of carbon, and we know that in every mole of carbon, that there is 12 .01 grams.

01:29 And when we multiply that out, you'll get 3 .33 moles of carbon.

01:36 Now, doing this is a little more complicated, because we know that the amount of hydrogen and oxygen combined is 60 grams, but we don't know how much hydrogen and how much oxygen there is individually.

01:48 But we can do this in a combined approach, because we know that the general empirical formula for the hydrogen and the oxygen is h2o.

01:59 Now, this is a really important distinction to make.

02:01 This does not mean that there is water.

02:03 This is just a relative ratio between hydrogen and oxygen, and we're going to use this to find the moles of that, of that hydrogen and oxygen component within our overall compound to combine this and make it a more efficient approach.

02:18 So we know that we have 60 grams of some h2o that has an empirical formula like that...

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