Determine the empirical formulas of the compounds with the...

Determine the empirical formulas of the compounds with the following compositions by mass: (a) $42.1 \% \mathrm{Na}, 18.9 \% \mathrm{P}$, and $39.0 \% \mathrm{O}$ (b) $18.7 \% \mathrm{Li}, 16.3 \% \mathrm{C},$ and $65.0 \% \mathrm{O}$ (c) $60.0 \% \mathrm{C}, 4.4 \% \mathrm{H},$ and the remainder $\mathrm{O}$

Determine the empirical formulas of the compounds with the following compositions by mass:
(a) $42.1 \% \mathrm{Na}, 18.9 \% \mathrm{P}$, and $39.0 \% \mathrm{O}$
(b) $18.7 \% \mathrm{Li}, 16.3 \% \mathrm{C},$ and $65.0 \% \mathrm{O}$
(c) $60.0 \% \mathrm{C}, 4.4 \% \mathrm{H},$ and the remainder $\mathrm{O}$

Key Concepts

Simplest Whole Number Ratio

Once the number of moles for each element is calculated, they are compared by dividing through by the smallest number of moles present. This process simplifies the ratios to the smallest whole numbers, resulting in the empirical formula that best represents the composition of the compound.

Mole Concept

The mole concept allows for the conversion of mass into number of atoms or molecules based on atomic or molecular weight. By dividing the mass percentage by the atomic mass of each element, the relative number of moles is determined, which is essential in finding the ratio between elements.

Empirical Formula

The empirical formula represents the simplest whole number ratio of atoms of each element in a compound. It provides a basic description of the composition of a compound without indicating the actual number of atoms present as found in the molecular formula.

Percent Composition

Percent composition breaks down the mass of each element as a percentage of the total mass of the compound. This information is fundamental for converting mass data into mole quantities, which is a key step in empirical formula determination.

Transcript

00:01 The key to determining the empirical formula when you are given percentages is to assume that you have 100 grams of the substance.

00:08 If you have 100 grams of the substance, then the percentage corresponds to the mass of each element that you have.

00:16 So if it is 42 .1 percent sodium, we have 42 .1 grams of sodium, which we can convert to moles of sodium in an attempt to determine the empirical formula by dividing by the molar mass of sodium.

00:33 We'll then do the same thing with phosphorus, convert it to grams, and divide by the molar mass of phosphorus, and then we'll take the percentage, now a mass of oxygen, and divide by the molar mass of oxygen.

00:47 This will give us 1 .83 moles of sodium for every 0 .610 moles of phosphorus, for every 2 .4, 4 moles of oxygen.

00:59 These are not whole numbers.

01:00 We need whole numbers for the empirical formula, so we'll divide each of these by the smaller of the three, giving us four moles oxygen for every one mole of phosphorus, for every three moles of sodium.

01:14 So the empirical formula then is na3, p -o -4.

01:20 Next, we have 18 .7 % lithium.

01:23 100 grams of the substance gives us 18 .7 grams of lithium.

01:28 Dividing that by its smaller mass will give us the moles of lithium.

01:31 We'll do the same thing with carbon.

01:34 Take the 16 .3 grams divided by its molar mass, and then take the 65 .0 grams of oxygen divide by its molar mass.

01:44 This gives us 2 .69 moles of lithium, 1 .35 moles of carbon, and 4 .06 moles of oxygen.

01:54 In an attempt to get whole numbers, we'll divide each of these by the smaller of the three, giving us 1 mole of carbon, every 3 moles of oxygen, for every 2 moles of lithium...

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