Question

The explosive trinitrotoluene (TNT) has the composition \(37.01 \% \mathrm{C}, 2.22 \% \mathrm{H}, 18.50 \% \mathrm{~N}\), and \(42.27 \% \mathrm{O}\). What is the empirical formula of TNT?

Short answer

The empirical formula of TNT is C3H2NO2.

Step-by-step solution

Convert percentages to grams

The problem gives the percentage composition of the compound by mass. Pretend there is a 100 gram sample of TNT. Then the mass of each element in that sample is equal to its percentile. This means there would be 37.01g of Carbon (C), 2.22g of Hydrogen (H), 18.50g of Nitrogen (N) and 42.27g of Oxygen (O).

Convert mass to moles

Next, convert the mass of each element into moles by dividing by its atomic mass. The atomic masses are approximately: C = 12.01 g/mol, H = 1.01 g/mol, N = 14.01 g/mol, and O = 16.00 g/mol. So, for each element we calculate: \(C: \frac{37.01g}{12.01g/mol} = 3.08 mol\), \(H: \frac{2.22g}{1.01g/mol} = 2.20 mol\), \(N: \frac{18.50g}{14.01g/mol} = 1.32 mol\), \(O: \frac{42.27g}{16.00g/mol} = 2.64 mol\)

Find ratio of moles to the smallest amount

To find the empirical formula, divide the number of moles of each element by the smallest number of moles you calculated. In this case, the smallest amount of moles is 1.32 for Nitrogen. So, we get \(C: \frac{3.08mol}{1.32mol} = 2.33\), \(H: \frac{2.20mol}{1.32mol} = 1.67\), \(N: \frac{1.32mol}{1.32mol} = 1\), \(O: \frac{2.64mol}{1.32mol} = 2\). Note that these numbers should be close to whole numbers. If not, you might have to round or multiply all of them by the same factor to get whole numbers.

Construct empirical formula

Based on the mole ratios obtained, the empirical formula can be represented as C2.33H1.67N1O2. Because these values should be close to whole numbers and we're only slightly off, the most probable empirical formula would be C3H2NO2 when rounded.

Key concepts

Mole Conversion

Converting mass to moles is a foundational step in determining the empirical formula of a compound. When you want to find the number of moles from a given mass, you use the atomic mass of each element as your conversion factor. This step is crucial because chemistry often deals with reactions in terms of moles rather than grams. Here’s how you do it:

• Identify the mass of each element in grams. For TNT, for example, we use the fictional 100g sample, so the amounts are equal to the percentage.
• Use the atomic mass of each element to convert grams to moles. For example, if you have 37.01g of Carbon, you divide by its atomic mass 12.01g/mol to get 3.08 moles.

Breaking down substances into moles allows chemists to better understand and predict how substances will react under various conditions.
Remember that these conversions are based on atomic masses in g/mol, which are usually found on the periodic table.

Percentage Composition

Percentage composition is a way to express how much of each element is contained in a compound by mass. This information provides insight into the compound's makeup:

• It tells us the mass percentage of each element in a given compound.
• For determining empirical formulas, it's often easiest to assume a 100g sample. This way, the percentages directly translate to grams.

For example, with TNT, the problem gives 37.01% Carbon, which translates to 37.01 grams in 100 grams of sample. This simple step is the basis for converting percentages into grams to proceed with further calculations like mole conversion.

Atomic Mass

Atomic mass is the mass of an atom, typically measured in atomic mass units (amu), and for practical chemistry purposes, it's expressed in grams per mole (g/mol). This is critical when working with mole conversions:

• Atomic mass provides the necessary factor to convert between the mass of an element and the number of moles.
• It reflects the average mass of atoms in an element, considering isotopic distribution.

For instance, the atomic mass of Carbon is 12.01 g/mol, meaning 1 mole of Carbon weighs 12.01 grams. Using these atomic masses helps chemists accurately weigh out substances for reactions or calculations like finding empirical formulas.

Chemical Composition

Understanding a compound's chemical composition means knowing what elements are present and in what quantities. This forms the basis of determining chemical formulas. Here are key points to know:

• The chemical composition of a compound gives insight into how it will react with other substances.
• The empirical formula, for instance, gives the simplest whole-number ratio of elements in a compound.

In the context of TNT, knowing the composition is essential for identifying its empirical formula. By knowing it’s composed of 37.01% Carbon, 2.22% Hydrogen, 18.50% Nitrogen, and 42.27% Oxygen, you can perform mole conversions to find the simplest ratio of these elements, leading to the empirical formula C3H2NO2.