Question

A sample of urea contains \(1.121 \mathrm{g} \mathrm{N}, 0.161 \mathrm{g} \mathrm{H}, 0.480 \mathrm{g} \mathrm{C}\) and \(0.640 \mathrm{g}\) O. What is the empirical formula of urea?

Short answer

The empirical formula of urea is \(N_2H_4CO\).

Step-by-step solution

Convert mass to moles

To find the number of moles, divide the mass of each element by its molar mass: - Nitrogen: \(1.121 \mathrm{g} \mathrm{N} \times \frac{1 \mathrm{mol} \mathrm{N}}{14.01 \mathrm{g} \mathrm{N}} = 0.080 \mathrm{mol} \mathrm{N}\) - Hydrogen: \(0.161 \mathrm{g} \mathrm{H} \times \frac{1 \mathrm{mol} \mathrm{H}}{1.008 \mathrm{g} \mathrm{H}} = 0.160 \mathrm{mol} \mathrm{H}\) - Carbon: \(0.480 \mathrm{g} \mathrm{C} \times \frac{1 \mathrm{mol} \mathrm{C}}{12.01 \mathrm{g} \mathrm{C}} = 0.040 \mathrm{mol} \mathrm{C}\) - Oxygen: \(0.640 \mathrm{g} \mathrm{O} \times \frac{1 \mathrm{mol} \mathrm{O}}{16.00 \mathrm{g} \mathrm{O}} = 0.040 \mathrm{mol} \mathrm{O}\)

Divide moles by smallest number of moles

The smallest number of moles among the elements is 0.040. Now divide the moles of each element by the smallest number of moles: - Nitrogen: \(\frac{0.080}{0.040} = 2\) - Hydrogen: \(\frac{0.160}{0.040} = 4\) - Carbon: \(\frac{0.040}{0.040} = 1\) - Oxygen: \(\frac{0.040}{0.040} = 1\)

Round ratios to nearest whole numbers

The current ratios of elements in the formula are: \(2 N : 4 H : 1 C : 1 O\) These ratios are already rounded to whole numbers.

Combine whole number ratios to form empirical formula

Finally, combine the whole number ratios found in step 3 to form the empirical formula: \(N_2H_4CO\) The empirical formula of urea is \(N_2H_4CO\).

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. Essentially, it is the calculation of reactants and products in chemical reactions. For example, when determining the empirical formula of a compound, such as urea, stoichiometry allows us to convert the mass of each element present in a sample to the number of moles. The concept empowers students to systematically approach chemical equations and balance them, relying on the law of conservation of mass which states that in a chemical reaction, matter is neither created nor destroyed.

One essential stoichiometric principle in finding an empirical formula is that the amount of each element must be converted from grams to moles since chemical reactions and formulas are based on moles rather than weight. This sets the foundation for understanding and quantifying the chemical composition of substances, as well as predicting the outcomes of chemical reactions.

Molar Mass

The molar mass of an element is defined as the mass of one mole of that element and is expressed in grams per mole (g/mol). It is a bridge between the atomic microscopic world of molecules and the macroscopic world we can measure. The molar mass tells us how many grams are in one mole of a substance and it directly corresponds to the atomic weight of an element, as seen on the periodic table.

To determine the empirical formula of a compound, you first need to calculate how many moles of each element is in your sample. This is done by dividing the mass of each element by its molar mass. For instance, carbon has a molar mass of approximately 12.01 g/mol. If you have 0.480 g of carbon, as in the urea example, you can find out the number of moles by dividing the mass (0.480 g) by its molar mass (12.01 g/mol). Understanding how to accurately calculate molar mass is crucial in stoichiometric calculations and in constructing empirical formulas.

Chemical Composition

Chemical composition refers to the identity and relative number of the elements that make up any particular compound. Every compound has a unique composition represented by a specific empirical or molecular formula. For example, determining the empirical formula of urea involves finding the simplest whole-number ratio between the atoms of the elements present.

In the urea example, the empirical formula is derived from the exact ratio of moles of each element in the sample. The chemical composition essentially determines the properties of the compound, such as reactivity, phase at room temperature, color, and biological activity. Knowledge of the chemical composition of substances is paramount in various industries, including pharmaceuticals, agriculture, and materials science. Additionally, an accurate understanding of the chemical composition is necessary for mixtures, solutions, and compounds, and is fundamental to nearly all chemical analyzes and experimental designs.

Mole to Mole Conversion

Mole to mole conversion is a key component of stoichiometry, often used to calculate the amount of reactants needed or products formed in a chemical reaction. It is based on Avogadro's number, which is approximately 6.022 x 10^23, representing the number of atoms or molecules in one mole of a substance.

In our context, after finding out the moles of each element in the compound, the next step is to divide these values by the smallest number of moles present to get a ratio. In the urea example, dividing the number of moles of nitrogen, carbon, hydrogen, and oxygen by the smallest number of moles (which was for carbon and oxygen, 0.040 moles), helps to normalize the ratio to the smallest whole numbers. Essentially, mole to mole conversions allow us to scale up from the microscopic level to macroscopic measurements, which can be practically used and measured, thus bridging the gap between the conceptual and practical aspects of chemistry.