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 ${\text{NH}}_2\text{CO}$.

Step-by-step solution

Convert grams to moles

We have the grams for each element as follows: - Nitrogen (N): 1.121 g - Hydrogen (H): 0.161 g - Carbon (C): 0.480 g - Oxygen (O): 0.640 g Use the molar mass of each element to convert grams to moles: - Moles of N = $\frac{1.121\text{ g}}{14.01\text{ g/mol}}$ - Moles of H = $\frac{0.161\text{ g}}{1.01\text{ g/mol}}$ - Moles of C = $\frac{0.480\text{ g}}{12.01\text{ g/mol}}$ - Moles of O = $\frac{0.640\text{ g}}{16.00\text{ g/mol}}$

Calculate the mole ratios

Now that we have the moles for each element, we will calculate the mole ratios. - Moles of N = $\frac{1.121}{14.01}=0.080$ - Moles of H = $\frac{0.161}{1.01}=0.160$ - Moles of C = $\frac{0.480}{12.01}=0.040$ - Moles of O = $\frac{0.640}{16.00}=0.040$

Determine the simplest whole-number ratio

Next, we need to derive the simplest whole-number ratio between the mole ratios calculated in Step 2. Divide each mole ratio by the smallest one, which in this case is 0.040 (moles of Carbon and Oxygen): - Ratio for N = $\frac{0.080}{0.040}=2$ - Ratio for H = $\frac{0.160}{0.040}=4$ - Ratio for C = $\frac{0.040}{0.040}=1$ - Ratio for O = $\frac{0.040}{0.040}=1$

Write the empirical formula

Lastly, we will write the empirical formula using the simplest whole number ratio obtained in Step 3: The empirical formula of urea is: ${\text{NH}}_2\text{CO}$

Key concepts

Mole Concept

The mole concept is a fundamental idea in chemistry. It's used to measure the amount of substance. One mole is equivalent to Avogadro's number, which is approximately $6.022\times {10}^{23}$ entities, such as atoms or molecules. In the context of finding an empirical formula, the mole allows us to convert from the mass of each element present in a compound to the number of moles. This is necessary because the atomic mass of elements in the periodic table is given in grams per mole. To determine how many moles of each element are present in a sample:- Divide the mass of the element (in grams) by its molar mass.- For example, to find the moles of nitrogen $(N)$ in a given sample: calculate $\frac{1.121\text{ g}}{14.01\text{ g/mol}}$.This process allows chemists to work with quantities that are easier to manipulate when determining chemical formulas.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It is essential for understanding the quantitative relationships in chemistry. At its core, it's about understanding how much of a substance is involved in a chemical reaction. For the empirical formula, stoichiometry helps us see the simplest ratio of moles between different elements in a compound. This is done by: - Calculating the mole of each element in a compound - Determining the simplest whole-number ratio of these moles. For example, by using stoichiometry with the computed values from the mole concept, we obtain the ratios such as 2:4:1:1 for nitrogen, hydrogen, carbon, and oxygen, respectively, for urea. These ratios are crucial as they define the proportional content of each element in the empirical formula.

Chemical Formula

A chemical formula is a concise way of expressing information about the atoms that constitute a particular chemical compound. It uses letters for elements and numbers to denote the elements' presence in a compound. There are two main types of formulas:

• Empirical Formula: Shows the simplest whole-number ratio of the elements in a compound.
• Molecular Formula: Provides the exact number of each type of atom present in the molecule.

The empirical formula is derived by first determining the mole ratio of elements, simplifying it to the smallest whole numbers (like 2:4:1:1 for NH₂CO). It is a foundational representation of the compound's composition but does not always reflect the total number of atoms in the actual molecule, which is given by the molecular formula.

Urea

Urea is a commonly encountered organic compound with significant relevance in both biology and chemistry. Its chemical formula is NH₂CONH₂, and it is prominently used as a fertilizer. In this exercise, we look at determining the empirical formula of urea, which can be simplified to NH₂CO using the mole concept and stoichiometry. Urea is composed of:

• Nitrogen (N)
• Hydrogen (H)
• Carbon (C)
• Oxygen (O)

While the empirical formula helps in understanding the basic composition and ratio of these elements, it's important to note the difference it holds with the molecular formula. Understanding urea's composition is key in many scientific applications, including biochemical processes and agricultural practices.