Question

Calculate the mass percent of each element in \(\mathrm{Na}_{2} \mathrm{CO}_{3}\).

Short answer

The mass percent of Sodium (Na) in \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is 43.40%, Carbon (C) is 11.32%, and Oxygen (O) is 45.28%.

Step-by-step solution

Calculate the molar mass

Firstly, determine the molar mass of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\). This can be calculated by adding up the atomic masses of all the atoms in the compound, weighted by their quantities. As per the periodic table, the atomic masses are approximately 23 g/mol for Sodium (Na), 12 g/mol for Carbon (C), and 16 g/mol for Oxygen (O). So, the molar mass of \(\mathrm{Na}_{2}\mathrm{CO}_{3}\) is \(2(23) + 12 + 3(16) = 106 g/mol\).

Calculate the mass of each element

Next, determine the mass contribution of each element in the compound. For Sodium (Na), it's \(2 \times 23 = 46 g/mol\). For Carbon (C), it's \(1 \times 12 = 12 g/mol\). For Oxygen (O), it's \(3 \times 16 = 48 g/mol\).

Calculate the mass percent

Finally, calculate the mass percent of each element by using the formula: \(\text{Mass Percent} = \frac{\text{mass of element}}{\text{molar mass of compound}} \times 100\%\). For Sodium (Na), the mass percent is \(\frac{46}{106} \times 100\% = 43.40\%\). For Carbon (C), the mass percent is \(\frac{12}{106} \times 100\% = 11.32\%\). For Oxygen (O), the mass percent is \(\frac{48}{106} \times 100\% = 45.28\%\)

Key concepts

Molar Mass

Understanding the concept of molar mass is foundational for chemistry. Molar mass refers to the mass of one mole of a chemical compound. It is typically expressed in grams per mole (g/mol), and it represents the total weight of all the atoms in a given compound. To calculate it, we sum up the atomic masses of all atoms present in the compound, each multiplied by its respective number in the formula.
For instance, in sodium carbonate, represented as \(\text{Na}_2\text{CO}_3\), the molar mass is found by adding:

• 2 Na atoms (23 g/mol each) = 46 g/mol
• 1 C atom (12 g/mol) = 12 g/mol
• 3 O atoms (16 g/mol each) = 48 g/mol

Adding these gives a molar mass of 106 g/mol for \(\text{Na}_2\text{CO}_3\). Understanding how to calculate the molar mass helps in many areas, from determining the mass percent of elements to calculating stoichiometric amounts in a reaction.

Atomic Mass

Atomic mass is the weight of a single atom of an element. It is usually expressed in atomic mass units (amu), where 1 amu is approximately the mass of one proton or neutron. The atomic mass found on the periodic table is often a weighted average of the isotopes of an element.
For instance, the atomic mass of sodium (Na) is about 23 amu, carbon (C) is about 12 amu, and oxygen (O) is about 16 amu.

• These values help in computing the molar mass for compounds like \(\text{Na}_2\text{CO}_3\).
• In practical applications, the atomic mass allows chemists to predict how elements will behave in chemical reactions and to calculate the masses of substances required or produced.

Understanding atomic mass is crucial, as it links the microscopic particles to the macroscopic properties we can measure.

Chemical Compound

A chemical compound is a substance formed from two or more elements that are chemically bonded together. The ratio of these elements in a compound is always fixed. This precise ratio defines the compound's unique properties.
For example, sodium carbonate \(\text{Na}_2\text{CO}_3\) comprises:

• 2 sodium atoms (Na)
• 1 carbon atom (C)
• 3 oxygen atoms (O)

Compounds can be represented using a chemical formula, which indicates the type and number of each atom. Chemical compounds are crucial in both natural processes and industrial applications, forming the basis for numerous materials and reactions we encounter daily. Understanding the nature of chemical compounds allows us to predict how they will react with other substances and guide their practical use in scientific and industrial settings.