Problem 78 - Chemistry The Molecular Nature of Matter

Question

How many atoms of each kind are represented in the following formulas? For each, name the elements present. (a) \(\mathrm{H}_{3} \mathrm{PO}_{4},\) (b) \(\mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}\), (c) \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br}\) (d) \(\mathrm{Fe}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\) (e) \(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3}\)

Step-by-Step Solution

Answer

a) 3 H, 1 P, 4 O b) 1 Ca, 4 H, 2 P, 8 O c) 4 C, 9 H, 1 Br d) 3 Fe, 2 As, 8 O e) 3 C, 8 H, 3 O. Elements are listed within each step.

Step 1 - Analyze the first compound

For \(\mathrm{H}_{3} \mathrm{PO}_{4}\), count the number of atoms for each element. There are 3 atoms of hydrogen (H), 1 atom of phosphorus (P), and 4 atoms of oxygen (O). Elements present: hydrogen, phosphorus, oxygen.

Step 2 - Analyze the second compound

For \(\mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2}\), multiply the subscript of each atom in the parenthesis by 2 because of the subscript outside the parenthesis. There is 1 calcium atom (Ca), 4 hydrogen atoms (H), 2 phosphorus atoms (P), and 8 oxygen atoms (O). Elements present: calcium, hydrogen, phosphorus, oxygen.

Step 3 - Analyze the third compound

For \(\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br}\), count the number of atoms for each element. There are 4 atoms of carbon (C), 9 atoms of hydrogen (H), and 1 atom of bromine (Br). Elements present: carbon, hydrogen, bromine.

Step 4 - Analyze the fourth compound

For \(\mathrm{Fe}_{3}\left(\mathrm{AsO}_{4}\right)_{2}\), multiply the subscripts inside the parenthesis by 2, due to the subscript 2 outside the parenthesis. There are 3 atoms of iron (Fe), 2 atoms of arsenic (As), and 8 atoms of oxygen (O). Elements present: iron, arsenic, oxygen.

Step 5 - Analyze the fifth compound

For \(\mathrm{C}_{3} \mathrm{H}_{5}(\mathrm{OH})_{3}\), count the number of atoms for each element and multiply the number of atoms in the (OH) group by 3. There are 3 atoms of carbon (C), 5+3=8 atoms of hydrogen (H), and 3 atoms of oxygen (O). Elements present: carbon, hydrogen, oxygen.

Key Concepts

Counting Atoms in Formulas

When analyzing chemical formulas, it's critical to understand how to count atoms of each element within a compound. A formula like \( \mathrm{H}_{2}O \) represents water, and tells us there are two atoms of hydrogen (H) and one atom of oxygen (O). Counting these atoms becomes slightly more complex with larger molecules that involve subscripts and parentheses.

For example, in \( \mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2} \), the subscript outside the parentheses means every atom inside is multiplied by two. It's important to distribute the subscript to all elements within the parentheses. So, we have 1 calcium atom, 4 hydrogen atoms (2 x 2 due to the subscript), 2 phosphorus atoms (1 x 2), and 8 oxygen atoms (4 x 2). By careful counting and multiplying, we ensure an accurate tally of each type of atom present in the compound.

Identifying Elements in Compounds

Understanding the types of elements that make up a chemical compound is essential. Every chemical element has a unique symbol, usually derived from its English or Latin name, like H for hydrogen or Fe for iron. In the formula \( \mathrm{Fe}_{3}\left(\mathrm{AsO}_{4}\right)_{2} \) we identify three different elements: iron (Fe), arsenic (As), and oxygen (O).

It's equally crucial to recognize that these symbols represent individual atoms in the chemical formula. The compound mentioned above contains 3 atoms of iron, as indicated by the subscript '3' after the iron symbol. Understanding the symbols and their quantities helps in comprehending the compound's composition and properties.

Chemical Nomenclature

Chemical nomenclature, the naming of compounds, is a methodical way to describe the composition of substances. For instance, \( \mathrm{C}_{4} \mathrm{H}_{9} \mathrm{Br} \) is read as 'butyl bromide'. 'Butyl' indicates a 4-carbon chain (from 'but-', indicating four), 'bromide' signifies the presence of bromine (Br).

Understanding nomenclature is valuable when translating between the name of a compound and its chemical formula. For example, 'phosphoric acid' refers to \( \mathrm{H}_{3} \mathrm{PO}_{4} \). Knowing this allows you to predict the formula from the name and vice versa. The systematic approach to naming ensures that the chemical composition of a compound is clear and universally understood among scientists.