Problem 54 - Chemistry Matter and Change

Question

What is the percent composition of phosphoric acid \(\left(\mathrm{H}_{3} \mathrm{PO}_{4}\right) ?\)

Step-by-Step Solution

Answer

The percent composition of phosphoric acid, H3PO4, is as follows: Hydrogen: 3.08%, Phosphorus: 31.61%, and Oxygen: 65.31%.

Step 1: Find Molar Mass of Each Element in H3PO4

First, we need to find the molar mass of hydrogen (H), phosphorus (P), and oxygen (O) using the periodic table. Hydrogen: 1.008 g/mol Phosphorus: 30.97 g/mol Oxygen: 16.00 g/mol

Step 2: Calculate Total Molar Mass of H3PO4

Now, we will calculate the molar mass of H3PO4 by multiplying the molar mass of each element by its quantity in the compound and add them together. Molar mass of H3PO4 = (3 × 1.008 g/mol) + (1 × 30.97 g/mol) + (4 × 16.00 g/mol) Molar mass of H3PO4 = 3.024 g/mol + 30.97 g/mol + 64.00 g/mol = 97.994 g/mol

Step 3: Calculate Percent Composition of Each Element

Now we will calculate the percent composition of each element by dividing the molar mass of the element by the total molar mass of H3PO4 and multiplying by 100. Percent composition of Hydrogen: \(\frac{3.024 \text{ g/mol}}{97.994 \text{ g/mol}} \times 100 \% = 3.08\%\) Percent composition of Phosphorus: \(\frac{30.97 \text{ g/mol}}{97.994 \text{ g/mol}} \times 100 \% = 31.61 \%\) Percent composition of Oxygen: \(\frac{64.00 \text{ g/mol}}{97.994 \text{ g/mol}} \times 100\% = 65.31 \%\)

Step 4: Present the Percent Composition

Now that we have calculated the percent composition of each element in H3PO4, we can present it as follows: Hydrogen: 3.08%, Phosphorus: 31.61%, Oxygen: 65.31%

Key Concepts

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental step in determining its percent composition. Each element in a compound, such as phosphoric acid (H\(_3\)PO\(_4\)), has a specific molar mass. These are values that describe the mass of one mole of each element, found on the periodic table.

Let's break it down:

• Hydrogen, H: 1.008 g/mol
• Phosphorus, P: 30.97 g/mol
• Oxygen, O: 16.00 g/mol

To find the total molar mass of H\(_3\)PO\(_4\):

• Multiply hydrogen's molar mass by 3 (since there are three hydrogen atoms): 3 × 1.008 g/mol = 3.024 g/mol
• Use phosphorus's molar mass as is (it appears once in the compound): 1 × 30.97 g/mol = 30.97 g/mol
• Multiply oxygen's molar mass by 4 (four oxygen atoms here): 4 × 16.00 g/mol = 64.00 g/mol

Adding these gives us the total molar mass of H\(_3\)PO\(_4\):\[3.024 \, \text{g/mol} + 30.97 \, \text{g/mol} + 64.00 \, \text{g/mol} = 97.994 \, \text{g/mol}\]

Phosphoric Acid

Phosphoric acid is a triprotic acid with the formula H\(_3\)PO\(_4\). It is a common inorganic substance found in many chemical processes and products ranging from fertilizer production to food additives.

Understanding phosphoric acid involves recognizing its structure and its implications. Here's what you need to know:

• It has three hydrogen atoms which can be donated as protons (H\(^+\)), making it a triprotic acid.
• Each oxygen atom in phosphoric acid is bonded to both hydrogen and phosphorus, forming a tetrahedral molecular geometry around the phosphorus atom.

These chemical properties are important because they affect not only phosphoric acid's reactions, but also its role in various industrial applications, including rust removal and water treatment.

In terms of nomenclature, the systematic IUPAC name for phosphoric acid is 'tri-hydron phosphate', yet it is commonly referred to simply as phosphoric acid.

Elemental Analysis

Elemental analysis is a process used to determine the composition of a chemical compound. By finding the percent composition of each element within phosphoric acid, chemists can better understand its structure and properties.

The percent composition is calculated using the molar mass derived in molar mass calculation. Here's how it works:

• The molar mass of each individual element in the compound is divided by the total molar mass of the compound.
• This fraction is then multiplied by 100 to convert it into a percentage.

For example:

• Hydrogen's percent composition in H\(_3\)PO\(_4\) is calculated as: \[\frac{3.024 \, \text{g/mol}}{97.994 \, \text{g/mol}} \times 100\% = 3.08\%\]
• Phosphorus's percent composition is: \[\frac{30.97 \, \text{g/mol}}{97.994 \, \text{g/mol}} \times 100\% = 31.61\%\]
• Oxygen's percent composition follows with: \[\frac{64.00 \, \text{g/mol}}{97.994 \, \text{g/mol}} \times 100\% = 65.31\%\]

These percentages help provide a clear and detailed understanding of the chemical identity and can be vitally important in fields like pharmaceuticals, materials science, and environmental chemistry.