How Many Hydrogen Atoms Are In 0.1488g Of Phosphoric Acid

How Many Hydrogen Atoms Are in 0.1488g of Phosphoric Acid?

At first glance, the question “how many hydrogen atoms are in 0.1488g of phosphoric acid?” seems like a simple, straightforward calculation. Yet, it opens a window into the fundamental language of chemistry—a world where invisible particles are counted not one by one, but in mind-boggling collections defined by the mole. This precise mass, 0.1488 grams, is not arbitrary; it carries with it four significant figures, demanding a calculation that honors that precision. Understanding how to navigate from a tangible, weighable mass to an abstract count of individual atoms is a cornerstone skill for any student of science and a critical tool in fields from pharmaceutical development to materials engineering. This article will dismantle the problem step-by-step, building from the molecular formula to the final, colossal number, ensuring you grasp not just the how, but the profound why behind each operation.

Understanding the Subject: Phosphoric Acid (H₃PO₄)

Before any calculation can begin, we must establish what we are working with. The compound in question is phosphoric acid, a triprotic acid with the molecular formula H₃PO₄. This formula is our most important piece of information. It tells us that a single, discrete molecule of phosphoric acid is composed of:

• Three hydrogen (H) atoms
• One phosphorus (P) atom
• Four oxygen (O) atoms

The "triprotic" nature is key—it means each molecule can donate up to three protons (H⁺ ions), which is directly why our final count of hydrogen atoms will always be exactly three times the number of phosphoric acid molecules we possess. Our goal, therefore, is a two-part journey: first, find the number of H₃PO₄ molecules in 0.1488g, and second, multiply that number by three.

The Step-by-Step Calculation: From Grams to Atoms

We will use the mole concept, the bridge between the macroscopic world we can measure (grams) and the atomic-scale world we need to count. The process follows a reliable, unit-canceling pathway.

Step 1: Calculate the Molar Mass of H₃PO₄

The molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It is the sum of the atomic masses of all atoms in the formula, using values from the periodic table.

• Atomic mass of H = 1.008 g/mol
• Atomic mass of P = 30.974 g/mol
• Atomic mass of O = 16.00 g/mol (often rounded for calculation, but we'll use 16.00 for consistency with the given precision).

Calculation: (3 × H) + (1 × P) + (4 × O) = (3 × 1.008) + (1 × 30.974) + (4 × 16.00) = 3.024 + 30.974 + 64.00 = 97.998 g/mol

This means one mole of phosphoric acid molecules weighs 97.998 grams and contains 6.022 × 10²³ molecules (Avogad