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Chapter 3: Problem 36

How many total atoms are there in seven dozen formulas of nitric acid, \(\mathrm{HNO}_{3}\) ?

Short Answer

Expert verified
420 atoms

Step by step solution

01

Understanding Dozen and Molecule Composition

A dozen is equal to 12. The formula for nitric acid \(\mathrm{HNO}_{3}\) includes one hydrogen (H) atom, one nitrogen (N) atom, and three oxygen (O) atoms.
02

Calculate Atoms in One Molecule of \(\mathrm{HNO}_{3}\)

Sum the total number of atoms in one molecule: \( 1 \mathrm{H} + 1 \mathrm{N} + 3 \mathrm{O} = 5 \mathrm{atoms} \ in \ one \ \mathrm{HNO}_{3} \ molecule \).
03

Calculate the Number of Formulas in Seven Dozen

Multiply the number of formulas in one dozen by seven: \[ 7 \cdot 12 = 84 \ \mathrm{formulas} \] in seven dozen.
04

Total Atoms in Seven Dozen Formulas

Multiply the total number of atoms in one formula by the total number of formulas: \[ 84 \ \mathrm{formulas} \ \cdot 5 \ \mathrm{atoms/formula} = 420 \ \mathrm{atoms} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

dozen calculation
To understand how many atoms are in seven dozen formulas of nitric acid, \(\text{HNO}_{3}\), we first need to grasp the concept of a dozen. A dozen is simply a way to group items and is equivalent to 12 items. Imagine having a dozen eggs: you would have 12 eggs. Similarly, a dozen molecules mean 12 molecules. So, for seven dozen molecules, you multiply 12 (one dozen) by 7, which gives you 84 molecules of \(\text{HNO}_{3}\).
atomic composition
Next, let's delve into the atomic composition of nitric acid (\(\text{HNO}_{3}\)). A single molecule of \(\text{HNO}_{3}\) consists of the following atoms:
  • 1 Hydrogen (H) atom
  • 1 Nitrogen (N) atom
  • 3 Oxygen (O) atoms
To determine the total number of atoms in one molecule, sum these counts together. So, you have 1 H + 1 N + 3 O, which equals 5 atoms in one molecule of \(\text{HNO}_{3}\).
multiplication in chemistry
Once you grasp the atomic composition, you can perform multiplication in chemistry to scale this up. We have already calculated that there are 84 molecules of \(\text{HNO}_{3}\) in seven dozen. To find the total number of atoms, you multiply the number of atoms in one molecule by the number of these molecules: \[ 84 \text{ molecules} \times 5 \text{ atoms/molecule} = 420 \text{ atoms} \] This step shows how mathematical operations like multiplication are critical in chemistry for scaling up quantities.
chemical formulas
Chemical formulas provide a shorthand way to represent chemical compounds. For instance, \(\text{HNO}_{3}\) is the chemical formula for nitric acid. Each symbol in the formula corresponds to an element, and subscripts show the number of atoms of each element in one molecule. Understanding these symbols and numbers is vital for calculating the total atoms in multiple molecules. In the case of \(\text{HNO}_{3}\), the formula tells you there are five atoms present in one molecule.

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Most popular questions from this chapter

The formula for vitamin \(\mathrm{B}_{12}\) is \(\mathrm{C}_{63} \mathrm{H}_{88} \mathrm{CoN}_{14} \mathrm{O}_{14} \mathrm{P}\). (a) How many atoms make up one molecule of vitamin \(\mathrm{B}_{12}\) ? (b) What percentage of the total atoms are carbon? (c) What fraction of the total atoms are metallic?

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