Problem 5 - General Chemistry: Principles and Modern Applications

Question

Calculate the total number of (a) atoms in one molecule of trinitrotoluene (TNT), \(\mathrm{CH}_{3} \mathrm{C}_{6} \mathrm{H}_{2}\left(\mathrm{NO}_{2}\right)_{3}\) (b) atoms in \(0.00102 \mathrm{mol} \mathrm{CH}_{3}\left(\mathrm{CH}_{2}\right)_{4} \mathrm{CH}_{2} \mathrm{OH}\) (c) \(\mathrm{F}\) atoms in \(1215 \mathrm{mol} \mathrm{C}_{2} \mathrm{HBr} \mathrm{ClF}_{3}\)

Step-by-Step Solution

Answer

(a) There are 21 atoms in one molecule of TNT. (b) There are \(1.83 \times 10^{25}\) atoms in 0.00102 mol of \(CH_{3}(CH_{2})_{4} CH_{2}OH. (c) There are \(2.19 \times 10^{27}\) Flourine atoms in 1215 mol of \(C_{2}HBrClF_{3}\).

Step 1: Count the number of atoms in TNT

The molecule of trinitrotoluene (TNT) is composed as \(CH_{3}C_{6}H_{2}(NO_{2})_{3}\). So, count each of the atoms: for Carbon (C) we have \(3+6\), for Hydrogen (H) we have \(3+2\), for Nitrogen (N) we have \(3\), and for Oxygen (O) we have \(6\). Adding them up, there are 21 atoms in total.

Step 2: Determine the number of atoms in 0.00102mol \(CH_{3}(CH_{2})_{4} CH_{2}OH

The molecule \(CH_{3}(CH_{2})_{4} CH_{2}OH\) has 9 Carbon, 20 Hydrogen, and 1 Oxygen atoms, and so has 9 + 20 + 1 = 30 atoms in its structure. To find the total number of atoms in 0.00102 mol, we multiply this by Avogadro's number: \(0.00102 \times 6.022 \times 10^{23} \times 30\) atoms.

Step 3: Calculate the number of F atoms in 1215 mol \(C_{2}HBrClF_{3}\)

Looking at the molecule \(C_{2}HBrClF_{3}\), it has 3 flourine atoms. Considering that we have 1215 mol of it, and each mole contains Avogadro's number of molecules, we will have \(1215 \times 6.022 \times 10^{23} \times 3\) Flourine atoms.

Key Concepts

Molecular Composition

Understanding molecular composition involves breaking down a chemical formula to determine the types and number of each atom in a molecule. Let's consider trinitrotoluene (TNT) which is represented by the molecular formula \( \mathrm{CH}_3 \mathrm{C}_6 \mathrm{H}_2(\mathrm{NO}_2)_3 \). To determine the total number of atoms, we need to count each type of atom:

• Carbon (C): The formula gives us 3 from \( \mathrm{CH}_3 \) and 6 from \( \mathrm{C}_6 \) making a total of 9 carbon atoms.
• Hydrogen (H): We have 3 hydrogen atoms from \( \mathrm{CH}_3 \) and 2 from \( \mathrm{H}_2 \), totaling 5 hydrogen atoms.
• Nitrogen (N): The \( (\mathrm{NO}_2)_3 \) specifies 3 nitrogen atoms.
• Oxygen (O): Since there are 3 \( \mathrm{NO}_2 \) groups, there are 6 oxygen atoms in total.

Adding these up, the total number of atoms in one molecule of TNT is 21. Breaking a compound into its atomic components is crucial for understanding its molecular structure and its chemical behavior. In exercises like these, being systematic in counting helps avoid mistakes.

Avogadro's Number

Avogadro's number is a fundamental constant in chemistry, which tells us how many molecules or atoms are present in one mole of substance. Specifically, this number is defined as \( 6.022 \times 10^{23} \), and it's a bridge between the microscopic world of atoms and the macroscopic scale we can observe.

For example, when calculating the total number of atoms in 0.00102 moles of \( \mathrm{CH}_3(\mathrm{CH}_2)_4 \mathrm{CH}_2\mathrm{OH} \), we first determine that each molecule contains 30 atoms (9 carbon, 20 hydrogen, and 1 oxygen). By multiplying the number of moles \( 0.00102 \) by Avogadro's number and the total number of atoms per molecule, we determine how many atoms are present in this quantity of substance:

• First calculate: \( 0.00102 \times 6.022 \times 10^{23} \)
• Then multiply the result by 30 atoms per molecule to get the total number of atoms.

Using Avogadro's number allows chemists to convert between moles and the number of entities, making it an essential tool for chemical calculations and stoichiometry.

Stoichiometry

Stoichiometry is about the quantitative relationships between the amounts of reactants and products in a chemical reaction or substance. It is underpinned by the law of conservation of mass, stating that matter is neither created nor destroyed during a chemical reaction.

In the example of \( 1215 \) moles of \( \mathrm{C}_2\mathrm{HBrClF}_3 \), stoichiometry guides us in determining the number of fluorine atoms present. The formula \( \mathrm{C}_2\mathrm{HBrClF}_3 \) indicates each molecule has 3 fluorine atoms. By using Avogadro's number, we know each mole contains \( 6.022 \times 10^{23} \) molecules. Thus, we calculate the total number of fluorine atoms as follows:

• Multiply 1215 moles by \( 6.022 \times 10^{23} \) molecules per mole.
• Then multiply that result by 3 fluorine atoms per molecule.

This helps ensure you're counting the correct number of atoms and correctly scaling reactions or quantities in laboratory contexts. Stoichiometry is vital for predicting yields, conducting accurate experiments, and managing resources efficiently in practical applications.