Problem 106 - Chemistry: The Central Science

Question

The compound chloral hydrate, known in detective stories as knockout drops, is composed of \(14.52 \% \mathrm{C}, 1.83 \% \mathrm{H}\), \(64.30 \% \mathrm{Cl}\), and \(13.35 \% \mathrm{O}\) by mass, and has a molar mass of \(165.4 \mathrm{~g} / \mathrm{mol}\). (a) What is the empirical formula of this substance? (b) What is the molecular formula of this substance? (c) Draw the Lewis structure of the molecule, assuming that the \(\mathrm{Cl}\) atoms bond to a single \(\mathrm{C}\) atom and that there are \(\mathrm{C}-\mathrm{C}\) bond and two \(\mathrm{C}-\mathrm{O}\) bonds in the compound.

Step-by-Step Solution

Answer

(a) The empirical formula of chloral hydrate is CH2Cl2O. (b) The molecular formula of chloral hydrate is CH2Cl2O. (c) The Lewis structure of chloral hydrate is as follows: H H \ / O = C - Cl - Cl / O

Step 1: Determine the moles of each element in the compound

Start by using the given percentages as the mass of each element in a 100-gram sample. Then, convert these masses to moles using their atomic masses. For Carbon (C): Mass: \(14.52 \mathrm{g}\) Moles: \(14.52 \mathrm{g} \times \frac{1 \mathrm{mol}}{12.01 \mathrm{g}} \approx 1.209 \mathrm{mol}\) For Hydrogen (H): Mass: \(1.83 \mathrm{g}\) Moles: \(1.83 \mathrm{g} \times \frac{1 \mathrm{mol}}{1.008 \mathrm{g}} \approx 1.816 \mathrm{mol}\) For Chlorine (Cl): Mass: \(64.30 \mathrm{g}\) Moles: \(64.30 \mathrm{g} \times \frac{1 \mathrm{mol}}{35.45 \mathrm{g}} \approx 1.813 \mathrm{mol}\) For Oxygen (O): Mass: \(13.35 \mathrm{g}\) Moles: \(13.35 \mathrm{g} \times \frac{1 \mathrm{mol}}{16.00 \mathrm{g}} \approx 0.834 \mathrm{mol}\)

Step 2: Calculate the simple mole ratio of elements

Divide the moles of each element by the smallest value among them to obtain the simple mole ratios: For Carbon (C): \(\frac{1.209}{0.834} \approx 1.450 \approx 1\) For Hydrogen (H): \(\frac{1.816}{0.834} \approx 2.177 \approx 2\) For Chlorine (Cl): \(\frac{1.813}{0.834} \approx 2.173 \approx 2\) For Oxygen (O): \(\frac{0.834}{0.834} \approx 1\) The empirical formula is thus CH2Cl2O. (a) The empirical formula of chloral hydrate is CH2Cl2O.

Step 3: Calculate the molecular formula

First, find the molar mass of the empirical formula: Molar mass of CH2Cl2O = 1(12.01) + 2(1.008) + 2(35.45) + 1(16.00) = 119.44 g/mol Now, divide the given molar mass of the compound, 165.4 g/mol, by the empirical formula's molar mass: \(\frac{165.4 \mathrm{g/mol}}{119.44 \mathrm{g/mol}} \approx 1.38 \approx 1\) Since the ratio is approximately 1, the molecular formula is equal to the empirical formula. (b) The molecular formula of chloral hydrate is CH2Cl2O.

Step 4: Draw the Lewis structure

Following the given conditions about the bonding of the compound, we can draw the Lewis structure for CH2Cl2O: 1. Place a C atom in the center, and bond two Cl atoms to it. 2. Bond one O atom to the C, using two C-O bonds. 3. Bond an H atom to each O atom. 4. Fill in the remaining valence electrons for each atom, making sure that each has an octet (except for H atoms, which should have two). H H \ / O = C - Cl - Cl / O (c) The Lewis structure of chloral hydrate is as drawn above, with the Cl atoms bonded to a single C atom, and two C-O bonds in the compound.

Key Concepts

Chemistry Education

Chemistry education is a branch of education that focuses on teaching the principles, theories, and practical applications of chemistry. It's aimed at developing students' understanding of chemical concepts, the ability to conduct experiments, and skills in scientific reasoning and problem-solving.

For example, when students are introduced to the exercises like determining empirical and molecular formulas, they gain insights into fundamental concepts such as percent composition and stoichiometry, essential for understanding reactions and compositions in chemistry. Exercises that require computation and conversion of mass percentages to moles, as in the case of chloral hydrate, further solidify their understanding of quantitative relationships in chemical substances.

Improving chemistry education involves not only providing comprehensive step-by-step solutions to exercises but also ensuring that learners understand the 'why' behind each step. By doing so, we aim to cultivate students' ability to apply these concepts to a variety of chemical problems they may encounter in real-world scenarios.

Stoichiometry

Stoichiometry is a key concept in chemistry that involves the calculation of reactants and products in chemical reactions. It is based on the law of conservation of mass and the concept that matter is neither created nor destroyed in chemical reactions. Understanding stoichiometry is critical for predicting the quantities of substances consumed and produced in reactions, which is integral for the fields of chemical manufacturing, pharmaceuticals, and environmental science.

In relation to the compound chloral hydrate, stoichiometry is applied to deduce the empirical formula from the mass percentage of each element. By using stoichiometric calculations, one can determine the molar ratios of the elements, which leads to the determination of the compound's empirical formula, CH₂Cl₂O. This kind of problem-solving is a practical application of stoichiometry and serves as a solid example for students to grasp the conversion of mass to moles and the relevance of mole ratios in chemistry.

Lewis Structures

Lewis structures, also known as Lewis dot diagrams, are graphical representations that show the bonding between atoms of a molecule and the lone pairs of electrons that may exist. They are a fundamental tool in chemistry education for visualizing molecule geometry, electron arrangements, and understanding how atoms bond in molecules.

For chloral hydrate, the Lewis structure is essential in visualizing the molecular layout and understanding the single and double bonds that give the molecule its shape. It also shows that chloral hydrate has two covalent bonds between the carbon and oxygen atoms, and single covalent bonds between the carbon atom and the chlorine and hydrogen atoms. The ability to draw Lewis structures is vital for students, as it not only aids in predicting the physical and chemical properties of a molecule but also helps in comprehending more advanced concepts such as polarity and molecular orbital theory.

Moreover, exercises that require drawing Lewis structures, as with chloral hydrate, encourage students to apply their knowledge of valence electrons and octet rule. This bolsters their understanding of chemical bonding and supports the development of their spatial reasoning skills.