Problem 39 - Chemistry

Question

Cinnamic alcohol is used mainly in perfumery, particularly in soaps and cosmetics. Its molecular for\(\begin{array}{lll}\text { mula is } & \text { C }_{9} \text { H }_{10} \text { O. }\end{array}\) (a) Calculate the percent composition by mass of \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) in cinnamic alcohol. (b) How many molecules of cinnamic alcohol are contained in a sample of mass \(0.469 \mathrm{~g} ?\)

Step-by-Step Solution

Answer

The mass percentage compositions of each element in cinnamic alcohol are: 72.73 \% C, 8.56 \% H, and 18.71 \% O. The 0.469 g sample of cinnamic alcohol contains approximately \(2.4 * 10^{21}\) molecules.

Step 1: Finding the molar mass of cinnamic alcohol

First, find the molar mass of cinnamic alcohol using the molecular formula \(C_{9}H_{10}O\) and the atomic masses of Carbon (C), Hydrogen (H), and Oxygen (O). The molar mass is calculated as follows: \(9 * MolarMass(C) + 10 * MolarMass(H) + 1 * MolarMass(O)\). The atomic masses of C, H and O are approximately 12.01 g/mol, 1.008 g/mol and 16.00 g/mol respectively. Plugging these values and calculating yields the molar mass as \(118.18\) g/mol.

Step 2: Calculating the percent composition

The percent by mass of each element is calculated by dividing the total mass contributed by the element in the molecule by the molar mass of the molecule, and then multiplying by 100. For Carbon: \((9 * MolarMass(C)/ MolarMass(C9H10O)) * 100\%. For Hydrogen: \((10 * MolarMass(H) / MolarMass(C9H10O)) *100\%. And for Oxygen: \(MolarMass(O) / MolarMass(C9H10O) *100\) \%. Inputting the values for each element and calculating yields the mass percentage of Carbon as 72.73 \%, Hydrogen as 8.56 \% and Oxygen as 18.71 \%.

Step 3: Calculating the number of molecules

To find the number of molecules in the given mass of cinnamic alcohol we first find the number of moles of cinnamic alcohol in 0.469 g using the equation Moles = mass/molar mass, yielding the moles of cinnamic alcohol in 0.469 g as 0.004 moles. We then multiply the moles of cinnamic alcohol by Avogadro's number \(6.022 * 10^{23}\) to find the number of molecules. The calculated result is approximately \(2.4 * 10^{21}\) molecules.

Step 4: Final Conclusions

The percent composition by mass of \(C_{9}H_{10}O\) is approximately 72.73 \% C, 8.56 \% H and 18.71 \% O. The number of molecules of cinnamic alcohol in 0.469 g is approximately \(2.4 * 10^{21}\) molecules.

Key Concepts

Cinnamic Alcohol

Cinnamic alcohol is an organic compound with a distinctive aroma often used in the perfume industry. It is valued for its fragrance, which makes it a popular ingredient in soaps and cosmetics. The compound is composed of carbon, hydrogen, and oxygen atoms, and its chemical formula is \(C_9H_{10}O\). Understanding the composition of cinnamic alcohol is essential for applications in fields such as chemistry and biochemistry. Knowing its molecular formula allows chemists to explore its reactivity, properties, and usage in various formulations. Moreover, calculating its percent composition, as detailed in problem-solving exercises, helps in determining the relative amounts of each element, which is crucial for the synthesis and chemical analysis of perfumes.

Molar Mass Calculation

Calculating the molar mass of a compound is a fundamental process in chemistry that is necessary to gain insight into the molecular make-up of substances like cinnamic alcohol. For a compound with the formula \(C_9H_{10}O\), you first look at each element in the formula and their respective atomic masses:

• Carbon (C) has an atomic mass of approximately 12.01 g/mol.
• Hydrogen (H) has an atomic mass of approximately 1.008 g/mol.
• Oxygen (O) has an atomic mass of approximately 16.00 g/mol.

To determine the molar mass, multiply the number of each type of atom by the atomic mass and sum the totals:

• 9 Carbons at \(12.01\) g/mol: \(9 \times 12.01 = 108.09\) g/mol.
• 10 Hydrogens at \(1.008\) g/mol: \(10 \times 1.008 = 10.08\) g/mol.
• 1 Oxygen at \(16.00\) g/mol: \(1 \times 16.00 = 16.00\) g/mol.

Adding these gives the molar mass of cinnamic alcohol, which is approximately \(134.17\) g/mol. This molar mass is critical for calculating further properties, such as percent composition and converting between mass and moles.

Avogadro's Number

Avogadro's number is a fundamental component in chemistry, acting as a bridge between the macroscopic and microscopic worlds. This constant, \(6.022 \times 10^{23}\), represents the number of atoms, ions, or molecules in one mole of a substance.

• It allows chemists to determine the number of particles in a given sample by relating it to moles.
• This understanding is crucial in chemical reactions, as reactions are balanced based on how particles interact at the molecular level.
• In the case of cinnamic alcohol, knowing the sample's mass and the molar mass, applying Avogadro's number allows us to determine the specific number of molecules present.

For instance, 0.469 g of cinnamic alcohol, divided by its molar mass, gives the moles, which are then multiplied by Avogadro's number to yield approximately \(2.4 \times 10^{21}\) molecules. This calculation exemplifies Avogadro's number's vital role in quantifying substances in chemistry.

Mole Concept

The mole concept is central in chemistry, providing a method to quantify the amount of a substance. By definition, a mole is a unit that contains \(6.022 \times 10^{23}\) entities, whether these are atoms, molecules, or other particles.

• This concept simplifies calculations in chemical equations and helps in predicting the results of reactions.
• In practical terms, it enables chemists to convert between mass, moles, and the number of atoms or molecules easily.
• For cinnamic alcohol, knowing its molar mass allows for conversion from grams to moles.

The calculation involves dividing the mass of the substance (in grams) by its molar mass to find the number of moles. This information can then be used for further exploration, such as calculating percent compositions or predicting quantities in chemical reactions. Understanding the mole concept is crucial for anyone studying chemistry or working in a chemical-related field, as it lays the groundwork for more complex chemical analyses.