Problem 94 - Chemistry: The Central Science in SI Units, Global Edition

Question

Fructose, commonly called fruit sugar, is a monosaccharide found in many plants. It contains \(40 \%\) C, \(6.71 \% \mathrm{H},\) and the remainder O. (a) What is the empirical formula for fructose? (b) A mass spectrum of fructose shows a peak at about \(180 \mathrm{u}\). What is the molecular formula of the substance?

Step-by-Step Solution

Answer

The empirical formula for fructose is CH2O, and the molecular formula is C6H12O6.

Step 1: Calculate moles of each element

Using the given mass percentages, let's assume we have 100g sample of fructose. This means we have 40g of Carbon (C), 6.71g of Hydrogen (H), and the remainder as Oxygen (O). First, find the moles of each element: - For Carbon: Moles_C = mass / molar_mass_C, where molar_mass_C = 12.01 g/mol - For Hydrogen: Moles_H = mass / molar_mass_H, where molar_mass_H = 1.01 g/mol - For Oxygen: we first find mass_O = 100g - mass_C - mass_H, and then Moles_O = mass / molar_mass_O, where molar_mass_O = 16.00 g/mol

Step 2: Find the mole ratios

Divide the moles of each element by the smallest value among them to find the mole ratios. Round the ratios to the nearest whole number if necessary.

Step 3: Write the empirical formula

Using the whole number mole ratios from step 2, write the empirical formula for fructose.

Step 4: Calculate the empirical formula mass

Find the empirical formula mass by adding the molar masses of each element multiplied by the number of atoms in the empirical formula.

Step 5: Determine the molecular formula

Using the mass spectrum () peak of 180 u (mass units), find the ratio between the molecular mass and the empirical formula mass. - Ratio = molecular_mass / empirical_formula_mass If the ratio is a whole number, multiply each element in the empirical formula by the ratio to find the molecular formula of fructose. Now, let's solve the problem step-by-step.

Step 1: Calculate moles of each element

- Moles_C = 40g / 12.01 g/mol ≈ 3.33 mol - Moles_H = 6.71g / 1.01 g/mol ≈ 6.64 mol - Mass_O = 100g - 40g - 6.71g = 53.29g - Moles_O = 53.29g / 16.00 g/mol ≈ 3.33 mol

Step 2: Find the mole ratios

Minimum moles = min(3.33, 6.64, 3.33) = 3.33 - Ratio_C = Moles_C / Minimum_moles = 3.33 / 3.33 = 1 - Ratio_H = Moles_H / Minimum_moles = 6.64 / 3.33 ≈ 2 - Ratio_O = Moles_O / Minimum_moles = 3.33 / 3.33 = 1

Step 3: Write the empirical formula

The empirical formula for fructose is CH2O.

Step 4: Calculate the empirical formula mass

Empirical formula mass = (1 x 12.01) + (2 x 1.01) + (1 x 16.00) = 12.01 + 2.02 + 16.00 ≈ 30.03 g/mol

Step 5: Determine the molecular formula

Ratio = molecular_mass / empirical_formula_mass = 180 u / 30.03 g/mol ≈ 6 Therefore, the molecular formula for the substance is C6H12O6, which is the molecular formula of fructose.

Key Concepts

Molecular Formula

The molecular formula of a compound specifies the exact number of each type of atom in a molecule of the compound. For fructose, a mass spectrum showed a peak at around 180 u (atomic mass units), indicating its molecular mass. By comparing this weight to the empirical formula mass, you can determine the molecular formula.

To find the molecular formula, calculate the empirical formula mass, which is the weight of your smallest unit of the compound, in this case, CH₂O. This was found to be approximately 30.03 g/mol. Next, divide the molecular mass (180 u) by the empirical formula mass. This gives a value of 6, indicating that the molecular formula consists of six empirical units. Thus, the molecular formula of fructose is C₆H₁₂O₆.

• The molecular formula provides insight into the actual number and types of atoms in a molecule.
• It's derived from the empirical formula when the molecular mass is known.

Mass Spectrum

A mass spectrum is like a fingerprint of a molecule, showcasing how the piece is weighted. When analyzing fructose, the mass spectrum displayed a significant peak at approximately 180 u. This peak corresponds to the molecular weight and helps in determining the molecular formula.

In mass spectrometry, different fragments of the molecule are separated based on their mass-to-charge ratio (m/z). For fructose, the key peak at 180 indicates the presence of an intact molecular ion or the molecular mass of fructose itself.

• Mass spectrometry can identify molecules and determine their quantities in a mixture.
• The height of the peaks can reflect the abundance of the respective ions.

Moles Calculation

Moles calculation is crucial for translating the weight of each sample into moles, which allows for the determination of the empirical formula. It's a critical bridge from mass to molecule. Transform the mass percent into moles by utilizing the molar masses of each element.

For fructose:

• Carbon (C): Start with 40 grams, using a molar mass of 12.01 g/mol, giving approximately 3.33 moles of Carbon.
• Hydrogen (H): With 6.71 grams and a molar mass of 1.01 g/mol, you get about 6.64 moles of Hydrogen.
• Oxygen (O): The remainder of 53.29 grams with a molar mass of 16.00 g/mol results in around 3.33 moles of Oxygen.

By doing so, these values are then used to find the simplest whole number ratio, leading to the empirical formula.

Fructose Analysis

Fructose is a type of sugar found naturally in many plants. It is known for its high sweetness and forms the basis of our analysis. The challenge is to use composition details and analytical techniques to derive its chemical equations.

When analyzing fructose, note:

• Elemental Composition: Fructose contains carbon, hydrogen, and oxygen, indicated by its chemical formula C₆H₁₂O₆.
• Empirical vs Molecular Formula: The empirical formula of CH₂O simplifies the composition ratio, but the actual molecule is more complex.

Understanding fructose through these formulas helps in categorizing its role in nature and use in industries such as food production.