Problem 125 - Chemistry and Chemical Reactivity

Question

Malic acid, an organic acid found in apples, contains \(\mathrm{C}, \mathrm{H},\) and \(\mathrm{O}\) in the following ratios: \(\mathrm{C}_{1} \mathrm{H}_{1.50} \mathrm{O}_{1.25} .\) What is the empirical formula of malic acid?

Step-by-Step Solution

Answer

The empirical formula of malic acid is \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{5}\).

Step 1: Identify the Element Ratios

Malic acid has element ratios given as \( \mathrm{C}_{1} \mathrm{H}_{1.50} \mathrm{O}_{1.25} \). This means that we have 1 atom of carbon (C), 1.5 atoms of hydrogen (H), and 1.25 atoms of oxygen (O) as a starting ratio.

Step 2: Divide by the Smallest Ratio

Identify the smallest value among the element ratios: 1 (C), 1.5 (H), 1.25 (O). The smallest value is 1 (C). Divide each element's ratio by 1. \[\frac{1}{1} = 1, \quad \frac{1.5}{1} = 1.5, \quad \frac{1.25}{1} = 1.25\] This keeps our ratios as \( \mathrm{C}_1 \mathrm{H}_{1.5} \mathrm{O}_{1.25} \).

Step 3: Multiply to Obtain Whole Numbers

To avoid fractions in empirical formulas, multiply all ratios by the same factor that will convert them to whole numbers. In this case, the smallest multiplier that converts 1.5 and 1.25 to whole numbers is 4. Multiply each ratio by 4: \[\mathrm{C}_1 \cdot 4 = 4, \quad \mathrm{H}_{1.5} \cdot 4 = 6, \quad \mathrm{O}_{1.25} \cdot 4 = 5\] This gives the whole number ratio \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{5}\).

Step 4: Identify the Empirical Formula

The whole number scores calculated in the previous step result in the empirical formula for malic acid, which is \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{5}\).

Key Concepts

Malic Acid

Malic acid is a naturally occurring organic compound widely found in fruits, especially apples. It contributes to the sour taste of fruits and is an essential part of the human diet.
It enhances flavor in food and beverages and is often used in the food industry as a natural acidulant.
Besides its gustatory role, malic acid plays a significant function in the Krebs cycle, an important energy-producing process in the cells of living organisms.
Its significance doesn't end there; malic acid is valued for its potential benefits in skincare, helping to remove dead skin cells and improve overall skin texture.

• Occurs naturally in fruits like apples and cherries.
• Used as a flavor enhancer in the food industry.
• Vital in the energy-producing Krebs cycle in cells.
• Potential skincare benefits.

Understanding malic acid's diverse roles can help appreciate its importance both nutritionally and industrially.

Ratio Calculation

Calculating ratios is fundamental when deciphering chemical formulas.
In chemistry, ratios help to establish the proportion of each element in a compound.
For malic acid, the given ratios were \( \mathrm{C}_1 \mathrm{H}_{1.5} \mathrm{O}_{1.25} \). These figures guide us in understanding the relative amounts of each type of atom in the compound.
The process begins by identifying the lowest value among the ratios, which, for malic acid, is 1 (for carbon).
Afterwards, each ratio is divided by this lowest value to simplify them. The resultant is a simplified but sometimes fractional ratio like \( \mathrm{H}_{1.5} \) or \( \mathrm{O}_{1.25} \).

• Start by identifying the smallest ratio value.
• Divide each ratio by this smallest value.
• Simplified ratios may not yet be whole numbers.

This initial simplification sets the stage for obtaining whole number ratios through further manipulation.

Chemical Formula

The chemical formula provides a clear and concise representation of a chemical compound's composition.
Each element in the compound is denoted by its chemical symbol, and its quantity is represented by a subscript number.
The empirical formula \, an outcome of ratio calculation \, is the simplest form reflecting the whole number ratio of elements present in the compound.
For example, the empirical formula for malic acid is \( \mathrm{C}_{4} \mathrm{H}_{6} \mathrm{O}_{5} \).
To achieve this from the ratio \( \mathrm{C}_{1} \mathrm{H}_{1.5} \mathrm{O}_{1.25} \), we multiplied the ratios by 4 to eliminate any fractions, simplifying each element's contribution to whole numbers.

• Represents the simplest form of the compound.
• Subscript numbers denote the quantity of each element.
• Empirical formulas are derived from ratios by simplifying and multiplying to obtain whole numbers.

The empirical formula is fundamental for identifying the proportionate composition of a compound.

Organic Chemistry

Organic chemistry is the study of carbon-containing compounds, which includes a vast array of substances found in living organisms and synthetic materials.
This branch of chemistry focuses on understanding the structure, properties, composition, reactions, and preparation of carbon-based compounds.
Malic acid, an example of an organic compound, showcases typical organic chemistry traits such as complex structures and specific functional groups.
Organic chemistry plays a crucial role in many industries, from pharmaceuticals to petrochemicals, and is integral to the development of new materials and medicines.

• Studies carbon-containing compounds.
• Includes both natural and synthetic substances.
• Involves knowledge of complex molecular structures and reactions.

Through the lens of organic chemistry, the significance of compounds like malic acid in biological processes and industrial applications shines brightly.