Problem 137 - Introductory Chemistry Atoms First

Question

Use Greek prefixes to express the relationship between the calorie and the Calorie.

Step-by-Step Solution

Answer

The relationship between the calorie (with a lowercase c) and the Calorie (with a capital C) can be expressed using the Greek prefix "kilo" as: 1 Calorie = 1 kilocalorie (kcal). This means that one Calorie is equivalent to 1,000 calories.

Step 1: Understanding the calorie and the Calorie

The calorie is a unit of energy. In the context of nutrition, the term "calorie" is commonly used to describe the amount of energy provided by food and beverages. The Calorie (with a capital C) is also a unit of energy, but it is precisely 1,000 times larger than the calorie (with a lowercase c). The relationship between the calorie and the Calorie can be expressed as follows: 1 Calorie = 1,000 calories

Step 2: Determine the Greek prefix

Since we need to use Greek prefixes to express the relationship between the calorie and the Calorie, we should look for the appropriate prefix that signifies the factor of 1,000. The Greek prefix for 1,000 is "kilo".

Step 3: Applying the Greek prefix to the units

Using the Greek prefix "kilo", we can express the relationship between the calorie and the Calorie as: 1 Calorie = 1 kilocalorie (kcal) This means that one Calorie (capital C) is equivalent to one kilocalorie (1,000 calories).

Key Concepts

Greek prefixes in chemistry

In chemistry, understanding prefixes, particularly those derived from Greek, is crucial for grasping the scale of measurements. Prefixes like 'kilo-', 'mega-', 'giga-', and 'tera-', correspond to multipliers of 10 to the power of 3, 6, 9, and 12, respectively. For instance, 'kilo-' signifies a thousand times the unit it precedes. This system helps to simplify large numbers, making them more manageable.

When applied to the calorie, the prefix 'kilo-' transforms it into a 'kilocalorie', indicating a thousand calories. This is fundamental to distinguish between the energy content expressed in food, which is typically measured in Calories (kilocalories), and energy expenditure in exercises or physics, often reported in calories (small 'c').

The practice of using Greek prefixes is common in various scientific fields, not just chemistry, highlighting the importance of a universal language in science.

Units of energy

Energy is a fundamental concept in both physics and daily life, and it is quantified using various units. The most basic unit of energy in the International System of Units (SI) is the joule (J). However, different units, such as calories, watt-hours, and electron-volts, are often utilized depending on the context and field of study.

A calorie (small 'c') is one such unit originally defined as the amount of energy needed to raise the temperature of 1 gram of water by 1 degree Celsius. This unit is not only essential in thermodynamics and physical sciences but is also commonly used in nutrition. Although the calorie is not the SI unit of energy, its simplicity makes it popular for expressing the energy content of food. It's critical to remember that when scientists and professionals refer to food energy, they commonly use the term Calorie (with a capital 'C'), which is a kilocalorie in scientific terms, equating to 1,000 calories.

Calorie as an energy unit

The term 'calorie' is frequently mentioned in discussions about food and diet. It refers to the energy that is consumed through food and beverages or expended through physical activities. A lower-case 'c' calorie, or gram calorie, symbolizes the energy required to heat 1 gram of water by 1 degree Celsius at a pressure of 1 atmosphere. However, in dietary contexts, 'Calorie' with an uppercase 'C' denotes a kilocalorie (kcal).

This differentiation is vital as it avoids underestimating the energy content within food by a factor of a thousand. Acknowledging the large and small calorie distinction is important not only for those studying nutrition and health sciences, but for anyone interested in maintaining a balanced diet. It's common to see food packaging and nutritional guidelines referencing Calories (with the capital 'C'), making it essential for consumers to understand that these are actually kilocalories, units of 1,000 calories each.