Question

Perform the indicated conversions. a. 85.21 cal into joules b. 672.1 J into calories c. \(8.921 \mathrm{~kJ}\) into joules d. 556.3 cal into kilojoules

Short answer

a. 85.21 cal = 356.36 J b. 672.1 J = 160.5 cal c. 8.921 kJ = 8921 J d. 556.3 cal = 2.327 kJ

Step-by-step solution

a. 85.21 cal into joules

To convert calories to joules, we will use the conversion factor 1 cal = 4.184 J: \(85.21 \text{ cal} \times \dfrac{4.184 \text{ J}}{1 \text{ cal}} = \boxed{356.36 \text{ J}}\)

b. 672.1 J into calories

To convert joules to calories, we will use the conversion factor 1 J = 0.239006 cal: \(672.1 \text{ J} \times \dfrac{0.239006 \text{ cal}}{1 \text{ J}} = \boxed{160.5 \text{ cal}}\)

c. 8.921 kJ into joules

To convert kilojoules to joules, we will use the conversion factor 1 kJ = 1000 J: \(8.921 \text{ kJ} \times \dfrac{1000 \text{ J}}{1 \text{ kJ}} = \boxed{8921 \text{ J}}\)

d. 556.3 cal into kilojoules

To convert calories to kilojoules, we will first convert calories to joules, then joules to kilojoules using the conversion factors 1 cal = 4.184 J and 1 J = 0.001 kJ: \(556.3 \text{ cal} \times \dfrac{4.184 \text{ J}}{1 \text{ cal}} \times \dfrac{0.001 \text{ kJ}}{1 \text{ J}} = \boxed{2.327 \text{ kJ}}\)

Key concepts

Calorie to Joule Conversion

When you see 'calories' on food packaging, it's a way of representing energy. However, scientists commonly use 'joules' as the unit of energy in the International System of Units. Understanding how to convert these units is essential in chemistry. To convert calories to joules, we use the specific conversion factor that 1 calorie equals 4.184 joules.

For example, if you have 85.21 calories and need to convert this to joules, simply multiply by the conversion factor:
\(85.21 \text{ cal} \times \frac{4.184 \text{ J}}{1 \text{ cal}} = 356.36 \text{ J}\).

This calculation helps you understand the energy content of food in universal terms that are applicable in various scientific contexts.

Joule to Calorie Conversion

Inversely, if you're working with joules and need to understand this value in terms of calories, you will do a joule to calorie conversion. This can be particularly useful when trying to relate the more abstract concept of joules to something more tangible, like dietary energy. The conversion factor is 1 joule equals approximately 0.239006 calories.

So, if you start with 672.1 joules, you convert to calories by multiplying by this factor:
\(672.1 \text{ J} \times \frac{0.239006 \text{ cal}}{1 \text{ J}} = 160.5 \text{ cal}\).

This process is a straightforward way to transition between different energy units commonly used in nutrition and science.

Kilojoule to Joule Conversion

A kilojoule is a larger unit of energy that's just 1000 times a joule. It's often used in scientific measurements because it's a more convenient number to work with for larger amounts of energy. To convert from kilojoules to joules, you multiply by 1000.

For an example, converting 8.921 kilojoules to joules would look like this:
\(8.921 \text{ kJ} \times \frac{1000 \text{ J}}{1 \text{ kJ}} = 8921 \text{ J}\).

This conversion is straightforward since it’s based on the metric system, which uses powers of ten.

Energy Units Conversion

Understanding how to convert between different energy units is not only important in chemistry but in daily life when dealing with electricity, fuel consumption, and even food. The key to mastering these computations is knowing the conversion factors and the relationship between units.

For example, calories to kilojoules requires two steps. You first convert calories to joules, and then joules to kilojoules. If we take 556.3 calories, the conversions would go as follows:
\(556.3 \text{ cal} \times \frac{4.184 \text{ J}}{1 \text{ cal}} \times \frac{0.001 \text{ kJ}}{1 \text{ J}} = 2.327 \text{ kJ}\).

Conversions like these are vital for comparing energy values in different scientific fields and even when comparing the energy costs of appliances or evaluating different foods for diet planning.