Question

Perform the indicated conversions. a. 625.2 cal into kilojoules b. \(82.41 \mathrm{~kJ}\) into joules c. 52.61 kcal into joules d. 124.2 kJ into kilocalories

Short answer

a. \(625.2\,\text{cal} = 2.615\,\text{kJ}\) \\ b. \(82.41\,\text{kJ} = 82,410\,\text{J}\) \\ c. \(52.61\,\text{kcal} = 220,167.44\,\text{J}\) \\ d. \(124.2\,\text{kJ} = 29.673\,\text{kcal}\)

Step-by-step solution

Convert calories to joules

Using the conversion factor, we can convert 625.2 cal into joules by multiplying it with the conversion factor: \(625.2\,\text{cal} \times 4.184\,\text{J/cal} = 2615.2248\,\text{J}\)

Convert joules to kilojoules

Next, we convert joules to kilojoules by dividing by 1000: \(2615.2248\,\text{J} \div 1000 = 2.615\,\text{kJ}\) The result is \(625.2\,\text{cal} = 2.615\,\text{kJ}\). #b. 82.41 kJ into joules#

Convert kilojoules to joules

Using the conversion factor, we can convert 82.41 kJ into joules by multiplying it with 1000: \(82.41\,\text{kJ} \times 1000 = 82,410\,\text{J}\) The result is \(82.41\,\text{kJ} = 82,410\,\text{J}\). #c. 52.61 kcal into joules#

Convert kilocalories to calories

First, we convert 52.61 kcal into calories by multiplying it with 1000: \(52.61\,\text{kcal} \times 1000\,\text{cal/kcal} = 52,610\,\text{cal}\)

Convert calories to joules

Next, we convert calories to joules by multiplying with the conversion factor: \(52,610\,\text{cal} \times 4.184\,\text{J/cal} = 220,167.44\,\text{J}\) The result is \(52.61\,\text{kcal} = 220,167.44\,\text{J}\). #d. 124.2 kJ into kilocalories#

Convert kilojoules to joules

First, we convert 124.2 kJ into joules by multiplying it with 1000: \(124.2\,\text{kJ} \times 1000\,\text{J/kJ} = 124,200\,\text{J}\)

Convert joules to calories

Next, we convert joules to calories by dividing with the conversion factor: \(124,200\,\text{J} \div 4.184\,\text{J/cal} = 29,673.032\,\text{cal}\)

Convert calories to kilocalories

Finally, we convert calories to kilocalories by dividing by 1000: \(29,673.032\,\text{cal} \div 1000\,\text{cal/kcal} = 29.673\,\text{kcal}\) The result is \(124.2\,\text{kJ} = 29.673\,\text{kcal}\).

Key concepts

Calories to Kilojoules

Understanding the conversion between calories and kilojoules is crucial in energy-related discussions, especially when dealing with chemistry and nutritional content of food. Calories, often used in dietary contexts, signify the amount of energy food provides. On the other hand, kilojoules is a more standard unit of energy commonly used in scientific studies.

Let's break down this conversion using the solution provided. To convert from calories to kilojoules, we apply the conversion factor, which states that 1 calorie equals 4.184 joules. To convert calories into kilojoules, you simply multiply the number of calories by 4.184 and then divide by 1000 (since 1 kilojoule equals 1000 joules).

For example, in solving part a of the exercise, the conversion goes as follows:

1. Multiply calories by 4.184 to get joules:
   \(625.2\text{ cal} \times 4.184\text{ J/cal} = 2615.2248\text{ J}\).
2. Divide joules by 1000 to convert to kilojoules:
   \(2615.2248\text{ J} \text{ ÷ } 1000 = 2.615\text{ kJ}\).

So, 625.2 calories convert to 2.615 kilojoules.

This method is a straightforward way to navigate through energy conversions, helping students understand energy intake from food or energy requirements for chemical reactions.

Kilojoules to Joules

Converting kilojoules to joules represents a simpler transition between units within the same energy measuring system, the International System of Units (SI). Kilojoules and joules are both used to quantify energy, work, or heat, with 1 kilojoule being equivalent to 1000 joules.

Following the exercise, when converting from kilojoules to joules, simply multiply the number of kilojoules by 1000. This step indicates how energy units can scale up or down, similar to meters and kilometers in distance measurement.

Calculation Example:

In part b of the exercise, converting 82.41 kilojoules into joules is simple:

1. Multiply the kilojoules by 1000:
   \(82.41\text{ kJ} \times 1000 = 82,410\text{ J}\).

Therefore, 82.41 kilojoules is equal to 82,410 joules.

This conversion underlines the important relationship between different magnitudes of energy units, which is fundamental to grasp for students studying energy-related concepts in chemistry and physics.

Kilocalories to Joules

When dealing with nutritional data, it's common to encounter energy content listed in kilocalories. However, to align with scientific measurements, we might need to convert this to joules—the SI unit of energy.

The journey from kilocalories to joules, as seen in the exercise, is a two-step process. First, we convert kilocalories to calories, knowing that 1 kilocalorie equals 1000 calories. Then, we use the conversion factor of 1 calorie to 4.184 joules to find the energy in joules.

In our example (part c), the steps are:

1. Convert kilocalories to calories:
   \(52.61\text{ kcal} × 1000 = 52610\text{ cal}\).
2. Convert calories to joules using the conversion factor:
   \(52610\text{ cal} × 4.184\text{ J/cal} = 220167.44\text{ J}\).

So, 52.61 kilocalories converts to 220,167.44 joules.

By performing these conversions, students can develop a more nuanced understanding of the energy content in the food they eat, and expand their ability to work within the international standard metric system.