Problem 34 - Chemistry A Molecular Approach

Question

Convert between energy units. a. 231 cal to kJ b. \(132 \times 10^{4} \mathrm{~kJ}\) to \(\mathrm{kcal}\) c. \(4.99 \times 10^{3} \mathrm{~kJ}\) to \(\mathrm{kWh}\) d. \(2.88 \times 10^{4} \mathrm{~J}\) to \(\mathrm{Cal}\)

Step-by-Step Solution

Answer

a. 966.744 kJ, b. 3152400 kcal, c. 1.386 kWh, d. 68.73888 Cal

Step 1: Convert calories to kilojoules

To convert calories to kilojoules, use the conversion factor 1 calorie = 4.184 kilojoules. Multiply the number of calories by the conversion factor: 231 cal × 4.184 kJ/cal.

Step 2: Convert kilojoules to kilocalories

To convert kilojoules to kilocalories, use the conversion factor 1 kJ = 0.239005736 kcal. Multiply the number of kilojoules by the conversion factor: (132 × 10^4 kJ) × 0.239005736 kcal/kJ.

Step 3: Convert kilojoules to kilowatt hours

To convert kilojoules to kilowatt hours, use the conversion factor 1 kJ = 2.77778x10^-4 kWh. Multiply the number of kilojoules by the conversion factor: (4.99 × 10^3 kJ) × 2.77778x10^-4 kWh/kJ.

Step 4: Convert joules to Calories

To convert joules to Calories (nutritional calories, which are actually kilocalories), use the conversion factor 1 J = 0.000239006 kcal. Multiply the number of joules by the conversion factor: (2.88 × 10^4 J) × 0.000239006 kcal/J.

Key Concepts

Calorie to Kilojoule Conversion

Understanding how to convert calories to kilojoules is significant when studying energy in a nutritional or physical context. A 'calorie' with a small 'c' measures the amount of energy required to heat one gram of water by one degree Celsius. However, when discussing food energy, we actually refer to 'Calories' with a capital 'C', which are also known as 'kilocalories' (kcal).

For scientific purposes, energy is commonly measured in 'joules', and the kilojoule (kJ) is often used as a larger unit. The conversion factor is straightforward: 1 calorie = 4.184 kilojoules. To convert calories to kilojoules, you simply multiply the number of calories by this factor. Simplified, this means for every calorie, you get a little over 4 kilojoules of energy.

Kilojoule to Kilocalorie Conversion

If you're transitioning from the metric kilojoule (kJ) to the kilocalorie (kcal), which is more commonly used in nutrition, it's essential to utilize the correct conversion factor. Here, we have 1 kilojoule equals approximately 0.239 kilocalories. Translating kilojoules to kilocalories, therefore, involves multiplying the number of kilojoules by 0.239.

When you're looking at food labels or discussing dietary energy intake, the kilocalorie is the unit that's often used. Since we tend to talk about food energy in calories (which are actually kilocalories), knowing how to convert between these units is invaluable for diet planning and understanding energy consumption.

Kilojoule to Kilowatt Hour Conversion

Conversion between kilojoules and kilowatt hours (kWh) comes into play in fields like electricity consumption and energy billing, where kWh is a common unit. To achieve this conversion, we use the factor: 1 kJ = 2.77778 x 10^-4 kWh.

Kilowatt hours are typically used to measure energy in terms of electricity usage over time, hence 'hour' is included in the unit. This conversion is essential when energy needs to be expressed in terms that are relevant for power generation, electrical appliances, and billing. To convert kilojoules to kilowatt hours, you simply multiply the amount in kilojoules by 0.000277778.

Joule to Calorie Conversion

When converting joules to Calories (with a capital 'C', equivalent to kilocalories), the equation to remember is 1 joule equals 0.000239006 kilocalories. This factor is pivotal as nutritional information is often given in Calories, and understanding the joule equivalent can be necessary in various scientific calculations involving energy.

In context, joules are the standard unit of work or energy in the International System of Units (SI), and they account for extremely small amounts of energy. As such, when you're translating a larger energy amount from joules to Calories, you end up with a more manageable number that corresponds to the energy typically found in food.