Problem 9 - Chemistry The Molecular Science

Question

(a) A 2 -inch piece of two-layer chocolate cake with frosting provides \(1670 \mathrm{~kJ}\) of energy. Calculate this in Cal. (b) If you were on a diet that calls for eating no more than 1200 Cal per day, calculate how many joules you could consume per day.

Step-by-Step Solution

Answer

(a) 400 Cal; (b) 5,020,800 Joules per day.

Step 1: Convert kJ to Cal (a)

First, let's convert the energy content of the cake from kilojoules to calories. We know that 1 joule equals 0.239 calories. Therefore, to convert kilojoules to calories, we use the conversion formula: \[ \text{Cal} = 1670 \times 0.239 = 399.73 \text{ Cal} \]Thus, a 2-inch piece of cake provides approximately 400 Cal.

Step 2: Convert Cal to Joules (b)

Next, let's determine how many joules are allowed on a 1200 Cal diet. We know that 1 Cal is equal to 4184 joules. To calculate the total joules, we use the formula:\[ \text{Joules} = 1200 \times 4184 = 5,020,800 \text{ Joules} \]So, on a 1200 Cal diet, you can consume 5,020,800 joules per day.

Key Concepts

Kilojoules to Calories

Understanding how to convert kilojoules to calories is an essential part of energy conversion. Kilojoules (kJ) and calories (Cal) are both units of energy. In dietary contexts, calories often refer to kilocalories, hence the two terms are used interchangeably. When you eat food, your body burns this energy to perform everyday tasks. To convert kilojoules to calories, one can use the conversion factor where 1 kilojoule equals approximately 0.239 kilocalories. Here's the step-by-step formula you can follow: - Multiply the number of kilojoules by the conversion factor of 0.239. - For example, converting 1670 kJ gives us: \[ \text{Cal} = 1670 \times 0.239 = 399.73 \text{ Cal} \]This means that the energy content of a 2-inch piece of cake is approximately 400 Cal, enabling a more intuitive understanding when tracking dietary energy in calories.

Calorie to Joules Conversion

Transforming calories into joules is a fundamental concept when discussing energy measurements, especially in scientific contexts. Calories describe the amount of energy stored in food, whereas joules are the SI unit for energy, used widely in physics and engineering discussions.The conversion is necessary in scientific applications to maintain consistency with SI units. Here's how you can convert calories to joules:- Recognize that 1 calorie equals 4184 joules.- For a specific energy intake, say 1200 Cal like in our exercise: \[ \text{Joules} = 1200 \times 4184 = 5,020,800 \text{ Joules} \]This calculation shows that on a 1200 Calorie diet, you consume 5,020,800 joules. This conversion will help in understanding how much scientific energy input comes from your food intake per day.

Dietary Energy Calculation

Dietary energy calculations play a significant role in understanding and maintaining a healthy lifestyle. By converting between kilojoules, calories, and joules, you gain insights into how much energy your body requires and uses. When managing dietary intake, knowing how many calories you're consuming is key. This is especially important if you're following a specific diet plan, like one that restricts you to 1200 calories per day. - From our previous examples: - The chocolate cake, converted from kilojoules to calories, gives insight into its energy content. - The calorie to joules conversion ensures you know the energy consumption in universal energy units. These conversions are essential for comparing food energy values and keeping track of what you're consuming. Armed with this knowledge, tailored energy intake can lead to better dietary decisions and help in achieving specific health and fitness goals.