Problem 10 - Chemistry The Molecular Science

Question

Sulfur dioxide, \(\mathrm{SO}_{2}\), is found in wines and in polluted air. If a \(32.1-\mathrm{g}\) sample of sulfur is burned in the air to get \(64.1 \mathrm{~g} \mathrm{SO}_{2}, 297 \mathrm{~kJ}\) of energy is released. Express this energy in (a) joules, (b) calories, and (c) kilocalories.

Step-by-Step Solution

Answer

(a) 297000 J; (b) 71016.03 cal; (c) 71.02 kcal.

Step 1: Converting kJ to Joules

Energy is commonly converted between different units for various applications. One kilojoule (kJ) is equivalent to 1000 joules (J). Given the energy released is 297 kJ, we convert it to joules by multiplying:\[297 \text{ kJ} \times 1000 \frac{J}{kJ} = 297000 \text{ J}\]

Step 2: Converting Joules to Calories

To convert joules to calories, we need to use the conversion factor that 1 calorie is equal to 4.184 joules. Using this, we can find out how many calories are equivalent to 297000 J:\[\frac{297000 \text{ J}}{4.184 \frac{J}{cal}} \approx 71016.03 \text{ cal}\]

Step 3: Converting Calories to Kilocalories

Finally, since 1 kilocalorie (kcal) is equal to 1000 calories (cal), we convert the calories to kilocalories by dividing by 1000:\[\frac{71016.03 \text{ cal}}{1000 \frac{cal}{kcal}} \approx 71.02 \text{ kcal}\]

Key Concepts

Sulfur Dioxide: An Essential Compound in Chemistry

Sulfur dioxide ( SO_{2} ) is a significant chemical compound extensively studied in chemistry. It is known for its presence in two major areas: wine production and air pollution. In winemaking, SO_{2} acts as a preservative to maintain the quality of the wine, preventing spoilage and oxidation. This ensures the wine’s freshness and stability.
In environmental contexts, sulfur dioxide is viewed as a pollutant. It is produced during the combustion of fossil fuels and volcanic activity.

• SO_{2} contributes to acid rain, which has harmful effects on ecosystems.
• It can affect human health by aggravating respiratory issues.

Understanding SO_{2} 's role is crucial in addressing its dual impact on nature and industry, necessitating strategies to mitigate its environmental impact while utilizing its beneficial properties.

Converting Kilojoules to Joules: A Fundamental Energy Conversion

Energy conversion between different units is a common practice in scientific calculations. The conversion from kilojoules to joules is straightforward yet essential. One kilojoule (kJ) is equal to 1000 joules (J).
For example, if a process releases 297 kJ of energy, you would multiply by 1000 to convert this to joules:

• Calculation: 297 kJ × 1000 = 297,000 J

This conversion is crucial in various fields such as physics, chemistry, and engineering, where precise energy measurements are necessary for accurate results.

Joules to Calories: Understanding the Conversion

Converting joules to calories helps in understanding energy content concerning food and metabolic processes. The conversion factor is 1 calorie (cal) equals 4.184 joules (J).
When you have an energy value in joules and need to express it in calories, divide the joules by 4.184. For instance, 297,000 J is converted as follows:

• Calculation: 297,000 J / 4.184 ≈ 71,016.03 cal

This conversion is often used in nutrition science to determine the caloric content of food, providing a measure of energy intake important for diet planning and energy balance.

Calories to Kilocalories: Simplifying Energy Measurements

In nutrition and science, the term "calories" often refers to "kilocalories" to simplify energy value discussions, especially related to food energy.

• 1 kilocalorie (kcal) is equal to 1000 calories (cal).

To convert calories to kilocalories, divide the number of calories by 1000. For example, if you have 71,016.03 calories:

• Calculation: 71,016.03 cal ÷ 1000 ≈ 71.02 kcal

This conversion helps in understanding food packaging labels, where energy values are often noted in kilocalories, making it easier for consumers to grasp energy intake related to diet and exercise.