Problem 117 - General Chemistry

Question

Calcium carbonate, a white powder used in toothpastes, antacids, and other preparations, decomposes when heated to about \(825^{\circ} \mathrm{C}\). What is this temperature in degrees Fahrenheit?

Step-by-Step Solution

Answer

The temperature is 1517°F.

Step 1: Understanding the Formula for Conversion

To convert temperatures from Celsius to Fahrenheit, we use the formula: \[ F = \frac{9}{5}C + 32 \] where \( F \) is the temperature in degrees Fahrenheit and \( C \) is the temperature in degrees Celsius.

Step 2: Substitute the Celsius Temperature

Insert the Celsius temperature given in the problem \( 825^{\circ} \text{C} \) into the conversion formula, replacing \( C \): \[ F = \frac{9}{5} \times 825 + 32 \]

Step 3: Perform the Multiplication

Calculate the product of \( \frac{9}{5} \) and \( 825 \): \[ \frac{9}{5} \times 825 = 1485 \]

Step 4: Add 32 to the Product

Add 32 to the value obtained from the multiplication to complete the conversion to Fahrenheit: \[ F = 1485 + 32 = 1517^{\circ} \text{F} \]

Key Concepts

Celsius to Fahrenheit conversion

The process of converting temperatures from Celsius to Fahrenheit is essential in various scientific and everyday contexts. By using the formula:

• \( F = \frac{9}{5}C + 32 \)

This equation allows us to easily shift between these two temperature scales. Understanding how each component interacts is key.

• The fraction \( \frac{9}{5} \) represents the proportional difference between the two scales.
• The constant 32 adjusts for where each scale sets its zero point, as freezing is 0°C but 32°F.

Hence, when we apply this formula to a given Celsius temperature, such as \( 825^{\circ} \text{C} \), we are essentially scaling it to find its equivalent on the Fahrenheit scale, resulting in \( 1517^{\circ} \text{F} \). Understanding this conversion is beneficial, as it strengthens skills in both temperature conversion and basic algebra.

calcium carbonate decomposition

Calcium carbonate, commonly found in chalk, marble, and more, undergoes a notable chemical change when heated to high temperatures. At temperatures around \( 825^{\circ} \text{C} \), decomposition occurs. This process is described by the reaction:

• \( \text{CaCO}_3 (s) \rightarrow \text{CaO} (s) + \text{CO}_2 (g) \)

Here, solid calcium carbonate decomposes into solid calcium oxide and carbon dioxide gas. This decomposition is critical in processes like cement production, where understanding the precise temperature is essential for efficiency.
This exercise not only highlights the role of temperature in causing chemical reactions but also emphasizes the precision needed in temperature measurement when conducting such reactions.

chemical reactions and temperature

Temperature plays a vital role in the rate and feasibility of chemical reactions, including the decomposition of calcium carbonate. When heat is applied, it provides the energy necessary to break chemical bonds, facilitating transformations from one substance into another. Higher temperatures generally increase reaction rates by:

• Providing energy that meets the activation threshold of the reaction
• Increasing molecular movement, thus enhancing collision frequency

The specific temperature at which calcium carbonate decomposes is crucial, as any deviation could affect the outcomes of the reaction. Understanding this aspect helps students grasp how temperature influences practical applications in industrial settings.

step-by-step problem-solving

Approaching complex problems using a step-by-step methodical approach simplifies the process and enhances understanding. Breaking down the task of converting temperatures involves clear steps:

• Understanding the conversion formula
• Substituting the given values
• Performing arithmetic calculations
• Interpreting the result

This approach not only aids in accurate calculations but also strengthens logical thinking skills. By practicing such techniques, students become adept at handling complex tasks efficiently and with confidence.