Problem 9 - Chemistry and Chemical Reactivity

Question

The specific heat capacity of copper is \(0.385 \mathrm{J} / \mathrm{g} \cdot \mathrm{K}\). What quantity of heat is required to heat 168 g of copper from \(-12.2^{\circ} \mathrm{C}\) to \(+25.6^{\circ} \mathrm{C} ?\)

Step-by-Step Solution

Answer

Approximately 2448 J of heat is required.

Step 1: Identify Given Values

In this problem, we are given the specific heat capacity of copper as \(0.385 \, \text{J/g} \cdot \text{K}\), the mass of copper as \(168 \, \text{g}\), the initial temperature \(-12.2^{\circ} \text{C}\), and the final temperature \(+25.6^{\circ} \text{C}\).

Step 2: Understand the Formula

The formula to calculate the heat energy required is:\[q = m \times c \times \Delta T\]where \(q\) is the heat energy in joules (J), \(m\) is the mass in grams (g), \(c\) is the specific heat capacity, and \(\Delta T\) is the change in temperature in Celsius or Kelvin.

Step 3: Calculate Temperature Change

Calculate the change in temperature \(\Delta T\) by subtracting the initial temperature from the final temperature:\[\Delta T = 25.6^{\circ} \text{C} - (-12.2^{\circ} \text{C}) = 37.8^{\circ} \text{C}\]

Step 4: Substitute Values into Formula

Substitute the known values into the heat energy formula:\[q = 168 \, \text{g} \times 0.385 \, \text{J/g} \cdot \text{K} \times 37.8^{\circ} \text{C}\]

Step 5: Perform the Calculation

Calculate the total heat energy required:\[q = 168 \times 0.385 \times 37.8 = 2447.712 \, \text{J}\]

Step 6: Round to Appropriate Significant Figures

Based on the given values, it is appropriate to round the final answer to three significant figures, giving:\[q \approx 2448 \, \text{J}\]

Key Concepts

Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in chemical reactions or physical changes. It helps in calculating the heat transfer during these changes. By understanding calorimetry, we can better comprehend how substances absorb or release heat.
To perform calorimetry, you need to work with the specific heat capacity, mass, and change in temperature of the substance involved. These elements help calculate the heat absorbed or released.

• Specific Heat Capacity: This is the amount of heat required to raise the temperature of 1 gram of a substance by 1°C. Different substances have different specific heat capacities, indicating how their temperatures change when they consume or emit heat.
• Mass: The quantity of the substance impacts how much heat is needed or released for a temperature change.
• Temperature Change (\( \Delta T \)): This is the difference between the initial and final temperatures, showing how much the temperature of the substance increased or decreased.

Using calorimetry, you can calculate heat exchanges during reactions, which is crucial in various scientific and engineering applications.

Heat Energy Calculation

Calculating heat energy is an essential part of understanding how substances transfer heat. In this process, we use the formula:\[q = m \times c \times \Delta T\]where:

• \(q\) is the heat energy required (in joules).
• \(m\) is the mass of the substance (in grams).
• \(c\) is the specific heat capacity (J/g∙K).
• \(\Delta T\) is the change in temperature (in degrees Celsius or Kelvin).

The formula helps us learn how much energy is necessary to raise the temperature of a certain mass of a substance.
The calculation requires substituting known values into the formula.In this example, \(m = 168 \, \text{g}\), \(c = 0.385 \, \text{J/g} \cdot \text{K}\), and \(\Delta T = 37.8^{\circ} \text{C}\). Substituting these values gives:\[q = 168 \times 0.385 \times 37.8 = 2447.712 \, \text{J}\]This means 2448 J (rounded to three significant figures) of energy is needed to heat the copper.

Temperature Change Calculation

Understanding temperature change calculations is vital for gauging how much a substance's temperature shifts due to heat absorption or release. Calculating the change in temperature involves the difference between the initial and final temperatures:\[\Delta T = T_{final} - T_{initial}\]In our example, the copper's initial temperature is \(-12.2^{\circ} \text{C}\), and the final temperature is \(+25.6^{\circ} \text{C}\). By subtracting these values, we calculate the change:\[\Delta T = 25.6^{\circ} \text{C} - (-12.2^{\circ} \text{C}) = 37.8^{\circ} \text{C}\]A positive \(\Delta T\) indicates that the copper's temperature increased as it absorbed heat. This change is crucial for understanding how energy shifts manifest as temperature alterations.
By comprehending and calculating temperature changes accurately, you can predict and analyze the thermal properties of different substances in various contexts, such as in environmental sciences and material engineering.