Problem 100 - General Chemistry

Question

The specific heat of copper metal was determined by putting a piece of the metal weighing \(35.4 \mathrm{~g}\) in hot water. The quantity of heat absorbed by the metal was calculated to be \(47.0 \mathrm{~J}\) from the temperature drop of the water. What was the specific heat of the metal if the temperature of the metal rose \(3.45^{\circ} \mathrm{C}\) ?

Step-by-Step Solution

Answer

The specific heat of the metal is approximately 0.385 J/g°C.

Step 1: Understand the Formula

The formula for specific heat capacity is \( Q = mc\Delta T \), where \( Q \) is heat absorbed, \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the change in temperature. We need the specific heat capacity \( c \).

Step 2: Identify Known Values

From the problem, we have the mass \( m = 35.4 \) g, the heat absorbed \( Q = 47.0 \) J, and the temperature change \( \Delta T = 3.45^{\circ} \mathrm{C} \).

Step 3: Rearrange the Formula

Rearrange the specific heat formula to solve for \( c \): \( c = \frac{Q}{m\Delta T} \).

Step 4: Calculate the Specific Heat

Substitute the known values into the rearranged formula: \( c = \frac{47.0 \, \mathrm{J}}{35.4 \, \mathrm{g} \times 3.45^{\circ} \mathrm{C}} \).

Step 5: Perform the Calculation

Calculate \( c \): \( c = \frac{47.0}{35.4 \times 3.45} \approx 0.385 \, \mathrm{J/g^{\circ}C} \).

Key Concepts

Calorimetry

Calorimetry is a process used to measure the amount of heat absorbed or released during a chemical reaction, phase transition, or physical change. In the context of specific heat capacity, calorimetry helps us understand how substances absorb heat energy when they are subjected to a change in temperature. By carefully measuring this heat transfer, we can determine various thermal properties of materials.

In the original exercise, calorimetry was applied by immersing the copper metal in hot water and observing the heat absorbed by the metal based on the temperature change. This method relies on the principle that heat lost by the water is equal to the heat gained by the metal, reflecting the law of conservation of energy.

Here are key points in calorimetry:

• It involves measuring temperature changes in a carefully controlled environment.
• Usually uses a calorimeter, which is an insulated device that prevents heat exchange with the surroundings.
• Ensures accurate results by assuming no heat is lost to the surroundings.

Heat Transfer

Heat transfer is the movement of thermal energy from one object or substance to another. It occurs through three main mechanisms: conduction, convection, and radiation. In the context of specific heat capacity, the focus is typically on conduction, as it refers to the transfer of heat through direct contact.

For our copper metal example, the heat transfer involved conduction from the hot water to the metal. The copper absorbed heat, increasing its temperature as calculated in the exercise. Understanding heat transfer is crucial for calculating specific heat because it defines how quickly an object heats up or cools down when exposed to heat energy.

Key aspects of heat transfer include:

• Conduction, needing direct contact between materials.
• Convection, which moves heat through fluid motion.
• Radiation, which transfers energy through electromagnetic waves.

Thermochemistry

Thermochemistry is the study of the energy and heat associated with chemical reactions and physical transformations. It focuses on changes in temperature and heat flow during such processes. In thermochemistry, we use concepts like enthalpy, entropy, and heat capacity to understand how substances respond to thermal energy.

Specific heat capacity is a key term within thermochemistry as it quantifies how much heat a specific substance can absorb without changing its temperature significantly. For the copper in the exercise, determining its specific heat was a way of probing its thermochemical properties directly related to its atomic structure.

Important concepts in thermochemistry include:

• Understanding how energy changes impact reactions.
• Measuring heat changes with tools like calorimeters.
• Relating heat capacity to molecular structure.

Temperature Change

Temperature change is a fundamental concept in studying thermal properties and heat transfer. It reflects how much an object's temperature increases or decreases when subjected to heat energy. In the context of specific heat capacity, the temperature change helps in determining how much heat a material can store. In the exercise, the copper metal underwent a temperature change of 3.45°C, which was crucial in calculating its specific heat. This demonstrates the relationship between heat absorbed and the intrinsic capacity of a material to hold energy without exhibiting an extreme rise in temperature. Temperature change in heat calculations:

• Indicates degree of heat exchange in calorimetry.
• Dependent on mass and specific heat capacity.
• Shows efficiency of heat absorption in materials.

Understanding temperature changes can give insights into material properties and reaction conditions.