Problem 10 - Chemistry Matter and Change

Question

Calculate the amount of heat absorbed when 5.50 g of aluminum is heated from 25.0ºC to 95.0ºC. The specific heat of aluminum is 0.897 J/(g?ºC)

Step-by-Step Solution

Answer

The amount of heat absorbed when 5.50 g of aluminum is heated from 25.0ºC to 95.0ºC is 342.9 Joules.

Step 1: Identify the given values

We are given the mass of aluminum (m = 5.50 g), the initial temperature (Ti = 25.0ºC), the final temperature (Tf = 95.0ºC), and the specific heat of aluminum (c = 0.897 J/g°C).

Step 2: Calculate ΔT

To find the change in temperature, subtract the initial temperature from the final temperature: ΔT = Tf - Ti ΔT = 95.0ºC - 25.0ºC ΔT = 70.0ºC

Step 3: Apply the heat equation

Now that we have the change in temperature, we can use the heat equation (q = mcΔT) to find the amount of heat absorbed by the aluminum: q = (5.50 g)(0.897 J/g°C)(70.0ºC)

Step 4: Calculate the heat absorbed

Multiply the mass, specific heat, and change in temperature to find the heat absorbed: q = (5.50 g)(0.897 J/g°C)(70.0ºC) = 342.9 J The amount of heat absorbed by the aluminum is 342.9 Joules.

Key Concepts

Specific Heat Capacity

Specific heat capacity is a property of a substance that tells us how much energy is needed to raise the temperature of 1 gram of the substance by 1 degree Celsius.
This concept is important as it helps us understand how different materials respond to changes in temperature. Different substances have different specific heat capacities.

• For example, water has a high specific heat capacity, which means it takes a lot of energy to change its temperature. This is why water is good at regulating temperatures.
• On the other hand, metals typically have a lower specific heat capacity than water. For instance, aluminum's specific heat capacity is 0.897 J/(g°C). This makes it quick to heat up or cool down.

Knowing the specific heat capacity is crucial when calculating the energy changes involved in heating or cooling a substance, as seen in our exercise with aluminum.

Heat Equation

The heat equation is a simple formula that helps us calculate the amount of heat energy absorbed or released during a temperature change. It is expressed as: \( q = mc\Delta T \) where:

• \( q \) is the heat energy (in Joules)
• \( m \) is the mass of the substance (in grams)
• \( c \) is the specific heat capacity (in J/(g°C))
• \( \Delta T \) is the change in temperature (in °C)

The heat equation tells us how much thermal energy is needed based on the mass and specific heat of the material and the temperature change it undergoes.
This equation is fundamental in chemistry and physics when dealing with thermal processes, as it ties together key variables that dictate energy transfer.

Temperature Change

Temperature change is a measure of how much the temperature of a substance has increased or decreased.
In the heat equation, the temperature change \( \Delta T \) is found by subtracting the initial temperature from the final temperature: \[ \Delta T = T_f - T_i \] For example, if a metal starts at 25.0°C and is heated to 95.0°C, the temperature change is 70.0°C. This temperature change is a critical factor in determining the amount of heat absorbed or released.
A greater temperature change typically requires more energy, assuming the mass and specific heat capacity remain constant.

• Understanding this concept helps explain why different environments and conditions require varying amounts of energy to achieve similar temperature changes.

In practical terms, knowing the temperature change allows us to predict and control the heating and cooling of materials effectively.