Problem 47 - Chemistry A Molecular Approach

Question

How much heat is required to warm \(1.50 \mathrm{~L}\) of water from \(25.0^{\circ} \mathrm{C}\) to \(100.0^{\circ} \mathrm{C}\) ? (Assume a density of \(1.0 \mathrm{~g} / \mathrm{mL}\) for the water.)

Step-by-Step Solution

Answer

The heat required is approximately 470,250 joules (J).

Step 1: Convert Volume to Mass

Given that the density of water is approximately 1.0 gram per milliliter (g/mL), convert the volume of water to mass. Since there are 1000 milliliters in 1 liter, multiply the volume in liters by 1000 to get the volume in milliliters, then use the density to find the mass in grams: Mass (g) = Volume (L) × 1000 (mL/L) × Density (g/mL).

Step 2: Calculate the Temperature Change

Subtract the initial temperature from the final temperature to find the temperature change (ΔT): ΔT = Final Temperature - Initial Temperature.

Step 3: Apply the Specific Heat Formula

Use the formula for heat transfer Q = mcΔT, where Q is the heat in joules (J), m is the mass in grams (g), c is the specific heat capacity (the specific heat capacity of water is approximately 4.18 J/g°C), and ΔT is the temperature change in degrees Celsius (°C).

Step 4: Calculate the Required Heat

Substitute the mass of water, the specific heat capacity of water, and the temperature change into the formula to calculate the heat required.

Key Concepts

Understanding Heat Transfer

When we talk about heat transfer, we are referring to the movement of thermal energy from one object or substance to another. Heat naturally moves from an area of higher temperature to one of lower temperature. This is a fundamental concept in physics and is crucial to many processes in daily life, such as warming up a cup of coffee or cooling a room.

Heat transfer can occur in three primary ways: conduction, which is the transfer of heat through a solid material; convection, the movement of heat in fluids (liquids and gases) due to the motion of the fluid itself; and radiation, where heat is transferred through electromagnetic waves without involving particles. In our exercise, we are dealing with liquid water, so the heat transfer mainly occurs through convection and conduction as the water molecules become energized and move faster when heated.

Exploring Temperature Change

A temperature change is the variation in the average kinetic energy of particles in a substance, which we commonly measure in degrees Celsius (°C) or Fahrenheit (°F). When heating up water, as in the given exercise, you're increasing the energy of the water molecules, which causes the temperature to rise. The temperature change (ΔT) is simply the difference between the final temperature and the initial temperature.

ΔT = Final Temperature - Initial Temperature

This difference is what determines the amount of heat energy required to achieve the desired temperature increase. Knowing the temperature change is vital because it directly influences the heat calculation discussed in chemistry and physics. The larger the temperature change required, the more heat energy will be needed to achieve it.

Heat Calculation in Chemistry

Heat calculation is a critical concept in chemistry, especially when examining thermal processes, chemical reactions, and phase changes. The equation used to calculate heat energy (Q) absorbed or released during a temperature change is:

Q = mcΔT

Here, Q stands for heat energy in joules (J), m is the mass in grams (g), c represents the specific heat capacity, and ΔT is the temperature change in degrees Celsius (°C). Specific heat capacity refers to the amount of heat required to change the temperature of one gram of a substance by one degree Celsius. Each substance has a unique specific heat capacity; for water, it's approximately 4.18 J/g°C.

In our exercise, we're effectively using this formula to find out how much energy is needed to warm water from one temperature to another. The mass of the water plays a role since heating a larger amount will require more energy. Recognizing these relationships helps in solving various chemistry-related problems that involve heat and temperature.