Question

How much heat is required to vaporize \(33.8 \mathrm{~g}\) of water at \(100^{\circ} \mathrm{C} ?\)

Short answer

The heat required to vaporize 33.8 g of water at 100 degrees Celsius is 76,388 Joules.

Step-by-step solution

Find the latent heat of vaporization for water

Determine the amount of heat energy required to convert one gram of water into vapor at its boiling point. This value is a constant known as the latent heat of vaporization. For water at 100 degrees Celsius, it is approximately 2260 Joules per gram.

Calculate the total heat required

Multiply the mass of the water to be vaporized by the latent heat of vaporization to find the total heat required. Use the formula: Heat (Q) = mass (m) * latent heat of vaporization (L).

Plug in the values and calculate

Substitute the mass of water and the constant value of latent heat into the formula: Q = 33.8 g * 2260 J/g.

Compute the result

After performing the multiplication, you obtain the total amount of heat required to vaporize the given mass of water at 100 degrees Celsius.

Key concepts

Latent Heat of Vaporization

When a substance changes from a liquid to a gas, it must absorb a specific amount of heat without changing its temperature. This heat is known as the latent heat of vaporization. It is the energy required to break the intermolecular forces that hold the liquid molecules together.

In our example with water, this is the heat energy needed to transition water at its boiling point of 100 degrees Celsius to steam without any increase in temperature. It's an intrinsic property, varying for different substances and is a crucial factor for calculations involving phase changes from liquid to vapor. For water, this value is given as 2260 Joules per gram, which means every gram of boiling water needs 2260 Joules of energy to become steam.

Phase Change

A phase change is a physical transition between different states of matter: solid, liquid, and gas. Each substance can exist in these phases and will transition from one to another at specific temperatures and pressures.

During a phase change, the substance absorbs or releases latent heat, but the temperature remains constant until the change is complete. For example, water changing to vapor at 100 degrees Celsius is a phase transition where latent heat is absorbed but the temperature stays the same. This process is endothermic, meaning heat is taken in. The opposite process, condensation, where gas turns back to liquid, is exothermic; the system releases heat.

Heat Energy Calculations

Understanding heat energy calculations is essential for a wide range of scientific and engineering disciplines. These calculations enable us to determine the amount of energy needed for a substance to undergo a physical change.

To calculate the total heat energy (Q) required for vaporization, we use the formula:
\[ Q = m \times L \]
where m is the mass of the substance and L is the latent heat of vaporization. By substituting the known values into the equation, such as the 33.8 grams of water and the latent heat of vaporization of water (2260 J/g), we find the total energy required for the phase change. In the case of our example, the calculation would be
\[ Q = 33.8 \text{g} \times 2260 \text{J/g} \]
Solving this provides us the exact amount of energy in Joules necessary to vaporize the given mass of water at its boiling point.