Question

The latent heat of vaporization of water is $2260\;{\text{J}}/{\text{g}}$. How many kilojoules per gram is this, and how many grams of water will be vaporized by the addition of $2.260 \times {10^3}{\text{J}}$ heat energy at ${100^\circ }{\text{C}}$ ?

Answer 1

In order to solve the first part of the question, we need to convert the given value in joules per gram into kilojoules per gram. It is a very simple conversion which can easily be done by unitary method. To solve the second part of the question, we must know the concept of latent heat of vaporization.

Formula Used:
We will use the following conversion factor to solve this question:
$1000{\text{ J}} = 1 {\text{kJ}}$

Complete step-by-step answer: For the first part of the question:
We know that $1000 J$ is equal to $1 kJ$
Then $2260\;{\text{J}}/{\text{g}}$ will be equal to
$2260 \dfrac{{\text{J}}}{{\text{g}}} \times \dfrac{{1 {\text{kJ}}}}{{1000 {\text{J}}}}$
On solving we get
$2260 {\text{J/g}} = 2.26 {\text{kJ/g}}$
For the second part of the question:
In the question, it is stated that $2260\;{\text{J}}/{\text{g}}$ is the latent heat of vaporization of water.
We can also observe the second part of the question that the quantity provided to us is $2.260 \times {10^3}J$
This is in turn equal to $2.260 \times {10^3}J = 2260 J$, that is, the latent heat of vaporization of water.
So, by the definition of latent heat of vaporization, we can say that $2.260 \times {10^3}J$ or $2260\;{\text{J}}$ is the heat required to vaporize $1 g$ of water at ${100^\circ }{\text{C}}$.
Hence,
The answer to the first part is $2.26 {\text{kJ/g}}$
The answer to the second part is $1 g$ of water

Note: Latent heat is defined as the heat or energy that during a phase change of a substance is absorbed or released. It could be from gas to liquid or from liquid to solid or vice versa. A heat property called enthalpy is related to latent heat. The heat consumed or discharged when matter disintegrates is the latent heat of vaporization, changing phase at a consistent temperature from fluid to gas stage.