Answer

Verified

409.2k+ views

**Hint:**The enthalpy of vaporization may be written below:

$\Delta {H_{vap}} = \Delta {U_{vap}} + p\Delta V$

Where $\Delta {U_{vap}}$ is the internal energy of vaporisation, $p$ is pressure and $\Delta V$ is the change of volume.

It is the increased internal energy of the vapour phase compared to the liquid phase, plus the work done against the ambient pressure. The rise within the internal energy is seen because the energy required to beat the intermolecular interactions within the liquid (or solid), within the case of the process of sublimation.

**Complete step by step answer:**

Given,

${H_2}O(l) \to {H_2}O(g)$ at $298K$

To calculate the moles of water to be converted into the gaseous state

Moles=given mass/molecular mass

We know that given mass of water$ = $$18$g

The molecular mass of ${H_2}O = 18$g

So the no. of moles of water$ = \dfrac{{18}}{{18}} = 1$mol

Heat is supplied to evaporate $18$g of water

$

= mol \times \Delta {{\rm H}_{vap}} \\

\\

$

Given, $\Delta {{\rm H}_{vap}}$ for water at $373K = $$40.66$$kJ/mo{l^{ - 1}}$

Substituting the values in the above equation, we can get the value of heat supplied to a given mass of water and we get:

$

= 1 \times 40.66 \\

= 40.66kJ \\

$

Now we can calculate the value of internal energy of vaporization,$\Delta {U_{vap}}$ at $373K$

Using steam as behaving like an ideal gas

$\Delta U = \Delta {\rm H} - p\Delta V$

$\Delta U = \Delta {\rm H} - \Delta {n_{(g)}}RT$

$\Delta {n_g}$ = change in gaseous moles of the products - change in gaseous moles of the reactants

$ = $ $1 - 0 = 1$

We know, the value of $R = 8.314 \times {10^{ - 3}}J/molK$

Given,

$T = 373K$

$ = 40.66kJ - $$\left[ {(1mol)(8.314 \times {{10}^{ - 3}}kJ/molK) \times 373K} \right]$

$\Delta {U_{Vap}} = 37.56kJ$

**Thus correct answer is option D.**

**Note:**

-The enthalpy of vaporization (symbol $\Delta {{\rm H}_{vap}}$ ), also called the (latent) heat of vaporization or heat of evaporation, can be defined as the amount of energy (enthalpy) that has to be added to a liquid substance to convert a quantity of that substance into a gas.

-The enthalpy of vaporization is actually a function of the pressure at which that transformation takes place.

-The gas law, also mentioned because the general gas equation is the equation of the state of a hypothetical perfect gas.

-In its empirical form, it is written as $PV = nRT$

Recently Updated Pages

What number is 20 of 400 class 8 maths CBSE

Which one of the following numbers is completely divisible class 8 maths CBSE

What number is 78 of 50 A 32 B 35 C 36 D 39 E 41 class 8 maths CBSE

How many integers are there between 10 and 2 and how class 8 maths CBSE

The 3 is what percent of 12 class 8 maths CBSE

Find the circumference of the circle having radius class 8 maths CBSE

Trending doubts

Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Fill the blanks with the suitable prepositions 1 The class 9 english CBSE

Which are the Top 10 Largest Countries of the World?

In 1946 the Interim Government was formed under a Sardar class 11 sst CBSE

10 examples of law on inertia in our daily life

Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE

Write a letter to the principal requesting him to grant class 10 english CBSE

Change the following sentences into negative and interrogative class 10 english CBSE