Question

The values of $\Delta H$ and $\Delta U$ for the reversible isothermal evaporation of $90.0$ g of water at $100^\circ C$ are x cal & y cal. Assume that water vapour behaves as an ideal gas and heat of evaporation of water is $540{\text{c}}al{g^{ - 1}}$. ($R = 2calmo{l^{ - 1}}{K^{ - 1}}$). The value of $x + y$ is:

Answer 1

In chemistry thermodynamics is one of the important topics for monitoring the reaction. In thermodynamics, the word meaning is thermos means heat and dynamic means flow. In thermodynamics we study the flow of the heat in the chemical reaction. In this topic we focus on three main things. There are systems, surroundings and boundaries. We consider our reaction system and environment to be surrounding and in between the junction is the boundary.
Formula used:
The enthalpy of the system depends on the internal energy, pressure and volume of the system.
The symbol of enthalpy is $H$.
The symbol of volume is $V$.
The symbol of pressure is $P$.
The symbol of internal energy is $U$.
The enthalpy formula is
$H = U + PV$
$\Delta H = \Delta U + P\Delta V$
$\Delta H = {H_f} - {H_i}$
$\Delta V = {V_f} - {V_i}$
$\Delta U = {U_f} - {U_i}$
Here, $\Delta V$ is the change in the volume of the system in the chemical reaction.
The change in the internal energy of the system in the chemical reaction is $\Delta U$.
The change in the enthalpy of the system in the chemical reaction is $\Delta H$.
Moles are defined as the given mass of the molecule is divided by the molecular mass of the molecule.
${\text{Moles = }}\dfrac{{{\text{Mass of the molecule}}}}{{{\text{Molecular weight of the molecule}}}}$
The molecular weight of the molecule is dependent on the atomic weight of the atom present in the molecule. The molecular weight of the molecule is equal to the sum of the molecular weight of the atom and the number of the respective atom in the molecule.
${\text{Molecular weight = Number of the atoms}} \times {\text{Atomic weight of the atom}}$
The ideal gas equation depends on the pressure, temperature, number of moles, volume of the gas molecules in ideal condition.
The ideal gas equation is,
$PV = nRT$
Here, the pressure of the gas is P
The volume of the gas is V
The temperature of the gas in kelvin is T
Gas constant is R
The number of moles of the Gas molecules is n

Complete answer:
The molecular weight of the water is $18$.
The amount of water in evaporation is $90$ g.
We calculate the moles of water under evaporation is
${\text{Moles = }}\dfrac{{{\text{Mass of the molecule}}}}{{{\text{Molecular weight of the molecule}}}}$
Now we can substitute the known given values we get,
$= \dfrac{{90}}{{18}}$
On simplification we get,
$= 5moles$
The moles of water under evaporation is $5moles$
We calculate enthalpy of the water is
$\Delta H = {\text{heat of evaporation}} \times {\text{the amount of water evaporate}}$
Now we can substitute the known given values we get,
$\Delta H = {\text{ }}540 \times 90$
On simplification we get,
$\Delta H = 48600cal$
The enthalpy formula is
$H = U + PV$
$\Delta H = \Delta U + P\Delta V$
Here we can apply the ideal gas equation, to change the terms.
The ideal gas equation is,
${\text{PV = nRT}}$
$\Delta H = \Delta U + {\text{nRT}}$
The temperature of the gas in kelvin T is $373k$
Gas constant is $R = 2calmo{l^{ - 1}}{K^{ - 1}}$
We substituent known values in the above formula and calculate $\Delta U$
$\Delta H = \Delta U + {\text{nRT}}$
We can change the formula for our concern.
$\Delta U = \Delta H - nRT$
Now we can substitute the known given values we get,
$\Delta U = 48600cal - {\text{(}}2 \times 373 \times 5)$
On simplification we get,
$\Delta U = 44870cal$
The value of x is $\Delta H = 48600cal$
The value of y is $\Delta U = 44870cal$
Known we are going to calculate the value of $x + y$ is
$\left( {x + y} \right) = \left( {48600 + 44870} \right)cal = 93470cal$
According to the above discussion, we conclude the values of $\Delta H$and $\Delta U$for the reversible isothermal evaporation of $90.0$ g of water at $100^\circ C$ are x cal & y cal. Assume that water vapour behaves as an ideal gas and heat of evaporation of water is $540cal{g^{ - 1}}$. ($R = 2calmo{l^{ - 1}}{K^{ - 1}}$). The value of $x + y$ is $93470cal$.

Note:
We need to know that the redox reaction is one of the types of the type of the chemical reaction. In this reaction reduction followed by oxidation in the reactants. The oxidation means the addition of oxygen or the removal of hydrogen or loss of electrons. The reduction means the addition of hydrogen or the removal of oxygen or the gain of electrons. The abbreviation of emf is electromotive force.