What is 'boiling point'?
Derive a relation between $△ H$ and $△ U$ for a chemical reaction Draw neat labelled diagram of calomel electrode. Resistance and conductivity of a cell containing $0.001 M K C l$ solution at $298 K$ are $1500 Ω$ and $1.46 \times 10^{- 4} S . c m^{- 1}$ respectively. What is the cell constant?

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Solution

Boiling point: The boiling point of a liquid is the temperature at which its vapour pressure becomes equal to the atmospheric pressure. Since at any temperature, the vapour pressure of a solution (containing non-volatile solute) is always higher than that of the pure solvent, the boiling point of a solution is always higher than that of the pure solvent.
Relation between $△ H$ and $△ U$ for a chemical reaction:
If a process is carried out at constant pressure, the work of expansion is given by $w = P Δ V . . . . (i)$
where $△ V$ is the increase in volume and $P$ is the constant pressure.
According to first law of thermodynamics
$q = △ U + w . . . . (i i)$
where $q$ is the heat absorbed by the system, $△ U$ is the increase in internal energy of the system and $w$ is the work done by the system.
Under condition of constant pressure, putting $w = P △ V$ and heat absorbed $q_{P}$ , we get $q_{P} = △ U + P △ V . . . . (i i i)$
Suppose when the system absorbs $q_{P}$ calories of heat, its internal energy increases from $U_{1}$ and $U_{2}$ and volume increases from $V_{1}$ to $V_{2}$ . Then $△ U = U_{2} - U_{1}$ and $△ V_{2} - V_{1}$ .
$△$ Equation (iii) becomes $q_{P} = ((U_{2} - U_{1}) + P (V_{2} - V_{1}) = (U_{2} - P V_{2}) - (U_{1} - P V_{1}) . . . (i v)$
The defining equation of enthalpy $(H)$ is $H = U + P V$
If $H_{2}$ is the enthalpy of the system in the final state and $H_{1}$ is the enthalpy in the initial state, then $H_{2} = V_{2} + P V_{2}$ and $H_{1} = U_{1} + P V_{1}$ putting these value in equation (iv) we get
$q_{P} = H_{2} - H_{1} = △ H . . . . (v)$
Further putting the value of $q_{P}$ from equation (v) to equation (iii) we get
$△ H = △ U = P △ V . . . (v i)$
$P △ V$ can be replaced by $△ n R T$ (where $△ n = c, R =$ universal gas constant and T is temperature in absolute scale)
Then equation (vi) becomes $△ H = △ U + △ n R T . . . (v i i)$
Equations (vi) and (vii) give relation between $△ H$ and $△ U$
Neat labelled diagram of calomel electrode $(H g - H g_{2} C l_{2} - K C l)$
Given,
Resistance $(R) = 1500 Ω$ , conductivity $(K) = 1.46 \times 10^{- 4} S c m^{- 1}$
$R = \frac{1}{K} \frac{l}{a}$
where $l$ is the distance between the electrodes of the cell and $a$ is the surface area of the electrode
or, $\frac{l}{a} = R K = 1500 \times 1.46 \times 10^{- 4} Ω \times Ω^{- 1} \times c m^{- 1} = 0.219 c m^{- 1}$
$∴$ Cell constant $(l / a) = 0.219 c m^{- 1}$ .

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What is 'boiling point'?Derive a relation between △H and △U for a chemical reaction Draw neat labelled diagram of calomel electrode. Resistance and conductivity of a cell containing 0.001 M KCl solution at 298 K are 1500Ω and 1.46×10−4S.cm−1 respectively. What is the cell constant?