To form a complete monolayer of acetic acid on $1 \mathrm{~g}$ of charcoal, $100 \mathrm{~mL}$ of $0.5 \mathrm{M}$ acetic acid was used. Some of the acetic acid remained unadsorbed. To neutralize the unadsorbed acetic acid, 40 $\mathrm{mL}$ of $1 \mathrm{M} \mathrm{NaOH}$ solution was required. If each molecule of acetic acid occupies $\mathbf{P} \times 10^{-23} \mathrm{~m}^2$ surface area on charcoal, the value of $\mathbf{P}$ is _____.
[Use given data: Surface area of charcoal $=1.5 \times 10^2 \mathrm{~m}^2 \mathrm{~g}^{-1}$; Avogadro's number $\left(\mathrm{N}_{\mathrm{A}}\right)=6.0 \times 10^{23}$ $\left.\mathrm{mol}^{-1}\right]$
The elevation of boiling point for solution in Vessel-1 is ________ $\%$ of the solution in Vessel-2.
For a double strand DNA, one strand is given below:
![JEE Advanced 2024 Paper 2 Online Chemistry - Biomolecules Question 1 English](https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lwpydf2w/e2b61bf4-e5fa-41d3-b918-c961c3d150cf/8de0a180-1cb2-11ef-853e-dba8720394f1/file-6y3zli1lwpydf2x.png?format=png)
The amount of energy required to split the double strand DNA into two single strands is _______ kcal $\operatorname{mol}^{-1}$.
[Given: Average energy per H-bond for A-T base pair $=1.0 ~\mathrm{kcal}~ \mathrm{mol}^{-1}$, G-C base pair $=1.5 ~\mathrm{kcal}$ $\mathrm{mol}^{-1}$, and A-U base pair $=1.25 ~\mathrm{kcal} ~\mathrm{mol}^{-1}$. Ignore electrostatic repulsion between the phosphate groups.]
A sample initially contains only U-238 isotope of uranium. With time, some of the U-238 radioactively decays into $\mathrm{Pb}-206$ while the rest of it remains undisintegrated.
When the age of the sample is $\mathbf{P} \times 10^8$ years, the ratio of mass of $\mathrm{Pb}-206$ to that of $\mathrm{U}-238$ in the sample is found to be 7. The value of $\mathbf{P}$ is _______.
[Given: Half-life of $\mathrm{U}-238$ is $4.5 \times 10^9$ years; $\log _e 2=0.693$ ]