Mixtures and Alligation

The vapour pressure of two miscible liquids $(A)$ and $(B)$ are $300$ and $500:mm$ of $Hg$ respectively. In a flask $10:mole$ of $(A)$ is mixed with $12:mole$ of $(B)$. However, as soon as $(B)$ is added,$(A)$ starts polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After $100:minute,:0.525:mole$ of a solute is dissolved which arrests the polymerisation completely. The final vapour pressure of the solution is $400:mm$ of $Hg$. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.

A mixture of two gases $A$ and $B$ in the mole ratio $2:3$ is kept in a $2$ litres vessel. A second $3$ litres vessel has the same gases in the mole ratio $3:5$. Both gas mixtures have the same temperature and same total pressure. They are allowed to intermix and the final temperature and total pressure are the same as the initial values, the final volume being $5$ litres. Given that the molar masses are $M_A$ and $M_B$ then what is the mean molar mass of the final mixture?

A tank consists of 50 litres of fresh water. Two litres of brine each litre containing 5 gms of dissolved salt are run into tank per minute; the mixture is kept uniform by stirring, and runs out at the rate of one litre per minute. If 'm' grams of salt are present in the tank after t minute, express 'm' in terms of t and find the amount of salt present after 10 minutes.

In order to determine the volume of blood in an animal without killing it, a 1.00 mL sample of an aqueous solution containing tritium is injected into the animal's blood-stream. The sample injected has an activity of $1.8\times 10^{6}$ cps(counts per second). After sufficient time for the sample to be completely mixed with the animal's blood due to normal blood circulation, 2.00 mL of blood are withdrawn from an animal, and the activity of the blood sample withdrawn is found to be $1.2\times 10^{4}$ cps. Calculate the volume of animal's blood?

A thermally insulated vessel contains two liquid at temperature $T_1$ and $T_2$ respectively and specific heats $C_1$ and $C_2$ separated by a non-conducting partition. The partition is removed and the difference between the initial temperature of one of the liquids and the temperature T established in the vessel turns out to be equal to half the difference between the initial temperature of the liquids. Determine the ratio $\displaystyle \dfrac{m_1}{m_2}$ (masses of the liquids).

A $5$ mole mixture of $H_2(g), O_2(g) $ and $He(g)$ are placed together in a closed container at pressure equal to $50 atm$. An electric spark is passed and pressure is noted as $20atm$ after cooling the content to original temperature.Oxygen gas is further introduced to increase the pressure to $50 atm$, keeping volume and temperature constant. Again electric spark is passed and pressure drops to $35atm$ under original temperature condition. Select the incorrect statement.