Considering acetic acid dissociates in water, its dissociation constant is $$6.25 \times 10^{-5}$$. If $$5 \mathrm{~mL}$$ of acetic acid is dissolved in 1 litre water, the solution will freeze at $$-x \times 10^{-2}{ }^{\circ} \mathrm{C}$$, provided pure water freezes at $$0{ }^{\circ} \mathrm{C}$$.

$$x=$$ _________. (Nearest integer)

$$\begin{aligned} \text{Given :} \quad & \left(\mathrm{K}_{\mathrm{f}}\right)_{\text {water }}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}-1 \\ & \text { density of acetic acid is } 1.2 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { molar mass of water }=18 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { molar mass of acetic acid= } 60 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { density of water }=1 \mathrm{~g} \mathrm{~cm}^{-3} \end{aligned}$$

Acetic acid dissociates as $$\mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons \mathrm{CH}_3 \mathrm{COO}^{\ominus}+\mathrm{H}^{\oplus}$$

Consider the following single step reaction in gas phase at constant temperature.

$$2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}$$

The initial rate of the reaction is recorded as $$\mathrm{r}_1$$ when the reaction starts with $$1.5 \mathrm{~atm}$$ pressure of $$\mathrm{A}$$ and $$0.7 \mathrm{~atm}$$ pressure of B. After some time, the rate $$r_2$$ is recorded when the pressure of C becomes $$0.5 \mathrm{~atm}$$. The ratio $$\mathrm{r}_1: \mathrm{r}_2$$ is _________ $$\times 10^{-1}$$. (Nearest integer)

The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products $$\mathrm{A}$$ and $$\mathrm{B}$$ along with the evolution of $$\mathrm{CO}_2$$. The sum of spin-only magnetic moment values of A and B is _________ B.M. (Nearest integer)

[Given atomic number : $$\mathrm{C}: 6, \mathrm{Na}: 11, \mathrm{O}: 8, \mathrm{Fe}: 26, \mathrm{Cr}: 24$$]

In the Claisen-Schmidt reaction to prepare $$351 \mathrm{~g}$$ of dibenzalacetone using $$87 \mathrm{~g}$$ of acetone, the amount of benzaldehyde required is _________ g. (Nearest integer)