$$ \text { The IUPAC name of the following compound is } $$

Gold crystallises in fcc lattice. The edge length of the unit cell is $4 \mathop {\rm{A}}\limits^{\rm{o}}$. The closest distance between gold atoms is ' $x$ ' $\mathop {\rm{A}}\limits^{\rm{o}}$ and density of gold is ' $y$ ' $\mathrm{g} \mathrm{cm}^{-3}$. What are $x$ and $y$ respectively?

(Molar mass of gold $=197 \mathrm{~g} \mathrm{~mol}^{-1} ; N=6 \times 10^{23} \mathrm{~mol}^{-1}$ )

248 g of ethylene glycol $\left(\mathrm{C}_2 \mathrm{H}_6 \mathrm{O}_2\right)$ is added to 200 g of water to prepare antifreeze. What is the molality of resultant solution?

$$ (\mathrm{C}=12 \mathrm{u} ; \mathrm{H}=1 \mathrm{u} ; \mathrm{O}=16 \mathrm{u}) $$

A solution containing 7.5 g of urea (molar mass $=60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) in 1 kg of water freezes at the same temperature as another solution containing 15 g of solute $X$, in the same amount of water. The molar mass of $X\left(\mathrm{~g} \mathrm{~mol}^{-1}\right)$ is