The rate for reaction $$2 \mathrm{~A}+\mathrm{B} \rightarrow$$ product is $$6 \times 10^{-4} \mathrm{~mol} \mathrm{~dm}^{-3} \mathrm{~s}^{-1}$$ Calculate the rate constant if the reaction is first order in $$\mathrm{A}$$ and zeroth order in $$\mathrm{B}$$. [Given $$[\mathrm{A}]=[\mathrm{B}]=0.3 \mathrm{M}]$$

Calculate molar conductivity of $$\mathrm{NH}_4 \mathrm{OH}$$ at infinite dilution if molar conductivities of $$\mathrm{Ba}(\mathrm{OH})_2$$ $$\mathrm{BaCl}_2$$ and $$\mathrm{NH}_4 \mathrm{Cl}$$ at infinite dilution are $$520,280,129 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$ respectively.

Calculate radius of third orbit of $$\mathrm{He}^{+}$$.

Calculate the depression in freezing point of solution when $$4 \mathrm{~g}$$ nonvolatile solute of molar mass $$126 \mathrm{~g} \mathrm{~mol}^{-1}$$ dissolved in $$80 \mathrm{~mL}$$ water [Cryoscopic constant of water $$=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$ ]