Chromium metal can be plated out from an acidic solution containing CrO₃ according to the following equation
CrO₃ (aq) + 6H⁺ (aq) + 6e^- $$\to$$ Cr(s) + 3H₂O
Calculate (i) how many grams of chromium will be plated out by 24,000 coulombs and (ii) how long will it take to plate out 1.5 g of chromium by using 12.5 amp current.

A first order reaction A $$\to$$ B, requires activation energy of 70 kJ mol^-1. When 20% solution of A was kept at 25^oC for 20 minutes, 25% decomposition tooks place. What will be the percentage decomposition in the same time in a 30% solution maintained at 40^oC? Assume that activation energy remains constant in this range of temperature.

Let $$a, b, c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i + \widehat k$$ and $$c\widehat i + c\widehat j + b\widehat k$$ lie in a plane, then $$c$$ is

Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ and $$\overrightarrow c = \widehat i + \widehat j - 2\widehat k - 2\widehat k$$ be three vectors. A vector in the plane of $${\overrightarrow b }$$ and $${\overrightarrow c }$$, whose projection on $${\overrightarrow a }$$ is of magnitude $$\sqrt {2/3,} $$ is :