The standard potential of the following cell is 0.23V at 15^oC and 0.21 V at 35^oC.
Pt | H₂ (g) | HCl (aq) | AgCl (s) | Ag (s)
(i) Write the cell reaction.
(ii) Calculate $$\Delta H^o$$ and $$\Delta S^o$$m for the cell reaction by assuming that these quantities remain unchanged in the range 15^oC to 35^oC.
(iii) Calculate the solubility of AgCl in water at 25^oC
Given : The standard reduction potential of the Ag⁺ (aq) / Ag (s) couple is 0.80 V at 25^oC

Hydrogen peroxide solution (20 ml) reacts quantitatively with a solution of KMnO₄ solution is just decolourised by 10 ml of MnSO₄ in neutral medium simultaneously forming a dark brown precipitate of hydrated MnO₂. The brown precipitated is dissolved in 10 ml of 0.2 M sodium oxalate under boiling condition in the presence of dilute H₂SO₄. Write the balanced equations involved in the reactions and calculate the molarity of H₂O₂.

Let $${a_1}$$, $${a_2}$$,.....,$${a_n}$$ be positive real numbers in geometric progression. For each n, let $${A_n}$$, $${G_n}$$, $${H_n}$$ be respectively, the arithmetic mean , geometric mean, and harmonic mean of $${a_1}$$,$${a_2}$$......,$${a_n}$$. Find an expression for the geometric mean of $${G_1}$$,$${G_2}$$,.....,$${G_n}$$ in terms of $${A_1}$$,$${A_2}$$,.....,$${A_n}$$,$${H_n}$$,$${H_1}$$,$${H_2}$$,........,$${H_n}$$.

Let $$\overrightarrow A \left( t \right) = {f_1}\left( t \right)\widehat i + {f_2}\left( t \right)\widehat j$$ and $$$\overrightarrow B \left( t \right) = {g_1}\left( t \right)\overrightarrow i + {g_2}\left( t \right)\widehat j,t \in \left[ {0,1} \right],$$$
where $${f_1},{f_2},{g_1},{g_2}$$ are continuous functions. If $$\overrightarrow A \left( t \right)$$ and $$\overrightarrow B \left( t \right)$$ are nonzero vectors for all $$t$$ and $$\overrightarrow A \left( 0 \right) = 2\widehat i + 3\widehat j,$$ $$\,\overrightarrow A \left( 1 \right) = 6\widehat i + 2\widehat j,$$ $$\,\overrightarrow B \left( 0 \right) = 3\widehat i + 2\widehat j$$ and $$\,\overrightarrow B \left( 1 \right) = 2\widehat i + 6\widehat j.$$ Then show that $$\,\overrightarrow A \left( t \right)$$ and $$\,\overrightarrow B \left( t \right)$$ are parallel for some $$t.$$