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[Legendre vs Taylor]Let L?[-1,1] be the inner product space of all rea] functions such that J_ (f(r))edr is finite withf . 9 = L,fl)g(r)dzLet W be the subspace spanned by S = {1,1,12}. Show that S is not an orthogonal set. Use Gram-Schmidt process on S to obtain an orthogonal basis S' of W. (The polynomials 5' are subset of the s0 called Legendre polynomials (iii) Use S' to approximate er Compare this with the second-order Taylor approximation of er (about z = 0) by comparing thei
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Iable 2. Solution at Non-Standard Condition (12 points) Cell Notation CuCu+2iAg+ TAg ZnZn+2iCu+2Cu Ecot from simulator, volts 0.437 1,099MglMg+2IZn+2lIZn588Concentration of solution at Anode,0.23M0.31M1,SMReaction al AnodeCuzan)" Agk) Agitaq) Znta) " Cuiaq) Cuo) Znt3q) Cue)Mgiaq) Znt) Znzaq) Mg() 0 SMConcentration of solution at calhode; M0.15M25MReaction ai CathodeAglaq) Cuts) Cudq) Agu)Znzaq) Cue) Zuaal CuzaqZnjt (eq) MJ ) Mg?tq) Zno)Calculated Ez Volts (at 25*C)% dlfference
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The reaction between ozone and nitrogen dioxide at $231 \mathrm{K}$ is first order in both $\left[\mathrm{NO}_{2}\right]$ and $\left[\mathrm{O}_{3}\right].$ $$2 \mathrm{NO}_{2}(\mathrm{g})+\mathrm{O}_{3}(\mathrm{g}) \rightarrow \mathrm{N}_{2} \mathrm{O}_{5}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$ (a) Write the rate equation for the reaction. (b) If the concentration of $\mathrm{NO}_{2}$ is tripled (and $\left[\mathrm{O}_{3}\right]$ is not changed), what is the change in the reaction rate? (c) W
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