RHETOR 115 Lecture 27: Rhet 115 Lecture 27 04.03.2018

Formic acid (H_2COO) has a K f 8 times 10 degree. What is the pH f a bu s luti on c nta ng 0 32 M H OOH a d 0 4 MH -? Nitr us acid (H 0 has a K, f 4 5 times 1 W at is the pH f a system c tain 0 00 M t s ac d and 0 00 M trite 0 w e 0 020 es f NaOH is added pe Excessive e ercise can ead p ucti n f ac ic ac by the usces an eease I t the b strea Expai h w t e carb I ac d bicarb nate bu7e system w ld w k t an e the inc ease in acid c ncentrat n t m I ze c anges I pH

Let V and W be finite dimensional vector s Let T V W and U W V be paces. linear and assume that dim(V) dim(W). rove that if U(T(r)) for all TE V then T (U(i)) y for all E W. Hint 1: Prove that nu 0 and use the given assumptions to conclude that T is onto. Hint 2: Since T is onto any i E W can be written as ij F T(2) for some 2 E V.