Bronsted-Lowry Definition:
Example: \[ NH_3 + H_2O \rightleftharpoons NH_4^+ + OH^- \] In this reaction, \( NH_3 \) acts as a Bronsted base (accepting a proton), while \( H_2O \) serves as a Bronsted acid (donating a proton).
Relationship Between pH and pOH: We know the following equations: \[ pH = -\log [H^+] \] \[ pOH = -\log [OH^-] \] Also, it holds that: \[ [H^+] [OH^-] = 10^{-14} \] Taking the logarithm of both sides: \[ pH + pOH = 14 \]
The pH of a 0.001 M HCl solution is ___________
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]