(Solved): you are asked to determine the identity of a compound (X). In a carefully controlled experiment a 2. ...

you are asked to determine the identity of a compound (X). In a carefully controlled experiment a 2.00 x 10-3 molal solution of X in water shows a boiling point elevation of 0.00304 K. Using this measurement determine the most likely chemical formula for X from among the following options: KCl, MgCl2, AlCl3, Glucose (C6H12O6) (Assume the solutions of above compounds behave ideally) Justify your answer showing relevant calculations.

Let $f(x,y,z)=x{y}^2+y{z}^2$ on the ball $B:x^2+y^2+z^2?1$. First look for interior critical points: $0=f_1=y^2,0=f_2=2xy+z^2,0=f_3=2yz$ All points on the $x$-axis are CPs, and $f=0$ at all such points. Now consider the boundary sphere $z^2=1?x^2?y^2$. On it $f(x,y,z)=x{y}^2+y\left(1?x^2?y^2\right)=x{y}^2+y?x^{2}y?y^3=g(x,y)\text{, }$ where $g$ is defined fo $x^2+y^2?1$. Look for interior CPs