Evaluate the change in z (i.e., ?z) in going from the point (0,0)to the point (1,1) for the differentials:
(1) dz = (x^2 + y^2) dx + xy dy and (2) dz = xy dx + xy dy
(a) Go from (0,0) to (0,1) keeping x constant and equal to 0; thento (1,1) keeping y constant and equal to 1
(b) Go along the path y=x
(c) Go along the path y = x2.

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1.Determine whether or not dz = xy dx + xy dy is exact byintegrating it around the closed curve formed by the paths y = xand y = x2 between the points (0,0) and (1,1). To do this, youshould sketch a graph of the function y = x and y = x2 and notethat the integral of dz is just the sum of the integrals for dx anddy..

2.Determine whether dq = (RT/p) dp â R dT is exact. If dq ismultiplied by 1/T, does that make dq exact?

Help with either or both would be great please and thank you :P

The normalized wavefunction for a particle trapped in a 3-dimensional box of dimensions 0 < x < a, 0 < y < b, 0 < z < c, is given by

Ïx,y,z = (2/a)^(1/2) (2/b)^(1/2) (2/c)^(1/2) sin (n_x pi y/b) sin (n_y pi y/b) sin (n_z pi z/c)

For the case in which a = b = c = 10 AÌ approximate the probability that an electron will be found in a volume element whose dimensions are Îx = Îy = Îz = 0.01 AÌ and whose center is at x = 2 AÌ, y = 3 AÌ, z = 5 AÌ for the three states

nx ny nz

2 1 1

1 2 1

1 1 2

*HINT: â _xâ _yâ _z ÏâÏ dx dy dz is the probability. When the argument ÏâÏ is nearly constant over xyz

the range it can be removed from the integral and the probability approximated as ÏâÏ ÎxÎyÎz.

Learning Goal:

To determine equilibrium concentrations from initial conditions.

The reversible reaction

XY(aq)âX(aq)+Y(aq)

has a reaction quotient Qc defined as

Qc=[X][Y][XY]

Because the reaction is reversible, both the forward and reverse reactions will occur simultaneously. The reaction will eventually reach equilibrium, at which point the concentrations do not change, and Qc is equal to a constant known as Kc.

Part C

Based on a Kc value of 0.180 and the data table given, what are the equilibrium concentrations of XY, X, and Y, respectively?

Express the molar concentrations numerically.