To calibrate a gas chromatograph for blood alcohol assays, the technician must prepare a standard 0.08%(w/v) alcohol solution. Describe how to prepare 100mL of 0.08%(w/w) from a “140 proof” ethanol-water commercial standard. Hint: 140 proof = 70%(w/v). Comment on the total volume of the 0.08%(w/v) calibration standard: Is 100 mL a sufficient volume to allow accurate preparation of the calibration standard… or would 1,000 mL be better? Defend your answer.

a) Find an equation of the plane tangent to the graph of f at the given point P. Write your answer in the form ax + by +cz= d, where a, b, c, and d are integers with no common factor, and a is greater or equal to 0. f(x,y)= 2x³y + 4x-y, P(1,3,7)

b) Use a multivariable chain rule to find a formula for the given derivative or partial derivative. w= f(x,y), x=g(u,v), y=h(u,v);  ∂w/ ∂v

A. Calculate the mass percent (m/m) of a solution prepared by dissolving 51.22 g of NaCl in 151.9 g of H2O.

B. Vinegar is a solution of acetic acid in water. If a 265 mL bottle of distilled vinegar contains 19.2 mL of acetic acid, what is the volume percent (v/v) of the solution?

C. Calculate the mass/volume percent (m/v) of 20.5 g NaCl in 75.0 mL of solution.

D. Calculate the molarity (M) of 155.2 g of H2SO4 in 1.330 L of solution.

A voltaic cell consists of a Zn/Zn²⁺ anode and a Ni/Ni²⁺ cathode at 25 ^∘C. The initial concentrations of Ni²⁺ and Zn²⁺ are 1.7 M and 0.12 M , respectively. The volume of half-cells is the same.

What is the concentration of Ni²⁺ when the cell potential falls to 0.456 V ?   

Enter your answer to 4 decimal places and in units of mM.

Zn²⁺ (aq) + 2 e-  ⟶Zn(s) E° = -0.76 V

Ni²⁺ (aq) + 2 e- ⟶   Ni(s) E° = -0.23 V

A particle of charge q and mass m is accelerated from rest through a potential difference V, after which it encounters a uniform magnetic field B perpendicular to its velocity v. If the particle moves in a plane perpendicular to B,

(a) Find an expression for the radius of its circular path in terms of q, V and B.

(b) If the particle is an electron, what must the potential difference be so it describes a circular path of radius 1.5 m in a magnetic field of 0.05 T?

12. (a) Is the subset { (e,0), (e,6), (e,12), (h,0), (h,6), (h,12) }, a subgroup of the direct product group ( V x Z18 )? (V is the Klein four group.) Carefully explain or justify your answer.

(b) Is the subgroup { (e,0), (e,6), (e,12), (h,0), (h,6), (h,12) }, a normal subgroup of the direct product group ( V x Z18 )? Carefully explain or justify your answer.

Explain how the performance of induction motor can be predicted by circle diagram. Draw the circle
diagram for a 3-phase, mesh-connected, 22.38 kW, 500-V, 4-pole, 50-Hz induction motor. The data
below give the measurements of line current, voltage and reading of two wattmeters connected to
measure the input :
No load 500 V 8.3 A 2.85 kW − 1.35 kW
Short circuit 100 V 32 A − 0.75 kW 2.35 kW

a. Using only P-v-T data, estimate the enthalpy of vaporization of water at T oC where, T is T= 38 and so on. b. If the enthalpy (h), as an unmeasured thermodynamic property is related to the temperature (T) and Pressure (P) as measured thermodynamic properties according to the following relation: h = f (T,P). Show that: dh = Cp dT +[ v – T (dv/dT)p] dP Where: Cp is the specific heat at constant pressure, v is the specific volume.

A positive charge q is fixed at the point x=0,y=0 and a negative charge -2q is fixed at the point x=a,y=0.

Part A:

Derive an expression for the potential V at points on the y-axis as a function of the coordinate y. Take V to be zero at an infinite distance from the charges.

Part B:

At which positions on the y-axis is V = 0?

Part C:

What does the answer to part A become when y>>a?

Part D:

Explain why this result is obtained.

A spherical raindrop falling through mist builds up mass. The mass accumlates at a rate proportional to its cross-sectional area and invers;ey proportional to its velocity, that is, dm/dt=k?r2/v, where r is the radius of the raindrop at a given time and v is the downard speed at the same time.Assuming the density P of the rain drop is a constant. Ignoring the resistance do to the fog and the air, calculate the instaneous acceleration of the raindrop as a function of v,r,P,g and k.