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Shreyansh A.
Chemical Engineering
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Physical Chemistry
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Question:

In a certain binary solution, the activity a1 of component 1 is given by the equation R ℓn a1 = R ℓn x1 + Ax22 + Bx23 where x1 and x2 are the respective mole fractions and A and B are constants. Derive an expression for the ac­tivity of component 2 given that the equation is valid over the entire concentration range from pure liquid 1 to pure liquid 2.

Shreyansh A.
Answer:

R ℓn a1 = R ℓn x1 + Ax22 + Bx23 or ℓn a1 = ℓn x1 + (Ax22 / R) + (Bx23 / R) (1) Differentiating equation (1) gives dℓna1 = (dx1 / x1) + [(2Ax2dx2) / R] + [(3Bx22dx2) / R] One form of the Gibbs-Duhem equation is given as x1dℓna1 + x2dℓna2 = 0 (2) where x1 and x2 denote the mole fraction of components 1 (solvent) and 2. Equation (2) can also be written as x2dℓna2 = – x1dℓna1 or dℓna2 = – (x1 / x2)dℓna1 = – (x1 / x2) [(dx1 / x1) + {(2Ax2dx2) / R} + {(3Bx22dx2) / R}] = – (dx1 / x2) – {(2Ax1dx2) / R} – {(3Bx1x2dx2) / R} Now x1 + x2 = 1. So dx1 + dx2 = 0, or dx1 = – dx2. After the appropriate substitutions, dℓna2 = (dx2 / x2) + {(2Ax1dx1) / R} + [{3Bx1 (1 – x1) dx1} / R] (ℓna2)(x)21 = (ℓnx2)(x)21 + (Ax12 / R)(x)10 + [(3B / R) {(x12 / 2) – (x13 / 3)}](x)10 Rℓna2 = Rℓnx2 + Ax12 + B[(3/2)x12 – x13]

Inorganic Chemistry
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Question:

Molecular geometry of thionyl chloride?

Shreyansh A.
Answer:

Trigonal Planar

Calculus
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Question:

A snail travels with velocity v(t) = 2 + 0.5sin t feet per second, where t is given in seconds. To the nearest foot, how far does the snail travel from time seconds to time t = 2π seconds?

Shreyansh A.
Answer:

The problem gives us a function for velocity and asks for distance travelled over a specified time interval. This means we need to use an integral. To get the distance the snail travels, we integrate the velocity function over the specified time interval. From to t = 2π seconds, the snail travels approximately 9 fee

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