Electroanalytical Chemistry Principles Best Practices And Case Studies 1st Edition Gary A. Mabbott - Solutions

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We have $25 \mathrm{ft}$ steel frame for manufacturing a window. The shape of window is shown in Figure. Estimate the optimum dimensions such that the area of the window will be maximum.Fig. 6.9Shape of the window. r h
Find the value of $x_{1}$ and $x_{2}$, which minimizes\[F=x_{1}^{2}+x_{2}^{2}-x_{1} x_{2}-3 x_{2}\]subject to\[\begin{aligned}& -x_{1}-x_{2} \geq-2 \\& x \geq 0, x_{2} \text { integer }\end{aligned}\]
The example proposed by Yuan et al. (1988). It involves three continuous variables and four binary variables. The formulation is\[\begin{aligned}& \min _{x, y}\left(y_{1}-1\right)^{2}+\left(y_{2}-2\right)^{2}+\left(y_{3}-1\right)^{2}-\ln \left(y_{4}-1\right) \\&
A linear programming problem with $n$ decision variables and $m$ constraints can be considered as an $n$-stage dynamic programming problem with $m$ state variables-Justify this statement with proper example.
Minimize the function (using dynamic programming)\[F=\left(50 x_{1}-0.2 x_{1}^{2}\right)+\left(50 x_{2}-0.2 x_{2}^{2}\right)+8\left(x_{1}-80\right)\]subject to the constraints\[\begin{aligned}& x_{1} \geq 75 \\& x_{1}+x_{2}=220 \\& x_{1}, x_{2} \geq 0\end{aligned}\]
What is the difference between an initial value problem and a final value problem?
A refinery needs to supply 50 barrels of petrol at the end of the first month, 80 barrels at the end of second month, and 100 barrels at the end of third month. The production cost of $x$ barrels of petrol in any month is given by $\$\left(450 x+20 x^{2}\right)$. It can produce more petrol in any
Find the maximum value of the function\[F=x_{1} x_{2}\]subject to the constraints\[\begin{aligned}& x_{1}^{2}+x_{2}^{2} \leq 4 \\& x_{1}, x_{2} \geq 0 \text { and integer }\end{aligned}\]
Discuss the termination criteria of GBD method.
Give some examples of uncertainties in chemical industry.
What is meant by expected value of any random variable?
When a chemical process is called stochastic process? Give some examples.
The effluent stream from a wastewater process is monitored to make sure that two process variables, the biological oxidation demand (BOD) and the solid content, meet specifications.Sample no1234567891011121314151617181920BOD
Develop the optimization problem of a fluid flow system with two objectives, minimization of installation cost as well as minimization of pumping cost.
What do you mean by utopia point? What is the significance of that point?
Write down the algorithm for solving a multi-objective optimization problem using Lexicographic method.
Why Evolutionary Multio-bjective Optimization is superior to conventional multi-objective optimization?
Develop optimization problem for controlling a batch reactor with a reaction\[\mathrm{A}+\mathrm{B} \xrightarrow{k_{1}} \mathrm{C}+\mathrm{D}\]where $\mathrm{C}$ is the desired product.
What are the advantages of MPC over PID control? Explain your answer considering both economic and technical point.
Write down the algorithm of a regulatory control system.
Covert these decimal number to binarya) 25b) 3c) 98
How do you calculate the fitness of a chromosomes during genetic reproduction?
Write the algorithm for solving the problem\[\min f(X)=80\left(x_{1}^{2}+x_{2}\right)^{2}+\left(1-x_{1}\right)^{2}\]subject to $X \in[0,5]$
Compare the crossover and mutation operation.
solve the given problem using PSO method\[f(X)=1200\left(2 x_{1} x_{3}+2 x_{2} x_{3}\right)+2500 x_{1} x_{2}+500\left(\frac{1000}{x_{1} x_{2} x_{3}}\right)+100\left(\frac{1000}{10 x_{1} x_{2} x_{3}}\right)\]
Compare different neighborhood topologies for PSO method.
Solve the optimization problem using SA\[\min f(X)=100\left(x_{1}^{2}+x_{2}\right)^{2}+\left(1-x_{1}\right)^{2}\]subject to $X \in[0,7]$
Show 3 iterations for solving the problem below\[\min f(X)=-12 x_{1}-7 x_{2}+x_{2}^{2}\]subject to $-2 x_{1}^{4}-x_{2}+2=0$\[0 \leq x_{1} \leq 3,0 \leq x_{2} \leq 3\]
Discuss the perturbation mechanism of simulated annealing.
Compare different cooling schedule of simulated annealing.
Discuss the termination criteria of simulated annealing. How the result depends on the final temperature?
What are the pros and cons of GA and SA? Can we conceive of a framework that combines the best of both worlds?
Are Genetic Algorithms useful if we do not have a full understanding of the objective function?
If two successive generations are identical then the Genetic Algorithm has found the optimal solution. Discuss if this statement is correct.
What are the important factors we need to consider during heat exchanger network design?
Develop an optimization problem, which minimizes the operating cost a heat exchanger.
Draw the HEN superstructure with four heat exchangers.
Develop the model equation for a continuous distillation column with two feed inlet. How do you select the feed inlet position?
Discuss the algorithm of Napthali and Sandholm for solving MESH equations.
Develop a reactor network superstructure as shown in Fig. 10.3, considering both CSTR with volume $V_{1}$ and $V_{2}$.
Data is given below; use least square method to find the linear model.$x$35791015202225$y$121822323853677278
Develop a model for wastewater treatment plant using MOO methods.
Why DOE is necessary for chemical process design?
What are the different stages used for DOE?
What is meant by replication? Why it is required?
Show that the Box-Behnken design of 3 factors is not a rotatable design.
Calculate the number of experiment required for B-B design with 4 factors.
When fractional factorial design is useful?
Show that a CCD is rotatable when $\alpha=\left(n_{F}\right)^{1 / 4}$ where $n_{F}$ is the number of points used in the factorial portion of the design.
Show that using the relation $\alpha=\sqrt{k}$ results in a rotatable CCD for $k=2$ and $k=4$, but not for $k=3$.
Consider the following response surface of two factors:\[\hat{y}_{i}=70+0.1 x_{1}+0.3 x_{2}+0.2 x_{1}^{2}+0.1 x_{2}^{2}+x_{1} x_{2}\]a. Find the coordinates of the stationary point.b. What type of response function is this?
What do you mean by D-Optimal design?
Give a list of variables required to optimize a heat exchanger.
Why proper selection of decision variables is required for optimization process?
Devise a scheme for optimizing a reactor-separator process, which maximizes the yield.
How do you classify the optimization algorithms based on various aspects?
Define degree of freedom. What is the significance of degree of freedom during optimization of a chemical process?
Why topological optimization is required for the optimization of a chemical process plant?
Give some examples of combinatorial optimization in the field of chemical engineering.
How the local optimization can be avoided?
Limitations of any decision variable can be implemented in process optimization, give some examples in the area of chemical engineering.
What are advantages of computer applications for optimization?
Refer to Table 4.4 for the selectivity coefficients for ions that interfere with the determination of creatinine by the experimental ISE described in Section 4.3. Assume that $\mathrm{Na}^{+}, \mathrm{K}^{+}, \mathrm{NH}_{4}^{+}$, and $\mathrm{Ca}^{2+}$ are present in a urine sample at
Draw a circuit and specify the resistances that will divide a voltage of $6 \mathrm{~V}$ to give $1 \mathrm{~V}$ at a point that you indicate.
The cyclic voltammogram below was recorded for a mixture of two different metal complexes, A and B, using a silver/silver chloride reference electrode (+0.197 V versus the normal hydrogen electrode [NHE]).(a) What is the formal potential for complex B on the NHE scale?(b) Comparing the oxidized
A bourbon distillery treats its discharge water (that remains behind after the whisky distills off) electrochemically to remove copper by plating it out on an electrode. After 42 days of continuous operation the electrode was replaced. It was weighed before sending it off to a copper recycling
Consider a carbon electrode with a circular shape and a diameter of $3.0 \mathrm{~mm}$ dipping into a $0.1 \mathrm{M} \mathrm{NaCl}$ solution with a double layer capacitance of $20 \mu \mathrm{F} / \mathrm{cm}^{2}$. If the electrode receives a pulse of $1.0 \times 10^{12}$ electrons, what
The diffusion coefficient for $\mathrm{NO}_{3}{ }^{-}$ion is bigger than the diffusion coefficient for $\mathrm{Na}^{+}$ ion. Consider measuring the electrochemical cell potential in which a salt bridge is used between the reference solution containing $3 \mathrm{M} \mathrm{NaNO}_{3}$ and a
Explain why ohmic loss is more likely to cause a serious error in a voltammetry experiment than it is for a potentiometric experiment.
If $250 \mu \mathrm{A}$ of current flows when a potentiostat applies $-0.351 \mathrm{~V}$ to an electrochemical cell with a resistance of $152 \Omega$, what is the ohmic loss in voltage?
Explain two different mechanisms that could cause the potential of a $\mathrm{pH}$ electrode to shift upon the addition of $3 \mathrm{~g}$ of $\mathrm{KCl}$ to $100 \mathrm{ml}$ of a solution of $0.1 \mathrm{M} \mathrm{HCl}$.
How many moles of electrons would be required to change the voltage on a Pt circular disk electrode with a $2.0 \mathrm{~mm}$ diameter from -0.100 to $-0.500 \mathrm{~V}$ in an electrolyte solution of $0.1 \mathrm{M} \mathrm{KCl}$ given the electrode solution capacitance of \(24 \mu
The average thermal energy (or the average kinetic energy) in three dimensions for a molecule is often give as $3 / 2 k T$ where $k$ is Boltzmann's constant and $T$ is the absolute temperature. How does the average thermal energy of a molecule at $25^{\circ} \mathrm{C}$ compare with \(1
How does the dissociation energy of the carbon-carbon bond in an ethane molecule compare with $1 \mathrm{eV}$ ?
How does the energy of a blue photon at $400 \mathrm{~nm}$ compare to $1 \mathrm{eV}$ ?
Calculate the reference electrode potential for a $\mathrm{Ag} / \mathrm{AgCl}$ electrode in a solution with a $0.10 \mathrm{M} \mathrm{KCl}$ activity.
If a null-point potential measurement device has a current meter capable of detecting a microamp of current, what is the maximum resistance that it can have in order to keep the error in the voltage (between point A and point B in Figure 2.1) $\leq 0.05\mathrm{mV}$ ?Figure 2.1 Battery
Is $\mathrm{H}_{2} \mathrm{O}_{2}$ a more powerful oxidizing agent in an acid solution or a basic solution? Justify your answer with a quantitative argument.
The limit to the precision of the potential measured by a null-point apparatus (as in Figure 2.1) is associated with the precision of the variable resistor used to adjust the voltage at point AA. Precision variable resistors are commonly available with a rotary control that moves the sliding
What is the difference in $\mathrm{mV}$ in the voltage that one would observe for a $\mathrm{Ag} / \mathrm{AgCl}$ reference electrode prepared using $0.50 \mathrm{M}$ chloride concentration compared to $0.50 \mathrm{M}$ chloride activity?
Consider the reduction of hydroxyl amine in an acid solution:\[\mathrm{NH}_{3} \mathrm{OH}^{+}+2 \mathrm{H}^{+}+2 \mathrm{e}^{-} ightleftarrows \mathrm{NH}_{4}^{+}+\mathrm{H}_{2} \mathrm{O} \quad E^{\mathrm{o}}=1.35 \mathrm{~V}\](a) Write the Nernst equation for the half reaction.(b) Calculate the
If a cell potential was measured to be $+0.150 \mathrm{~V}$ using a saturated calomel reference electrode, what would the measured potential be if the reference electrode were replaced by a $\mathrm{Ag} / \mathrm{AgCl}$ electrode in a $0.10 \mathrm{M} \mathrm{KCl}$ solution? (Assume that the
Temperature affects a reference electrode in several ways. Consider a drop in temperature from 25 to $20^{\circ} \mathrm{C}$ for a saturated calomel electrode (SCE). Explain the different mechanisms that lead to a change in the electrode's potential. (Can you describe four different influences?)
Ferric ion is not very soluble at neutral $\mathrm{pH}$. (The $\mathrm{K}_{\mathrm{sp}}$ for $\mathrm{Fe}(\mathrm{OH})_{3}$ is $\sim 3 \times 10^{-38}$.) Yet evidence of iron is often observed in water pumped directly from simple, hand-operated pumps in rural locations. (It is noticeable in
Consider the titration of samples solutions of $\sim 0.1\mathrm{M} \mathrm{Sn}^{2+}$ in $0.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$ solution using $0.1 \mathrm{M} \mathrm{Cr}_{2} \mathrm{O}_{7}{ }^{2-}$ titrant in $0.5 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}$.(a) What would the
(a) Write the Nernst equation for the half reaction for the reduction of permanganate ion to $\mathrm{MnO}_{2}$.\[\mathrm{MnO}_{4}^{-}+4 \mathrm{H}^{+}+3 \mathrm{e}^{-} ightleftarrows \mathrm{MnO}_{2}+2 \mathrm{H}_{2} \mathrm{O} \quad E^{\circ}=1.70\](b) Calculate the formal potential for this
What potential would be expected for a cell with a platinum indicator electrode in an aqueous solution of $1.65 \mathrm{mM} \mathrm{Br}_{2}, 0.1\mathrm{M} \mathrm{HCl}$, and $0.753 \mathrm{mM} \mathrm{NaBrO}_{3}$ versus a saturated calomel electrode (SCE) (neglecting activity coefficients and
What would be expected for a cell with a platinum indicator electrode in an aqueous solution of $1.65 \mathrm{mM} \mathrm{Br}_{2}$ and $0.753 \mathrm{mM} \mathrm{NaBrO}_{3}$ versus a saturated calomel electrode (SCE) accounting for activity coefficients in a supporting electrolyte solution of
Consider the salt bridge for a $\mathrm{Ag} / \mathrm{AgCl}$ reference electrode with a $1.0 \mathrm{M} \mathrm{KCl}$ internal solution dipping into sample solution with a $1.0 \mathrm{M} \mathrm{NaCl}$ supporting electrolyte solution. Explain the effect of the $\mathrm{Na}^{+}$ion,
A technician puts a new membrane on a nitrate ISE and records the following data for a series of calibration standards in an appropriate ionic strength buffer.(a) Plot the appropriate form of the data for a calibration curve.(b) Calculate the slope for the electrode response in the linear range.(c)
Using the Henderson equation and table of diffusion coefficients in Appendix C, calculate the junction potential for a salt bridge with $3 \mathrm{M} \mathrm{KCl}$ solution contacting a sample solution with $0.1 \mathrm{M} \mathrm{NaOH}$.Data from Henderson equation and table of diffusion
A calcium ion ISE gives a response of $+170 \mathrm{mV}$ in a $100.00 \mathrm{ml}$ sample solution. The same solution is spiked with $5.00 \mathrm{ml}$ of $0.125 \mathrm{M}$ calcium standard solution. After thorough mixing the same electrode combination gave a reading of \(+193
A nitrate ISE with a new membrane gave the following response to nitrate standard solutions prepared in an appropriate ionic strength buffer. Each solution also contained $2.00 \times 10^{-2} \mathrm{MClO}_{4}{ }^{-}$. Graph the data and calculate the apparent selectivity coefficient for the
A colleague brings you her $\mathrm{Pb}^{2+}$ ISE based on a liquid membrane that uses the ionophore, ETH 5435. She said that it exhibited a slow, continuous voltage drift ( $\sim 5 \mathrm{mV} / \mathrm{min}$ ) when she was measuring trace lead levels on pond sediment samples in the field. You
The following data were obtained by preparing each standard solution by diluting the appropriate volume of a $1.00 \times 10^{-2} \mathrm{M} \mathrm{Cl}^{-}$stock solution into $250 \mathrm{ml}$ volumetric flasks and diluting to the mark with deionized water. Before measuring, \(100.0
How many $\mathrm{Ca}^{2+}$ ions cross the membrane/solution boundary corresponding to a $0.050 \mathrm{~V}$ increase in potential for a sensor with a $0.090 \mathrm{~cm}^{2}$ area assuming a capacitance of $3 \times 10^{-6} \mathrm{~F} / \mathrm{cm}^{2}$ ?
Using the Henderson equation and table of diffusion coefficients in Appendix C, calculate the junction potential for a salt bridge with $3 \mathrm{M} \mathrm{NaCl}$ solution contacting a sample solution with $0.2 \mathrm{M} \mathrm{HNO}_{3}$.Data from Henderson equation and table of diffusion
A cell using a potassium ISE based on a liquid membrane using valinomycin as an ionophore and a silver/silver chloride electrode gives a voltage of $-0.273 \mathrm{~V}$ in a solution of $7.50 \times 10^{-6} \mathrm{M} \mathrm{KCl}$ standard solution (using an ionic strength buffer). Assuming
After treating the sample solution $1: 1$ with TISAB containing $1 \mathrm{M} \mathrm{NaCl}$, what would the approximate junction potential be for a salt bridge containing $3 \mathrm{M} \mathrm{KCl}$ ?
If the liquid junction potential for a combination $\mathrm{pH}$ electrode drifts by $5 \mathrm{mV}$, what is the relative error in the apparent $\mathrm{H}^{+}$concentration?

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Electroanalytical Chemistry Principles Best Practices And Case Studies 1st Edition Gary A. Mabbott - Solutions

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