Seawater containing 3.50 wt% salt passes through a series of 10 evaporators. Roughly equal quantities of water are vaporized in each of the 10 units and then condensed and combined to obtain a product stream of fresh water. The brine leaving each evaporator but the tenth is fed to the next evaporator. The brine leaving the tenth evaporator contains 5.00 wt% salt. (a) Draw a flowchart of the process showing the first, fourth, and tenth evaporators. Label all the streams entering and leaving these three evaporators. (b) Write in order the set of equations you would solve to determine the fractional yield of fresh water from the process ( kg $\mathrm{H}_2 \mathrm{O}$ recovered/ kg $\mathrm{H}_2 \mathrm{O}$ in process feed) and the weight percent of salt in the solution leaving the fourth evaporator. Each equation you write should contain no more than one previously undetermined variable. In each equation, circle the variable for which you would solve. Do not do the calculations. ( c) Solve the equations derived in part (b) for the two specified quantities.

Seawater containing $3.50 \mathrm{wt} \%$ salt passes through a series of 10 evaporators. Roughly equal quantities of water are vaporized in each of the 10 units and then condensed and combined to obtain a product stream of fresh water. The brine leaving each evaporator but the tenth is fed to the next evaporator. The brine leaving the tenth evaporator contains $5.00 \mathrm{wt} \%$ salt.

Write in order the set of equations you would solve to determine the fractional yield of fresh water from the process $\left(\mathrm{kg} \mathrm{H}_2 \mathrm{O}\right.$ recovered/ $\mathrm{kg} \mathrm{H}_2 \mathrm{O}$ in process feed) and the weight percent of salt in the solution leaving the fourth evaporator. Each equation you write should contain no more than one previously undetermined variable. In each equation, circle the variable for which you would solve. Do not do the calculations.

The density of a fluid is given by the empirical equation $\rho=70.5 \exp \left(8.27 \times 10^{-7} P\right)$ where $\rho$ is density $\left(\mathrm{lb}_{\mathrm{m}} / \mathrm{ft}^{3}\right)$ and P is pressure $\left(\mathrm{lb}_{\mathrm{f}} / \mathrm{in}^{2}\right)$. a) What are the units of 70:5 and $8.27 \times 10^{-7}$? b) Calculate the density in $\mathrm{g} / \mathrm{cm}^{3}$ for pressure of $9.00 \times 10^{6} \mathrm{N} / \mathrm{m}^{2}$. c) Derive a formula for $\rho\left(\mathrm{g} / \mathrm{cm}^{3}\right)$ as a function of $P\left(\mathrm{N} / \mathrm{m}^{2}\right)$. Check your result using the solution of Part (b).

A liquid mixture contains $60.0 \text{wt} \%$ ethanol (E), $5.0 \text{wt} \%$ of a dissolved solute (S), and the balance water. A stream of this mixture is fed to a continuous distillation column operating at steady state. Product streams emerge at the top and bottom of the column. The column design calls for the product streams to have equal mass flow rates and for the top stream to contain $90.0 \text{wt} \%$ ethanol and no S.

a) Assume a basis of calculation, draw and fully label a process flowchart, do the degree-of-freedom analysis, and verify that all unknown stream flows and compositions can be calculated. (Don’t do any calculations yet.)

b) Calculate

(i) the mass fraction of S in the bottom stream and

(ii) the fraction of the ethanol in the feed that leaves in the bottom product stream (i.e., kg E in bottom stream/kg E in feed) if the process operates as designed.

c) An analyzer is available to determine the composition of ethanol–water mixtures. The calibration curve for the analyzer is a straight line on a plot on logarithmic axes of mass fraction of ethanol, x (kg E/kg mixture) , versus analyzer reading, R. The line passes through the points $(R = 15, x = 0.100)$ and $(R = 38, x = 0.400)$. Derive an expression for x as a function of $R(x=\cdots)$ based on the calibration, and use it to determine the value of R that should be obtained if the top product stream from the distillation column is analyzed.

d) Suppose a sample of the top stream is taken and analyzed and the reading obtained is not the one calculated in Part (c). Assume that the calculation in Part (c) is correct and that the plant operator followed the correct procedure in doing the analysis. Give five significantly different possible causes for the deviation between $R_{\text {measured }} \text { and } R_{\text {predicted }}$, including several assumptions made when writing the balances of Part (c). For each one, suggest something that the operator could do to check whether it is in fact the problem.

A stream consisting of 44.6 mole% benzene and 55.4% toluene is fed at a constant rate to a process unit that produces two product streams, one a vapor and the other a liquid. The vapor flow rate is initially zero and asymptotically approaches half of the molar flow rate of the feed stream. Throughout this entire period, no material accumulates in the unit. When the vapor flow rate has become constant, the liquid is analyzed and found to be 28.0 mole% benzene. a) Sketch a plot of liquid and vapor flow rates versus time from startup to when the flow rates become constant. b) Is this process batch or continuous? Is it transient or steady-state before the vapor flow rate reaches its asymptotic limit? What about after it becomes constant? c) For a feed rate of 100 mol/min, draw and fully label a flowchart for the process after the vapor flow rate has reached its limiting value, and then use balances to calculate the molar flow rate of the liquid and the composition of the vapor in mole fractions.

Water enters a $2.00-\mathrm{m}^{3}$ tank at a rate of 6.00 kg/s and is withdrawn at a rate of 3.00 kg/s. The tank is initially half full. a) Is this process continuous, batch, or semibatch? Is it transient or steady state? b) Write a mass balance for the process. Identify the terms of the general balance equation (Equation 4.2-1) present in your equation and state the reason for omitting any terms. c. How long will the tank take to overflow?

Draw a Fischer projection for the following amino acid:

L-Serine

Two streams flow into a 500-gallon tank. The first stream is 10.0 wt% ethanol and 90.0% hexane (the mixture density, $\rho_{1}$, is $0.68 \mathrm{g} / \mathrm{cm}^{3}$ and the second is 90.0 wt% ethanol, 10.0% hexane $\left(\rho_{2}=0.78 \mathrm{g} / \mathrm{cm}^{3}\right)$. After the tank has been filled, which takes 22 min, an analysis of its contents determines that the mixture is 60.0 wt% ethanol, 40.0% hexane. You wish to estimate the density of the final mixture and the mass and volumetric flow rates of the two feed streams. a) Draw and label a flowchart of the mixing process and do the degree-of-freedom analysis. b)

A liquid-phase chemical reaction $\mathrm{A} \rightarrow \mathrm{B}$ takes place in a well-stirred tank. The concentration of $\mathrm{A}$ in the feed is $C_{\mathrm{A} 0}\left(\mathrm{~mol} / \mathrm{m}^3\right)$, and that in the tank and outlet stream is $C_{\mathrm{A}}\left(\mathrm{mol} / \mathrm{m}^3\right)$. Neither concentration varies with time. The volume of the tank contents is $V\left(\mathrm{~m}^3\right)$ and the volumetric flow rate of the inlet and outlet streams is $\dot{V}\left(\mathrm{~m}^3 / \mathrm{s}\right)$. The reaction rate (the rate at which $\mathrm{A}$ is consumed by reaction in the tank) is given by the expression

$$r(\mathrm{~mol} \mathrm{~A} \text { consumed } / \mathrm{s})=k V C_{\mathrm{A}}$$

where $k$ is a constant.

Write a differential balance on A, stating which terms in the general balance equation (accumulation $=$ input + generation - output - consumption) you discarded and why you discarded them. Use the balance to derive the following relation between the inlet and outlet reactant concentrations:

$$C_{\mathrm{A}}=\frac{C_{\mathrm{A} 0}}{1+k V / \dot{V}}$$

Verify that this relation predicts the results in Part (b).

A liquid-phase chemical reaction $\mathrm{A} \rightarrow \mathrm{B}$ takes place in a well-stirred tank. The concentration of $\mathrm{A}$ in the feed is $C_{\mathrm{A} 0}\left(\mathrm{~mol} / \mathrm{m}^3\right)$, and that in the tank and outlet stream is $C_{\mathrm{A}}\left(\mathrm{mol} / \mathrm{m}^3\right)$. Neither concentration varies with time. The volume of the tank contents is $V\left(\mathrm{~m}^3\right)$ and the volumetric flow rate of the inlet and outlet streams is $\dot{V}\left(\mathrm{~m}^3 / \mathrm{s}\right)$. The reaction rate (the rate at which $\mathrm{A}$ is consumed by reaction in the tank) is given by the expression

$$r(\mathrm{~mol} \mathrm{~A} \text { consumed } / \mathrm{s})=k V C_{\mathrm{A}}$$

where $k$ is a constant.

Is this process continuous, batch, or semibatch? Is it transient or steady-state?

A liquid mixture containing 30.0 mole% benzene (B), $25.0 \%$ toluene (T), and the balance xylene (X) is fed to a distillation column. The bottoms product contains 98.0 mole% X and no B, and $96.0 \%$ of the X in the feed is recovered in this stream. The overhead product is fed to a second column. The overhead product from the second column contains $97.0 \%$ of the B in the feed to this column. The composition of this stream is 94.0 mole% B and the balance T.

Calculate (i) the percentage of the benzene in the process feed (i.e., the feed to the first column) that emerges in the overhead product from the second column and (ii) the percentage of toluene in the process feed that emerges in the bottom product from the second column.

Following is a labeled flowchart for a steady-state two-unit process, with boundaries shown to denote subsystems about which balances can be taken. State the maximum number of balances that can be written for each subsystem and the order in which you would write balances to determine the unknown process variables.

The $\mathrm{SO}_2$ scrubbing tower described in Problem 4.36 is to be used to reduce the $\mathrm{SO}_2$ mole fraction in the waste gas to a level that meets air-quality standards. The solvent feed rate must be large enough to keep the $\mathrm{SO}_2$ mass fraction in the exit liquid below a specified maximum value.

Enter the equations of Part (b) into an equation-solving program. Use the program to calculate $R_3$ and $\dot{V}_2$ corresponding to $T_1=75, P_1=150, h_1=210, R_1=82.4, x_4=0.10$, and $y_3=0.05,0.025$, $0.01,0.005$, and 0.001, and then $T_1=75, P_1=150, h_1=210, R_1=82.4, x_4=0.02$, and $y_3=$ $0.05,0.025,0.01,0.005$, and 0.001. If you did not already do so in Part (c), draw on a single graph plots of $\dot{V}_2$ versus $y_3$ for each of the two given values of $x_4$ and briefly explain the shape of the curves and their position relative to each other.

The $\mathrm{SO}_2$ scrubbing tower described in Problem 4.36 is to be used to reduce the $\mathrm{SO}_2$ mole fraction in the waste gas to a level that meets air-quality standards. The solvent feed rate must be large enough to keep the $\mathrm{SO}_2$ mass fraction in the exit liquid below a specified maximum value.

Create a spreadsheet to store input values of $T_1, P_1, h_1, R_1, x_4$, and $y_3$ and to calculate $R_3$ and $\dot{V}_2$. In the first five rows, insert the values $T_1=75, P_1=150, h_1=210, R_1=82.4, x_4=010$, and $y_3=0.05,0.025,0.01,0.005$, and 0.001 . In the next five rows, insert the same input values except make $x_4=0.02$. On a single graph, draw plots of $\dot{V}_2$ versus $y_3$ for each of the two given values of $x_4$ (preferably using the spreadsheet program to generate the graph). Briefly explain the shape of the curves and their position relative to each other.