Draw and label the given streams and derive expressions for...

Draw and label the given streams and derive expressions for the indicated quantities in terms of labeled variables. The solution of Part (a) is given as an illustration. (a) A continuous stream contains 40.0 mole\% benzene and the balance toluene. Write expressions for the molar and mass flow rates of benzene, $\dot{n}_{\mathrm{B}}\left(\operatorname{mol} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right)$ and $\dot{m}_{\mathrm{B}}\left(\mathrm{kg} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right),$ in terms of the total molar flow rate of the stream, $\dot{n}(\mathrm{mol} / \mathrm{s})$ (b) The feed to a batch process contains equimolar quantities of nitrogen and methane. Write an expression for the kilograms of nitrogen in terms of the total moles $n($ mol) of this mixture. (c) A stream containing ethane, propane, and butane has a mass flow rate of $100.0 \mathrm{g} / \mathrm{s}$. Write an expression for the molar flow rate of ethane, $\dot{n}_{\mathrm{E}}\left(\text { Ib-mole } \mathrm{C}_{2} \mathrm{H}_{6} / \mathrm{h}\right)$, in terms of the mass fraction of this species, $x_{\mathrm{E}}$. (d) A continuous stream of humid air contains water vapor and dry air, the latter containing approximately 21 mole $\% \mathrm{O}_{2}$ and $79 \% \mathrm{N}_{2}$. Write expressions for the molar flow rate of $\mathrm{O}_{2}$ and for the mole fractions of $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{O}_{2}$ in the gas in terms of $\dot{n}_{1}\left(\mathrm{lb}-\mathrm{mole} \mathrm{H}_{2} \mathrm{O} / \mathrm{s}\right)$ and $\dot{n}_{2}(\text { lb-mole dry air/s })$ (e) The product from a batch reactor contains $\mathrm{NO}, \mathrm{NO}_{2},$ and $\mathrm{N}_{2} \mathrm{O}_{4} .$ The mole fraction of $\mathrm{NO}$ is 0.400. Write an expression for the gram-moles of $\mathrm{N}_{2} \mathrm{O}_{4}$ in terms of $n(\mathrm{mol}$ mixture) and $y_{\mathrm{NO}_{2}}\left(\operatorname{mol} \mathrm{NO}_{2} / \mathrm{mol}\right)$

Draw and label the given streams and derive expressions for the indicated quantities in terms of labeled variables. The solution of Part (a) is given as an illustration.
(a) A continuous stream contains 40.0 mole\% benzene and the balance toluene. Write expressions for the molar and mass flow rates of benzene, $\dot{n}_{\mathrm{B}}\left(\operatorname{mol} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right)$ and $\dot{m}_{\mathrm{B}}\left(\mathrm{kg} \mathrm{C}_{6} \mathrm{H}_{6} / \mathrm{s}\right),$ in terms of the total molar flow rate of the stream, $\dot{n}(\mathrm{mol} / \mathrm{s})$
(b) The feed to a batch process contains equimolar quantities of nitrogen and methane. Write an expression for the kilograms of nitrogen in terms of the total moles $n($ mol) of this mixture.
(c) A stream containing ethane, propane, and butane has a mass flow rate of $100.0 \mathrm{g} / \mathrm{s}$. Write an expression for the molar flow rate of ethane, $\dot{n}_{\mathrm{E}}\left(\text { Ib-mole } \mathrm{C}_{2} \mathrm{H}_{6} / \mathrm{h}\right)$, in terms of the mass fraction of this species, $x_{\mathrm{E}}$.
(d) A continuous stream of humid air contains water vapor and dry air, the latter containing approximately 21 mole $\% \mathrm{O}_{2}$ and $79 \% \mathrm{N}_{2}$. Write expressions for the molar flow rate of $\mathrm{O}_{2}$ and for the mole fractions of $\mathrm{H}_{2} \mathrm{O}$ and $\mathrm{O}_{2}$ in the gas in terms of $\dot{n}_{1}\left(\mathrm{lb}-\mathrm{mole} \mathrm{H}_{2} \mathrm{O} / \mathrm{s}\right)$ and $\dot{n}_{2}(\text { lb-mole dry air/s })$
(e) The product from a batch reactor contains $\mathrm{NO}, \mathrm{NO}_{2},$ and $\mathrm{N}_{2} \mathrm{O}_{4} .$ The mole fraction of $\mathrm{NO}$ is
0.400. Write an expression for the gram-moles of $\mathrm{N}_{2} \mathrm{O}_{4}$ in terms of $n(\mathrm{mol}$ mixture) and $y_{\mathrm{NO}_{2}}\left(\operatorname{mol} \mathrm{NO}_{2} / \mathrm{mol}\right)$

Key Concepts

Conversion Between Moles and Mass

This concept involves using the molecular weight of a species to convert between moles and mass. It is a key calculation in processes where compositions are given in mole percentages or mass percentages, but the analysis requires interconversion between these units to determine flow rates or reaction stoichiometry.

Mass Fraction

Mass fraction is the ratio of the mass of a specific component to the total mass of the mixture. Similar to mole fraction, it provides a component’s contribution to the overall mass, and it is used in conjunction with molecular weights to convert between mass and moles.

Mole Fraction

Mole fraction is the ratio of the moles of a specific component to the total moles in a mixture. It is a dimensionless quantity that provides a normalized measure of composition, which is especially useful when relating the total flow of a stream to the flow of individual components.

Mass and Mole Balances

This concept involves setting up and solving equations that account for the conservation of mass or moles in a process. It is fundamental in chemical engineering to ensure that all mass or moles entering a system are accounted for in the system outputs and accumulations, whether in batch or continuous processes.

Molar Flow Rate

Molar flow rate is a measure of the amount of substance (in moles) passing per unit time. It is essential for quantifying how much of a chemical species is being transferred in a process stream and forms the basis for further calculations involving composition and reaction stoichiometry.

Mass Flow Rate

Mass flow rate quantifies the mass of material flowing per unit time. This concept is used to determine the rate at which mass is transported in a process, and it is closely related to the molar flow rate through the molecular weight of the species.

Continuous and Batch Processes

Understanding the distinction between continuous and batch processing is crucial. In continuous processes, material flows steadily in and out of the system, leading to steady-state conditions, while batch processes involve the processing of a fixed amount of material with no material entering or leaving during the reaction phase.

Transcript

00:01 So the first thing we're looking to solve in this podcast is the model compositions of each component that are equal to the molar flow rate equation divided by the total flow rate.

00:12 So we can solve that as follows.

00:15 N dot c total 49 .403.

00:22 These are all in units of kilomol per hour.

00:28 We have yc, co2.

00:34 That is equal to 0 .1976, gamma c, c0, 0 .988, gamma c, h2, 0 .2, 51111, gamma c .n2, 0 .0405, gamma c .n2, 0 .040, gamma c .m.

01:11 C .m.

01:14 0 .5, 1211.

01:21 So for the streams, d and e, after first separated, the methanol and water are separated out into stream d, and the other components continue into stream e.

01:31 So now we can look at stream d in the molar compositions, so we have end up the total 25 .478.

01:43 So again, this is unit of kilomol per hour, but i just went right out every time to save it space so we have gamma dm 0 .993 gamma d h20 .0 .07 then we can look at stream e so we have n .e total 23 .925.

02:15 Following this we have gamma e co2, 0 .2015, gamma eco, 0 .2040, gamma e h2, 0 .5109, 0 .5109, gamma e .n2, nitrogen.

02:36 That is 0 .0836.

02:41 So the streams f and g, oil is the nitrogen and 90 % of the hydrogen, is fed into the second separator, and they are separated into stream f, and the other gases are recycled into stream g.

02:53 So now we can look at the molar compositions of stream f.

02:58 So we have n .f total, 13 .001, gamma f, h2, 0 .8462, gamma fn2, 0 .1 .1538, and then we can look at stream g...

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