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Introduction to Chemical Engineering Thermodynamics

J. M. Smith, Hendrick C Van Ness, Michael Abbott, Hendrick Van Ness

Chapter 4

HEAT EFFECTS - all with Video Answers

Educators

Chapter Questions

04:18

Problem 1

For steady flow in a heat exchanger at approximately atmospheric pressure, what is the final temperature:
(a) When $10 \mathrm{~mol}$ of $\mathrm{SO}_2$ is heated from 473.15 to $1373.15 \mathrm{~K}\left(200\right.$ to $\left.1100^{\circ} \mathrm{C}\right)$ ?
(b) When $12 \mathrm{~mol}$ of propane is heated from 523.15 to $1473.15 \mathrm{~K}\left(250\right.$ to $\left.1200^{\circ} \mathrm{C}\right)$ ?

Ahmed Kamel
Ahmed Kamel
Numerade Educator
06:26

Problem 2

For steady flow through a heat exchanger at approximately atmospheric pressure, what is the final temperature,
(a) When heat in the amount of $800 \mathrm{~kJ}$ is added to $10 \mathrm{~mol}$ of ethylene initially at $473.15 \mathrm{~K}$ $\left(200^{\prime \prime} \mathrm{C}\right)$ ?
(b) When heat in the amount of $2500 \mathrm{~kJ}$ is added to $15 \mathrm{~mol}$ of 1-butene initially at $533.15 \mathrm{~K}\left(260^{\circ} \mathrm{C}\right)$ ?
(c) When heat in the amount of $1055 \mathrm{GJ}$ is added to $18.14 \mathrm{kmol}$ of ethylene initially at $533.15 \mathrm{~K}\left(260^{\circ} \mathrm{C}\right)$ ?

Vipender Yadav
Vipender Yadav
Numerade Educator
07:14

Problem 3

If $7.08 \mathrm{~m}^3 \mathrm{~s}^{-1}$ of air at $322.15 \mathrm{~K}\left(50^{\circ} \mathrm{C}\right)$ and approximately atmospheric pressure is preheated for a combustion process to $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$, what rate of heat transfer is required?

Dading Chen
Dading Chen
Numerade Educator
04:28

Problem 4

How much heat is required when $10000 \mathrm{~kg}$ of $\mathrm{CaCO}_3$ is heated at atmospheric pressure from 323.15 to $1153.15 \mathrm{~K}\left(50^{\circ} \mathrm{C}\right.$ to $\left.880^{\circ} \mathrm{C}\right)$ ?

Lottie Adams
Lottie Adams
Numerade Educator
02:22

Problem 5

If the heat capacity of a substance is correctly represented by an equation of the form,
$$
C_P=A+B T+C T^2
$$
show that the error resulting when $\left\langle C_P\right\rangle_H$ is assumed equal to $C_P$ evaluated at the arithmetic mean of the initial and final temperatures is $C\left(T_2-T_1\right)^2 / 12$.

Lottie Adams
Lottie Adams
Numerade Educator
02:22

Problem 6

If the heat capacity of a substance is correctly represented by an equation of the form,
$$
C_P=A+B T+D T^{-2}
$$
show that the error resulting when $\left\langle C_P\right\rangle_H$ is assumed equal to $C_P$ evaluated at the arithmetic mean of the initial and final temperatures is:
$$
\frac{D}{T_1 T_2}\left(\frac{T_2-T_1}{T_2+T_1}\right)^2
$$

Lottie Adams
Lottie Adams
Numerade Educator
03:08

Problem 7

Calculate the heat capacity of a gas sample from the following information: The sample comes to equilibrium in a flask at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and $121.3 \mathrm{kPa}$. A stopcock is opened briefly, allowing the pressure to drop to $101.3 \mathrm{kPa}$. With the stopcock closed, the flask warms, returning to $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$, and the pressure is measured as $104.0 \mathrm{kPa}$. Determine $C_P$ in $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ assuming the gas to be ideal and the expansion of the gas remaining in the flask to be reversible and adiabatic.

Narayan Hari
Narayan Hari
Numerade Educator
03:05

Problem 8

A process stream is heated as a gas from 298.15 to $523.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right.$ to $\left.250^{\circ} \mathrm{C}\right)$ at constant pressure. A quick estimate of the energy requirement is obtained from Eq. (4.3), with $C_P$ taken as constant and equal to its value at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Is the estimate of $\mathrm{Q}$ likely to be low or high? Why?

Narayan Hari
Narayan Hari
Numerade Educator
13:29

Problem 9

Handbook values for the latent heats of vaporization in $\mathrm{J} \mathrm{g}^{-1}$ are given in the table for a number of pure liquids at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ and at $T_n$, the normal boiling point (App. B).
$$
\begin{array}{l|c|c}
& \Delta H^{i v} \text { at } 298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right) & \Delta H^{l v} \text { at } T_n \\
\hline \text { n-Pentane } & 366.3 & 357.2 \\
\text { n-Hexane } & 366.1 & 336.7 \\
\text { Benzene } & 433.3 & 393.9 \\
\text { Toluene } & 412.3 & 363.2 \\
\text { Cyclohexane } & 392.5 & 358.2 \\
\hline
\end{array}
$$
For one of these substances, calculate:
(a) The value of the latent heat at $T_n$ by Eq. $(4.13)$, given the value at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$.
(b) The value of the latent heat at $T_n$ by Eq. $(4,12)$.

By what percentages do these values differ from the one listed in the table?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
05:55

Problem 10

Table 9.1 lists the thermodynamic properties of saturated liquid and vapor tetrafluoroethane. Making use of the vapor pressures as a function of temperature and of the saturated-liquid and saturated-vapor volumes, calculate the latent heat of vaporization by Eq. (4.11) at one of the following temperatures and compare the result with the value calculated from the enthalpy values given in the table.
(a) $258.15 \mathrm{~K}\left(-15^{\circ} \mathrm{C}\right),($ b $) 272.15 \mathrm{~K}\left(-1^{\circ} \mathrm{C}\right),($ c $) 286.15 \mathrm{~K}\left(13^{\circ} \mathrm{C}\right),(d) 300.15 \mathrm{~K}\left(27^{\circ} \mathrm{C}\right)$,
(e) $313.15 \mathrm{~K}\left(40^{\circ} \mathrm{C}\right)$.

Ali Beker
Ali Beker
Numerade Educator
13:29

Problem 11

Handbook values for the latent heats of vaporization in $\mathrm{J} \mathrm{g}^{-1}$ are given in the table for several pure liquids at $273.15 \mathrm{~K}\left(0^{\circ} \mathrm{C}\right)$ and at $T_n$, the normal boiling point (App. B).
$$
\begin{array}{l|c|c}
& \Delta H^{l v} \text { at } 273.15 \mathrm{~K}\left(0^{\circ} \mathrm{C}\right) & \Delta H^{l v} \text { at } T_n \\
\hline \text { Chloroform } & 270.9 & 246.9 \\
\text { Methanol } & 1189.5 & 1099.5 \\
\text { Tetrachloromethane } & 217.8 & 194.2 \\
\hline
\end{array}
$$
For one of these substances, calculate:
(a) The value of the latent heat at $T_n$ by Eq. $(4.13)$, given the value at $273.15 \mathrm{~K}\left(0^{\circ} \mathrm{C}\right)$.
(b) The value of the latent heat at $T_n$ by Eq. $(4.12)$.

By what percentages do these values differ from the one listed in the table?

Susan Hallstrom
Susan Hallstrom
Numerade Educator
02:24

Problem 12

For one of the following liquids, determinethe heat of vaporization at its normal boiling point by application of the Clapeyron equation to the given vapor-pressure equation. Use generalized correlations from Chap. 3 to estimate AV.
(a) Benzene:
$$
\ln P^{\text {sat }} / \mathrm{kPa}=13.8594-\frac{2773.78}{T / \mathrm{K}-53.00}
$$
(b) Ethylbenzene:
$$
\ln \mathrm{P}^{\text {sat }} / \mathrm{kPa}=14.0045-\frac{3279.47}{T / \mathrm{K}-59.95}
$$
(c) n-Heptane:
$$
\text { In } \mathrm{P}^{\text {sat }} / \mathrm{kPa}=13.8587-\frac{2911.32}{T / \mathrm{K}-56.51}
$$
(d) n-Pentane:
$$
\ln P^{\text {sat }} / \mathrm{kPa}=13.8183-\frac{2447.07}{T / \mathrm{K}-39.94}
$$
(e) Toluene:
$$
\ln P^{\text {sat }} / \mathrm{kPa}=14.0098-\frac{3103.01}{T / \mathrm{K}-53.36}
$$

Narayan Hari
Narayan Hari
Numerade Educator
14:16

Problem 13

A method for determinationo the second virial coefficient of a pure gas is based on the Clapeyron equation and measurements of the latent heat of vaporization $\mathrm{A} H^{l v}$, the molar volume of saturated liquid $V^l$, and the vapor pressure $\mathrm{P}^{\text {sat }}$. Determine $\mathrm{B}$ in $\mathrm{cm}^3 \mathrm{~mol}^{-1}$ for methyl ethyl ketone at $348.15 \mathrm{~K}\left(75^{\circ} \mathrm{C}\right)$ from the following data at this temperature:
$$
\begin{aligned}
\Delta H^{l v} & =31600 \mathrm{~J} \mathrm{~mol}^{-1} \quad V^l=96.49 \mathrm{~cm}^3 \mathrm{~mol}^{-1} \\
\ln P^{\text {sat }} / \mathrm{kPa} & =48.157543-5622.7 / T-4.70504 \ln T \quad[T=\mathrm{K}]
\end{aligned}
$$

Susan Hallstrom
Susan Hallstrom
Numerade Educator
01:18

Problem 14

One hundred $\mathrm{kmol}$ per hour of subcooled liquid at $300 \mathrm{~K}$ and 3 bar is superheated to $500 \mathrm{~K}$ in a steady-flow heat exchanger. Estimate the exchangerduty (in $\mathrm{kW}$ ) for one of the following:
(a) Methanol, for which $\mathrm{T}^{\mathrm{sat}}=368.0 \mathrm{~K}$ at 3 bar.
(b) Benzene, for which $T^{\text {sat }}=392.3 \mathrm{~K}$ at 3 bar.
(c) Toluene, for which $\mathrm{T}^{\text {sat }}=426.9 \mathrm{~K}$ at 3 bar.

Lottie Adams
Lottie Adams
Numerade Educator
04:10

Problem 15

Saturated-liquid benzene at pressure $P_1=10 \mathrm{bar}\left(T_1^{\text {sat }}=451.7 \mathrm{~K}\right)$ is throttled in a steady-flow process to a pressure $P_2=1.2$ bar $\left(T_2^{\text {sat }}=358.7 \mathrm{~K}\right)$, where it is a liquid/vapor mixture. Estimate the molar fraction of the exit stream that is vapor. For liquid benzene, $C_P=162 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. Ignore the effect of pressure on the enthalpy of liquid benzene.

Mukesh Devi
Mukesh Devi
Numerade Educator
01:53

Problem 16

Estimate $\Delta H_{f_{x s}}^{\nabla}$ for one of the following compounds as a liquid at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. (a) Acetylene, (b) 1,3-Butadiene, (c) Ethylbenzene, (d) n-Hexane, (e) Styrene.

Sima Sarker
Sima Sarker
Numerade Educator
04:31

Problem 17

A reversible compression of $1 \mathrm{~mol}$ of an ideal gas in a piston/cylinder device results in a pressure increase from 1 bar to $P_2$ and a temperature increase from $400 \mathrm{~K}$ to $950 \mathrm{~K}$. The path followed by the gas during compression is given by
$$
P V^{1.55}=\text { const }
$$
and the molar heat capacity of the gas is given by
$$
C_P / R=3.85+0.57 \times 10^{-3} T \quad[T=\mathrm{K}]
$$

Determine the heat transferred during the process and the final pressure.

Uma Kumari
Uma Kumari
Numerade Educator
03:45

Problem 18

Hydrocarbon fuels can be produced from methanol by reactions such as the following, which yields 1-hexene:
$$
6 \mathrm{CH}_3 \mathrm{OH}(\mathrm{g}) \rightarrow \mathrm{C}_6 \mathrm{H}_{12}(\mathrm{~g})+6 \mathrm{H}_2 \mathrm{O}(\mathrm{g})
$$

Compare the standard heat of combustion at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ of $6 \mathrm{CH}_3 \mathrm{OH}(\mathrm{g})$ with the standard heat of combustion at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ of $\mathrm{C}_6 \mathrm{H}_{12}(\mathrm{~g})$ for reaction products $\mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$.

Cheryl Glor
Cheryl Glor
Numerade Educator
04:51

Problem 19

Calculate the theoretical flame temperature when ethyleneat $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ is burned with:
(a) The theoretical amount of air at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$.
(b) $25 \%$ excess air at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$.
(c) $50 \%$ excess air at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$.
(d) $100 \%$ excess air at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$.
(e) $50 \%$ excess air preheated to $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
03:05

Problem 20

What is the standard heat of combustion of n-pentane gas at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ if the combustion products are $\mathrm{H}_2 \mathrm{O}(l)$ and $\mathrm{CO}_2(g)$ ?

Nicole Smina
Nicole Smina
Numerade Educator
01:22

Problem 21

Determine the standard heat of each of the following reactions at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ :
(a) $\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \rightarrow 2 \mathrm{NH}_3(g)$
(b) $4 \mathrm{NH}_3(\mathrm{~g})+5 \mathrm{O}_2(\mathrm{~g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$
(c) $3 \mathrm{NO}_2(g)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow 2 \mathrm{HNO}_3(l)+\mathrm{NO}(g)$
(d) $\mathrm{CaC}_2(s)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{C}_2 \mathrm{H}_2(g)+\mathrm{CaO}(s)$
(e) $2 \mathrm{Na}(s)+2 \mathrm{H}_2 \mathrm{O}(g) \rightarrow 2 \mathrm{NaOH}(s)+\mathrm{H}_2(g)$
(f) $6 \mathrm{NO}_2(\mathrm{~g})+8 \mathrm{NH}_3(\mathrm{~g}) \rightarrow 7 \mathrm{~N}_2(\mathrm{~g})+12 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$
(g) $\mathrm{C}_2 \mathrm{H}_4(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow\left\langle\left(\mathrm{CH}_2\right)_2\right\rangle \mathrm{O}(\mathrm{g})$
(h) $\mathrm{C}_2 \mathrm{H}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow\left\langle\left(\mathrm{CH}_2\right)_2\right\rangle \mathrm{O}(\mathrm{g})$
(i) $\mathrm{CH}_4(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+4 \mathrm{H}_2(\mathrm{~g})$
(j) $\mathrm{CO}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightarrow \mathrm{CH}_3 \mathrm{OH}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$
(k) $\mathrm{CH}_3 \mathrm{OH}(\mathrm{g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{HCHO}(g)+\mathrm{H}_2 \mathrm{O}(g)$
(l) $2 \mathrm{H}_2 \mathrm{~S}(\mathrm{~g})+3 \mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})+2 \mathrm{SO}_2(\mathrm{~g})$
(m) $\mathrm{H}_2 \mathrm{~S}(g)+2 \mathrm{H}_2 \mathrm{O}(g) \rightarrow 3 \mathrm{H}_2(g)+\mathrm{SO}_2(g)$
(n) $\mathrm{N}_2(\mathrm{~g})+\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{NO}(g)$
(o) $\mathrm{CaCO}_3(s) \rightarrow \mathrm{CaO}(s)+\mathrm{CO}_2(g)$
(p) $\mathrm{SO}_3(g)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{H}_2 \mathrm{SO}_4(l)$
(q) $\mathrm{C}_2 \mathrm{H}_4(g)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)$
(r) $\mathrm{CH}_3 \mathrm{CHO}(g)+\mathrm{H}_2(g) \rightarrow \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(g)$
(s) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)+\mathrm{O}_2(g) \rightarrow \mathrm{CH}_3 \mathrm{COOH}(l)+\mathrm{H}_2 \mathrm{O}(l)$
(t) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{CH}: \mathrm{CH}_2(\mathrm{~g}) \rightarrow \mathrm{CH}_2: \mathrm{CHCH}: \mathrm{CH}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g})$
(u) $\mathrm{C}_4 \mathrm{H}_{10}(\mathrm{~g}) \rightarrow \mathrm{CH}_2: \mathrm{CHCH}_2 \mathrm{CH}_2(\mathrm{~g})+2 \mathrm{H}_2(\mathrm{~g})$
(v) $\mathrm{C}_2 \mathrm{H}_5 \mathrm{CH}: \mathrm{CH}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CH}_2: \mathrm{CHCH}_2 \mathrm{CH}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$
(w) $4 \mathrm{NH}_3(g)+6 \mathrm{NO}(g) \rightarrow 6 \mathrm{H}_2 \mathrm{O}(g)+5 \mathrm{~N}_2(g)$
(x) $\mathrm{N}_2(g)+\mathrm{C}_2 \mathrm{H}_2(g) \rightarrow 2 \mathrm{HCN}(g)$
(y) $\mathrm{C}_6 \mathrm{H}_5 \cdot \mathrm{C}_2 \mathrm{H}_5(g) \rightarrow \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_{:} \mathrm{CH}_2(g)+\mathrm{H}_2(g)$
(z) $\mathrm{C}(s)+\mathrm{H}_2 \mathrm{O}(l) \rightarrow \mathrm{H}_2(g)+\mathrm{CO}(g)$

Ronald Prasad
Ronald Prasad
Numerade Educator
02:33

Problem 22

Determine the standard heat for one of the reactions of $\mathrm{Pb} .4 .21$ : Part (a) at $873.15 \mathrm{~K}$ $\left(600^{\circ} \mathrm{C}\right)$, Part (b) at $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$, Part (f) at $923.15 \mathrm{~K}\left(650^{\circ} \mathrm{C}\right)$, Part (i) at $973.15 \mathrm{~K}$ $\left(700^{\circ} \mathrm{C}\right)$, Part $(j)$ at $583.15 \mathrm{~K}\left(310^{\circ} \mathrm{C}\right)$, Part $(l)$ at $683.15 \mathrm{~K}\left(410^{\circ} \mathrm{C}\right)$, Part $(\mathrm{m})$ at $850 \mathrm{~K}$, Part (n) at $1300 \mathrm{~K}, \operatorname{Part}(o)$ at $1073.15 \mathrm{~K}\left(800^{\circ} \mathrm{C}\right)$, Part (r) at $723.15 \mathrm{~K}\left(450^{\circ} \mathrm{C}\right)$, Part $(t)$ at $733.15 \mathrm{~K}\left(460^{\circ} \mathrm{C}\right)$, Part (u) at $750 \mathrm{~K}, \operatorname{Part}(\mathrm{v})$ at $900 \mathrm{~K}, \operatorname{Part}(\mathrm{w})$ at $673.15 \mathrm{~K}\left(400^{\circ} \mathrm{C}\right)$, Part $(x)$ at $648.15 \mathrm{~K}\left(375^{\circ} \mathrm{C}\right)$, Part $(y)$ at $1083.15 \mathrm{~K}\left(810^{\circ} \mathrm{C}\right)$.

Anthony Han
Anthony Han
Numerade Educator
01:15

Problem 23

Develop a general equation for the standard heat of reaction as a function of temperature for one of the reactions given in parts $(a),(\mathrm{b}),(e),(\mathrm{f}),(\mathrm{g}),(\mathrm{h}),(j),(\mathrm{k}),(\mathrm{l}),(\mathrm{m}),(\mathrm{n}),(\mathrm{o})$, $(r),(t),(u),(v),(w),(x),(y)$, and $(z)$ of $\mathrm{Pb} .4 .21$.

Aadit Sharma
Aadit Sharma
Numerade Educator
00:42

Problem 24

Natural gas (assume pure methane) is delivered to a city via pipeline at a volumetric rate of 4.0 mega normal $\mathrm{m}^3$ per day. If the selling price of the gas is $$\$ 5.00$$ per GJ of higher heating value, what is the expected revenue in dollars per day? Normal conditions are $273.15 \mathrm{~K}$ ( PC) and $1 \mathrm{~atm}$.

Hast Aggarwal
Hast Aggarwal
Numerade Educator
04:13

Problem 25

Natural gases are rarely pure methane; they usually also contain other light hydrocarbons and nitrogen. Determine an expression for the standard heat of combustion as a function of composition for a natural gas containing methane, ethane, propane, and nitrogen. Assume liquid water as a product of combustion. Which of the following natural gases has the highest heat of combustion?
(a) $y_{\mathrm{CH}_4}=0.95, y_{C_2 \mathrm{H}_6}=0.02, y_{C_3 \mathrm{H}_3}=0.02, y_{N_2}=0.01$.
(b) $y_{C_4 H_4}=0.90, y_{C_2 H_6}=0.05, y_{C_3 H_3}=0.03, y_{N_2}=0.02$.
(c) $y_{C_{H_4}}=0.85, y_{C_2 H_6}=0.07, y_{C_3 H_8}=0.03, y_{N_2}=0.05$.

David Collins
David Collins
Numerade Educator
03:10

Problem 26

If the heat of combustion of urea, $\left(\mathrm{NH}_2\right)_2 \mathrm{CO}(s)$, at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ is $631660 \mathrm{~J} \mathrm{~mol}^{-1}$ when the products are $\mathrm{CO}_2(g), \mathrm{H}_2 \mathrm{O}(l)$, and $\mathrm{N}_2(g)$, what is $\Delta H_{f_{2 s 8}}^{\circ}$ for urea at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ ?

Jorge Villanueva
Jorge Villanueva
Numerade Educator
02:46

Problem 27

The higher heating value (HHV) of a fuel is its standard heat of combustion at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ with liquid water as a product; the lower heating value (LHV) is for water vapor as product.
(a) Explain the origins of these terms.
(b) Determine the HHV and the LHV for natural gas, modeled as pure methane.
(c) Determine the HHV and the LHV for a home-heating oil, modeled as pure liquid $\mathrm{n}$-decane. For n-decane as a liquid $\mathrm{A} H_{f_{258}}^{\circ}=-249700 \mathrm{~J} \mathrm{~mol}^{-1}$.

Penny Riley
Penny Riley
Numerade Educator
01:29

Problem 28

A light fuel oil with an average chemical composition of $\mathrm{C}_{10} \mathrm{H}_{18}$ is burned with oxygen in a bomb calorimeter. The heat evolved is measured as $43960 \mathrm{~J} \mathrm{~g}^{-1}$ for the reaction at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Calculate the standard heat of combustion of the fuel oil at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ with $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ and $\mathrm{CO}_2(\mathrm{~g})$ as products. Note that the reaction in the bomb occurs at constant volume, produces liquid water as a product, and goes to completion.

Lottie Adams
Lottie Adams
Numerade Educator
01:48

Problem 29

Methane gas is burned completely with $30 \%$ excess air at approximately atmospheric pressure. Both the methane and the air enter the furnace at $303.15 \mathrm{~K}\left(30^{\circ} \mathrm{C}\right)$ saturated with water vapor, and the flue gases leave the furnace at $1773.15 \mathrm{~K}\left(1500^{\circ} \mathrm{C}\right)$. The flue gases then pass through a heat exchanger from which they emerge at $323.15 \mathrm{~K}\left(50^{\circ} \mathrm{C}\right)$. Per mole of methane, how much heat is lost from the furnace, and how much heat is transferred in the heat exchanger?

Penny Riley
Penny Riley
Numerade Educator
08:00

Problem 30

Ammonia gas enters the reactor of a nitric acid plant mixed with $30 \%$ more dry air than is required for the complete conversion of the ammonia to nitric oxide and water vapor. If the gases enter the reactor at $348.15 \mathrm{~K}\left(75^{\circ} \mathrm{C}\right)$, if conversion is $80 \%$, if no side reactions occur, and if the reactor operates adiabatically, what is the temperature of the gases leaving the reactor? Assume ideal gases.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
01:23

Problem 31

Ethylene gas and steam at $593.15 \mathrm{~K}\left(320^{\circ} \mathrm{C}\right)$ and atmospheric pressure are fed to a reaction process as an equimolar mixture. The process produces ethanol by the reaction:
$$
\mathrm{C}_2 \mathrm{H}_4(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}(l)
$$

The liquid ethanol exits the process at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. What is the heat transfer associated with this overall process per mole of ethanol produced?

Adriano Chikande
Adriano Chikande
Numerade Educator
03:22

Problem 32

A gas mixture of methane and steam at atmospheric pressure and $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$ is fed to a reactor, where the following reactions occur:
$$
\mathrm{CH}_4+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}+3 \mathrm{H}_2 \text { and } \mathrm{CO}+\mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{CO}_2+\mathrm{H}_2
$$

The product stream leaves the reactor at $1123.15 \mathrm{~K}\left(850^{\circ} \mathrm{C}\right)$. Its composition (mole fractions) is:
$$
y_{\mathrm{CO}_2}=0.0275 \quad y_{\mathrm{CO}}=0.1725 \quad y_{\mathrm{H}_2 \mathrm{O}}=0.1725 \quad y_{\mathrm{H}_2}=0.6275
$$

Determine the quantity of heat added to the reactor per mole of product gas.

Eric Mockensturm
Eric Mockensturm
Numerade Educator
01:48

Problem 33

A fuel consisting of $75 \mathrm{~mol}-\%$ methane and $25 \mathrm{~mol}-\%$ ethane enters a furnace with $80 \%$ excess air at $303.15 \mathrm{~K}\left(30^{\circ} \mathrm{C}\right)$. If $800 \mathrm{GJ}$ per $\mathrm{kmol}$ of fuel is transferred as heat to boiler tubes, at what temperature does the flue gas leave the furnace? Assume complete combustion of the fuel.

Penny Riley
Penny Riley
Numerade Educator
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Problem 34

The gas stream from a sulfur burner consists of $15 \mathrm{~mol}-\% \mathrm{SO}_2, 20 \mathrm{~mol}-\% \mathrm{O}_2$, and $65 \mathrm{~mol}-\% \mathrm{~N}_2$. The gas stream at atmospheric pressure and $673.15 \mathrm{~K}\left(400^{\circ} \mathrm{C}\right)$ enters a catalytic converter where $86 \%$ of the $\mathrm{SO}_2$ is further oxidized to $\mathrm{SO}_3$. On the basis of $1 \mathrm{~mol}$ of gas entering, how much heat must be removed from the converter so that the product gases leave at $773.15 \mathrm{~K}\left(500^{\circ} \mathrm{C}\right)$ ?

Aishwarya Krishnakumar
Aishwarya Krishnakumar
Numerade Educator
08:28

Problem 35

Hydrogen is produced by the reaction:
$$
\mathrm{CO}(g)+\mathrm{H}_2 \mathrm{O}(g) \rightarrow \mathrm{CO}_2(g)+\mathrm{H}_2(g)
$$

The feed stream to the reactor is an equimolar mixture of carbon monoxide and steam, and it enters the reactor at $398.15 \mathrm{~K}\left(125^{\circ} \mathrm{C}\right)$ and atmospheric pressure. If $60 \%$ of the $\mathrm{H} 20$ is converted to $\mathrm{H}_2$ and if the product stream leaves the reactor at $698.15 \mathrm{~K}\left(425^{\circ} \mathrm{C}\right)$, how much heat must be transferred from the reactor?

Nicholas Majtenyi
Nicholas Majtenyi
Numerade Educator
02:35

Problem 36

A direct-fired dryer bums a fuel oil with a net heating value of $44200 \mathrm{~kJ} \mathrm{~kg}^{-1}$. [The net heating value is obtained when the products of combustion are $\mathrm{CO}_2(\mathrm{~g})$ and $\mathrm{H}_2 \mathrm{O}(\mathrm{g})$.] The composition of the oil is $85 \%$ carbon, $12 \%$ hydrogen, $2 \%$ nitrogen, and $1 \%$ water by weight. The flue gases leave the dryer at $477.15 \mathrm{~K}\left(204^{\circ} \mathrm{C}\right)$, and a partial analysis shows that they contain $3 \mathrm{~mole}-\% \mathrm{CO}_2$ and $11.8 \mathrm{~mole}-\% \mathrm{CO}$ on a dry basis. The fuel, air, and material being dried enter the dryer at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. If the entering air is saturated with water and if $30 \%$ of the net heating value of the oil is allowed for heat losses (including the sensible heat carried out with the dried product), how much water is evaporated in the dryer per $\mathrm{kg}$ of oil burned?

Lottie Adams
Lottie Adams
Numerade Educator
01:52

Problem 37

An equimolar mixture of nitrogen and acetylene enters a steady-flow reactor at $298.15 \mathrm{~K}$ $\left(25^{\circ} \mathrm{C}\right)$ and atmospheric pressure. The only reaction occurring is:
$$
\mathrm{N}_2(g)+\mathrm{C}_2 \mathrm{H}_2 \rightarrow 2 \mathrm{HCN}(g)
$$

The product gases leave the reactor at $873.15 \mathrm{~K}\left(600^{\circ} \mathrm{C}\right)$ and contain $24.2 \mathrm{~mole}-\% \mathrm{HCN}$. How much heat is supplied to the reactor per mole of product gas?

Manik Pulyani
Manik Pulyani
Numerade Educator
04:38

Problem 38

Chlorine is produced by the reaction:
$$
4 \mathrm{HCl}(g)+\mathrm{O}_2(g) \rightarrow 2 \mathrm{H}_2 \mathrm{O}(g)+2 \mathrm{Cl}_2(g)
$$

The feed stream to the reactor consists of $60 \mathrm{~mol}-\% \mathrm{HCl}, 36 \mathrm{~mol}-\% \mathrm{O}_2$, and $4 \mathrm{~mol}-\%$ $\mathrm{N}_2$, and it enters the reactor at $823.15 \mathrm{~K}\left(550^{\circ} \mathrm{C}\right)$. If the conversion of $\mathrm{HCl}$ is $75 \%$ and if the process is isothermal, how much heat must be transferred from the reactor per mole of the entering gas mixture?

Ronald Prasad
Ronald Prasad
Numerade Educator
02:28

Problem 39

A gas consisting only of $\mathrm{CO}$ and $\mathrm{N}_2$ is made by passing a mixture of flue gas and air through a bed of incandescent coke (assume pure carbon). The two reactions that occur both go to completion:
$$
\mathrm{CO}_2+\mathrm{C} \rightarrow 2 \mathrm{C} 0 \quad \text { and } \quad 2 \mathrm{C}+\mathrm{O}_2 \rightarrow 2 \mathrm{C} 0
$$
They yield a flue gas of composition: $12.8 \mathrm{~mol}-\% \mathrm{CO}, 3.7 \mathrm{~mol}-\% \mathrm{CO}_2, 5.4 \mathrm{~mol}-\% \mathrm{O}_2$, and $78.1 \mathrm{~mol}-\% \mathrm{~N}_2$. The flue gas/air mixture is so proportioned that the heats of the two reactions cancel, and the temperature of the coke bed is therefore constant. If this temperature is $1148.15 \mathrm{~K}\left(875^{\circ} \mathrm{C}\right)$, if the feed stream is preheated to $1148.15 \mathrm{~K}\left(875^{\circ} \mathrm{C}\right)$, and if the process is adiabatic, what ratio of moles of flue gas to moles of air is required, and what is the composition of the gas produced?

Kratika Bhadauria
Kratika Bhadauria
Numerade Educator
01:48

Problem 40

A fuel gas consisting of 94 mole- $\%$ methane and 6 mole- $\%$ nitrogen is burned with $35 \%$ excess air in a continuous water heater. Both fuel gas and air enter dry at $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$. Water is heated at a rate of $34.0 \mathrm{~kg} \mathrm{~s}^{-1}$ from $298.15 \mathrm{~K}\left(25^{\circ} \mathrm{C}\right)$ to $368.15 \mathrm{~K}\left(95^{\circ} \mathrm{C}\right)$. The flue gases leave the heater at $483.15 \mathrm{~K}\left(210^{\circ} \mathrm{C}\right)$. Of the entering methane, $70 \%$ burns to carbon dioxide and $30 \%$ burns to carbon monoxide. What volumetric flow rate of fuel gas is required if there are no heat losses to the surroundings?

Penny Riley
Penny Riley
Numerade Educator
08:29

Problem 41

A process for the production of 1,3-butadiene results from the catalytic dehydrogenation at atmospheric pressure of 1-butene according to the reaction:
$$
\mathrm{C}_4 \mathrm{H}_8(g) \rightarrow \mathrm{C}_4 \mathrm{H}_6(g)+\mathrm{H}_2(g)
$$

To suppress side reactions, the 1-butene feed stream is diluted with steam in the ratio of 10 moles of steam per mole of 1-butene. The reaction is carried out isothermally at $798.15 \mathrm{~K}\left(525^{\circ} \mathrm{C}\right)$, and at this temperature $33 \%$ of the 1-butene is converted to $1,3-$ butadiene. How much heat is transferred to the reactor per mole of entering 1-butene?

Narayan Hari
Narayan Hari
Numerade Educator