Introduction to Chemical Engineering Processes/Chapter 1 Practice Problems

From Wikibooks, the open-content textbooks collection

Jump to: navigation, search

[edit] Chapter 1 Practice Problems

Example
Problem:

1. Perform the following conversions, using the appropriate number of significant figures in your answer:

a) 1.5 \frac{g}{s} \rightarrow \frac{lb}{hr}

b) 4.5 * 10^2 \mbox{ W} \rightarrow \frac{btu}{min}

c) 34 \frac{\mu g}{\mu m^3} \rightarrow \frac{oz}{in^3}

d) 4.18 \frac{J}{g*oC} \rightarrow \frac{kWh}{lb*oF} (note: kWh means kilowatt-hour)

e) 1.00 \mbox{ m}^3 \rightarrow L \rightarrow dm^3 \rightarrow mL \rightarrow cm^3

Example
Problem:

2. Perform a dimensional analysis on the following equations to determine if they are reasonable:

a) v = dt, where v is velocity, d is distance, and t is time.

b) F = \frac{m*v^2}{r} where F is force, m is mass, v is velocity, and r is radius (a distance).

c) Fbouy = ρ * V * g where ρ is density, V is volume, and g is gravitational acceleration.

d) \dot{m} = \frac{\dot{V}}{\rho} where \dot{m} is mass flow rate, \dot{V} is volumetric flow rate, and ρ is density.

Example
Problem:

3. Recall that the ideal gas law is PV = nRT where P is pressure, V is volume, n is number of moles, R is a constant, and T is the temperature.

a) What are the units of R in terms of the base unit types (length, time, mass, and temperature)?

b) Show how these two values of R are equivalent: R=0.0821\frac{L*atm}{mol*K} = 8.31\frac{J}{mol*K}

c) If an ideal gas exists in a closed container with a molar density of 0.03 \frac{mol}{L} at a pressure of 0.96 * 105 Pa, what temperature is the container held at?

d) What is the molar concentration of an ideal gas with a partial pressure of 4.5 * 105 Pa if the total pressure in the container is 6 atm?

e) At what temperatures and pressures is a gas most and least likely to be ideal? (hint: you can't use it when you have a liquid)

f) Suppose you want to mix ideal gasses in two separate tanks together. The first tank is held at a pressure of 500 Torr and contains 50 moles of water vapor and 30 moles of water at 70oC. The second is held at 400 Torr and 70oC. The volume of the second tank is the same as that of the first, and the ratio of moles water vapor to moles of water is the same in both tanks.

You recombine the gasses into a single tank the same size as the first two. Assuming that the temperature remains constant, what is the pressure in the final tank? If the tank can withstand 1 atm pressure, will it blow up?

Example
Problem:

4. Consider the reaction H_2O_2 <-> H_2O + \frac{1}{2} O_2 , which is carried out by many organisms as a way to eliminate hydrogen peroxide.

a). What is the standard enthalpy of this reaction? Under what conditions does it hold?

b). What is the standard Gibbs energy change of this reaction? Under what conditions does it hold? In what direction is the reaction spontaneous at standard conditions?

c). What is the Gibbs energy change at biological conditions (1 atm and 37oC) if the initial hydrogen peroxide concentration is 0.01M? Assume oxygen is the only gas present in the cell.

d). What is the equilibrium constant under the conditions in part c? Under the conditions in part b)? What is the constant independent of?

e). Repeat parts a through d for the alternative reaction H_2O_2 \rightarrow H_2 + O_2 . Why isn't this reaction used instead?

Example
Problem:

5. Two ideal gasses A and B combine to form a third ideal gas, C, in the reaction A + B \rightarrow C . Suppose that the reaction is irreversible and occurs at a constant temperature of 25oC in a 5L container. If you start with 0.2 moles of A and 0.5 moles of B at a total pressure of 1.04 atm, what will the pressure be when the reaction is completed?

Example
Problem:

6. How much heat is released when 45 grams of methane are burned in excess air under standard conditions? How about when the same mass of glucose is burned? What is one possible reason why most heterotrophic organisms use glucose instead of methane as a fuel? Assume that the combustion is complete, i.e. no carbon monoxide is formed.

Example
Problem:

7. Suppose that you have carbon monoxide and water in a tank in a 1.5:1 ratio.

a) In the literature, find the reaction that these two compounds undergo (hint: look for the water gas shift reaction). Why is it an important reaction?

b) Using a table of Gibbs energies of formation, calculate the equilibrium constant for the reaction.

c) How much hydrogen can be produced from this initial mixture?

d) What are some ways in which the yield of hydrogen can be increased? (hint: recall Le Chatlier's principle for equilibrium).

e) What factors do you think may influence how long it takes for the reaction to reach equilibrium?

Solutions

Retrieved from "http://en.wikibooks.org/wiki/Introduction_to_Chemical_Engineering_Processes/Chapter_1_Practice_Problems"