Homework #2ΒΆ

Questions:

  1. High-fructose corn syrup (HFCS) is used as a sweetener in many food and beverage products.

    HFCS 42 is a commonly used HFCS; \(\SI{1}{kg}\) of HFCS 42 has the following approximate composition:

    \(\SI{440}{grams}\) glucose (\(\ce{C6H12O6}\)) + \(\SI{320}{grams}\) fructose (\(\ce{C6H12O6}\)) + \(\SI{240}{grams}\) water (\(\ce{H2O}\)).

    1. How many \(\si{gmol}\) of each component are in \(\SI{1.0}{kg}\) of HFCS 42?

    2. The density of HFCS 42 is \(\SI{1.335}{kg/l}\). What is the density of HFCS 42 in \(\si{lb_{m}/ft^{3}}\) and \(\si{lb_{m}/gal}\)?

    3. Find the equivalent molar concentrations of each component in \(\si{gmol/l}\), \(\si{kgmol/m^{3}}\), and \(\si{lbmol/ft^{3}}\).

    4. Find the mole fraction of each component in HFCS 42.

    5. A steady-state process uses \(\SI{1000}{l/hr}\) of HFCS 42. What is the corresponding mass flow rate in \(\si{lb_{m}/hr}\)? What is the molar flow rate of each component in \(\si{lbmol/hr}\)?

    6. The HFCS 42 is pumped through a pipe. Partway down the pipeway, a water stream is introduced to dilute the HFCS. The water stream has a mass flowrate that is twice that of the HFCS 42 stream. Indicate whether the dilution step causes each of the following in the diluted stream to increase, decrease, or stay the same, compared to the HFCS feed stream alone. Also indicate the dimensions of each quantity:

      1. \(x_{water}\)

      1. \(\dot{m}_{water}\)

      1. \(y_{fructose}\)

      1. \(\dot{n}_{fructose}\)

      1. \(c_{glucose}\)

      1. \(\dot{V}\)

      1. \(\dot{m}\)

    7. A fully loaded tanker truck carries \(\SI{4800}{gal}\) of HCFS 42. What is the weight of the HCFS 42 in each of the systems of units listed in Table 4.3 of Introduction to Chemical Engineering: Tools for Today and Tomorrow (5th Edition)?

  1. Convert each of the following quantities to the units indicated:

    1. \(\SI{133}{lb_{m}.min^{-1}} \rightarrow \si{kg.hr^{-1}}\)

    2. \(\SI{15}{hp} \rightarrow \si{kW}\)

    3. \(\SI{4}{\degree C} \rightarrow \si{\degree F}\)

    4. \(\SI{7}{J/(kg. \degree C)} \rightarrow \si{Btu/(lbm. \degree F)}\)

    5. \(\SI{50000}{ft.lb_{f}} \rightarrow \si{kPa.m^{3}}\)

The following refer to the book Introduction to Chemical Engineering: Tools for Today and Tomorrow (5th Edition).

  1. Consider the Bernoulli equation introduced in Homework Problem 9 (p. 59) from Chapter 4. To show that the equation is dimensionally consistent, use the following steps:

    1. Find the units of each quantity (e.g. \(P_{start}\), \(P_{end}\), \(\rho\), \(v^{2}_{start}\), etc.).

    2. Convert the units of each quantity to the correct combinations of the fundamental dimensions listed in Table 4.1 (p. 44).

    3. Substitute these dimensions into the equation to show that terms added, subtracted or equated have the same dimensions, and that arguments of transcendental functions are dimensionless.

  1. Consider the base-ball-game system of units. The fundamental units are as follows:

    • length: \(\SI{1}{base} = \SI{90}{ft}\)

    • mass: \(\SI{1}{ball} = \SI{146}{g}\)

    • time: \(\SI{1}{game} = \SI{2}{hr}, \SI{54}{min}, \SI{39}{s}\)

    • moles: \(\SI{1}{ballmol} = \SI{146}{gmol}\)

    Find each of the following important physical constants in the base-ball-game system of units:

    1. R - the Universal Gas Constant (see S&H, bottom of p. xxiii)

    2. c - the speed of light (\(\SI{299792458}{m/s}\))

    3. G - Newtonian constant of gravitation (\(\SI{6.673848d-11}{m^{3}.kg^{-1}.s^{-2}}\))

Review your responses to all of the homework questions before class so that you are prepared for the quiz on Tuesday!