I'm confused in lb-mol, can you clarify it.?

I am answering this question 15kmol to lb-mol

1) At first, I tried to convert it by using 1lb-mol = 453.59mol

2) My second attempt is to converted 15kmol to kg using its molar mass and converted kg to lb afterward.

Which one is correct? can you explain why

Update:

Thanks, the answer of Ash is the same when using the 1lb-mol=453.59 mol.

Also, I was able to understand how kg-mol and lb-mol works through his conversion. 

2 Answers

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  • Dr W
    Lv 7
    1 month ago
    Favorite Answer

    Let me start by answering your question first

    .. 15 kmol.. . 1000 g-mol... .. .. 1 lb-mol

     ---- ---- ---- x ---- ----- ---- x ---- ----- ----- --- = 33 lb-mol

    . .. . . 1.. .. . . .. 1 kmol . .. .... 453.59 g-mol

    FYI.. you won't find that very often in chemistry and probably most of the people writing answers here in the chemistry section haven't heard of it. BUT.. we chemical engineers and those of you studying chemical engineering use it ALL THE TIME. As I suspect you're finding out. right?

    next... 

    *****

    Let's take an example. copper.. Cu

    .. relative atomic mass = 63.55

    agreed? (see a ptable if needed)

    Let's read that as...

    .. 63.55 amu's per 1 atom

    or..

    .. .. .. ... ... ... ... .. .. .. 63.55 amu

    .. atomic mass Cu = ---- ----- -----

    .... ... .. ... ... ... ... ... .... 1 atom

    multiplying by avogadro's # / avogadro's #

    .. .. ... ... ... ... .. .. ... 63.55 amu .. ... 6.022x10^23

    .. atomic mass Cu = ---- ----- ----- x ----- ---- ---- ---

    .... ... ... ... ... ... ... ..... 1 atom.. ... .. 6.022x10^23

    and then since

    .. 1 amu = 1.66x10^-24g... i.e.. 6.022x10^23 amu = 1g

    and

    .. 1 mol = 6.022x10^23 entities.

    we can write

    .. .. ... ... ... ... .. .. ... 63.55 amu .. ... 6.022x10^23 .. . .. .. 63.55g

    .. atomic mass Cu = ---- ----- ----- x ----- ---- ---- --- = ---- ---- ----- ----

    .... ... ... ... ... ... ... ..... 1 atom.. ... .. 6.022x10^23.. . 1 mol of atoms

    catch that?

    .. 63.55 amu.. .. 63.55 grams

    .. ----- ----- ---- = ---- ---- ---- -----

     .. . 1 atom ..... . 1 mol of atoms

    note the numbers

    .. 63.55 and 63.55 are identical

    note the units

    .. 1 amu / 1 atom are NOT the same as 1 gram / 1 mole of atoms

    the numbers are the same because of how amu and moles are defined.

    *************

    let's use a less abstract example.

    .. let's say I have a dozen cookies

    . .each cookie is 1.33 oz.

    I can write

    .. 1.33oz / 1 cookie = 12*1.33oz / 12 cookies

    .. .. ... ... .. ... .. . .... = 16 oz / 1 dozen cookies

    .. .... ... ... .. ... ... ... = 1 lb / 1 dozen cookies

    now if I make a new unit.. and call it "cmu".. cookie mass unit

    and if I let 1 cmu = 1.33oz, I can write

    .. 1 cmu / 1 cookie = 1 lb / 1 dozen cookies

    The numbers are the same.. the units are different! This is due to how I defined cmu and dozen. That is exactly what we're doing with relative atomic mass vs molar mass. in chemistry.

    now lets say I make three styles of cookies.  ginger snaps, chocolate chip and peanut butter.  The ginger snaps weigh 2 cmu / cookie, the chocolate chip cookies weigh 4 cmu / cookie and the peanut butter weigh 5 cmu / cookie.  I can now write

    .. 2 cmu / cookie = 2 lbs / dozen... . .ginger snaps

    .. 4 cmu / cookie = 4 lbs / dozen.. .. .chocolate chip

    .. 5 cmu / cooke = 5 lbs / dozen.. ...  peanut butter

    and now I make a table of cookie trends and post it on the wall and write

    .. Gs = 2

    .. Cc = 4

    .. Pb = 5

    and tell you to read those numbers as cmu per 1 cookie and as lbs per dozen cookies... you could do that right?  Same thing with atoms.

    ***********

     let's go back to the periodic table. Any of those atomic mass can be read as

    .. amu's / 1 atom

    and

    .. grams / 1 mole of atoms.. grams / 6.022x10^23 atoms

    but what happens if I multiply that g/mole * 453.59 / 453.59?

    .. 63.55g.. . 453.59

     ----- ------ x ----- ---- = what?

    ... 1 mole.. . 453.59

    while since 1 lb = 453.59g,

    and IF I define 1 lb-mole as 453.59 mol

    I can then write..

    .. 63.55g.. . 453.59 .. .. ... (1lb / 453.59g).. ... ... . 63.55 lb

     ----- ------ x ----- ---- x ---- ---- ----- ---- ---- ----- = ----- -----

    ... 1 mole.. . 453.59.. .. (1lb-mol / 453.59 mol).. . 1 lb-mol

    i.e

    .. 63.55 amu.. . 63.55 grams.. .. . . . .. . 63.55 lbs.. ... ... .. . .. 63.55 lbs

     ---- ---- ---- --- = ---- ---- ----- ---- = ---- ---- ---- ---- ----- --- = ---- ---- ---- ---- ----

    .. . .1 atom .. ... 1 mole of atoms.. .453.59 mol of atoms.. .. .lb-mol of atoms

    *********

    yup that's abstract, not for the faint of heart and not usually covered in chemistry courses. Let's continue by looking at a few different elements

    Copper

    .. atomic mass = 63.55 amu / 1 atom

    .. molar mass = 63.55g / 1 mole of atoms... 63.55g / 6.022x10^23 atoms

    .. molar mass = 63.55lb / 1 lb-mol of atoms = 453.59*6.022x10^23 atoms

    carbon

    .. atomic mass = 12.011 amu / 1 atom

    .. molar mass = 12.011g / mol = 12.011lb / lb-mol

    tungsten

    .. atomic mass = 183.84 amu / 1 atom

    .. molar mass = 183.84 lb / lb-mol = 183.84 g / mol = 183.84 kg / kg-mol

    where

    .. 1 lb-mol = 453.59 * 6.022x10^23 atoms

    .. 1 kg-mol = 1000 * 6.022x10^23 atoms

    .. 1 ton-mol = 2000 lb-mol = 2000 * 453.59 * 6.022x10^23 atoms

    **************

    Do you understand? Now you can read relative atomic mass on a periodic table as

    .. g / mol.... .aka.. g / g-mol

    .. lb / lb-mol

    .. kg / kg-mol

    .. ton / ton-mol

    etc. As long as you remember that

    .. 1 lb-mole = 453.59 * g-mole

    .. 1 kg-mole = 1000 g-mol

    .. 1 ton mole = 2000 * 453.59 g-mol

    .. 1 tonne mole = 1000 kg-mol = 1000 * 1000 * 6.022x10^23 atoms

    ************

    ************

    so you gotta be asking yourself.. why in the he!! do we use this crazy stuff in chemical engineering? why not just use the normal ole mole that we've been using for years?

    great question.. let's take an example.

    .. 2 C8H18 + 25 O2 --> 16 CO2 + 18 H2O

    question..

    .. let's assume 1.5x10^6 tons of C8H18 are burned everyday in the US

    .. how many tons of CO2 are produced everyday?

    we could certainly do this

    . 1.5e6 ton C8H18... 2000lb.. 453.59g.. 1 mol.. .16 mol CO2.. .44.01g

     ---- ---- ---- ---- ---- x ---- ---- x ----- ----- x---- ---- x ---- ---- --- --- x ---- ---- x

    .... .. ... 1 day.... .. . . 1 ton... .. .1 lb.. . .. 114g. .. 2 mol C8H18... mole

    .. .. . . .. 1 lb.. .. .1 ton

    .. .. .x ---- ----- x ---- ----- = ___ ton CO2 / day

    .. .. . .453.59g .. 2000lb

    and we calc that by entering

    .. 1.5e6 * 2000 * 453.59 / 114 * 16 / 2 * 44.01 / 453.59 / 2000 =

    right?

    but... if we use "ton-mole"

    .. 1.5e6 ton C8H18.. . 1 ton-mol C8H18.. 16 ton-mol CO2.. 44.01 ton CO2

     ----- ----- ---- ---- ---- x ---- ---- ---- ---- --- x ---- ----- ----- ---- x --- ----- ---- ---- = ?

    .. .. ... 1 day.. ... .... .. 114 ton C8H18.. .... 2 ton-mol CO2.. . ton-mol CO2

    and we calc that like this

    .. 1.5 / 114 * 16 / 2 * 44.01

    and we've just saved ourselves half the work.

    ***********

    now imagine we're doing that on a process that has a feedstock to a distillation tower at a particular plate. Then we have a top stream from a condensor and a bottom stream from a reboiler. Those streams are then fed into a series of other distillation towers. And let's say the feed steam was from a reactor and contained multiple components. And we had feed streams to that reactor in lb/hr and flowrates through the process in lb-mol/hr. And you were trying to model this system on... oh.. Aspen. Imagine all the conversions you save by using lb-mol instead of your common old g-mole. It adds up.

    ***********

    any questions about this?

    It's covered extensively in Felder and Rousseau's book and you are expected to know this for every ChE class after that. 

    **********

    **********

    by the way.. you're mixing units.  Although kmol and kg-mole have the same numerical conversion, they really aren't the same

    .. kg-mol... kilogram mole

    .. kmol... . .kilomole

    kilogram and kilo are not the same thing

    the problem should be written 

    .. "convert 15 kg-mol to lb-mol"

  • Ash
    Lv 7
    1 month ago

    kmol is just 1000 mol. 

    Maybe you meant kg-mol

    Now 1 kg = 2.2 lb

    so 15 kg-mol x ( 2.2 lb/1 kg) = 33 lb-mol

    Is that what you are looking for ?

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