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Homework Help: How to get moles from MO having % of mass?

  1. Aug 12, 2018 #1
    1. The problem statement, all variables and given/known data
    This is a question from a chemistry book
    Two oxides of a metal contain 27.6% and 30% of oxygen respectively. If the formula of the first oxide is MO, find that of the second?

    3. The attempt at a solution

    In the first MO, if the total amount is 100g, then O is 27.6g similarly,
    in the second MO, if the total amount is 100g, then O is 30g respectively
    1.725 mole of O is 27.6g.
    in the MO, 72.4g of M left.
    But my question is how to calculate the mole of M? because I don't know the molar mass of M
     
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  3. Aug 12, 2018 #2

    Ygggdrasil

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    You have sufficient information to calculate the molecular weight of M. For 100g of MO, you calculated that you have 1.725 mol of oxygen. Given the chemical formula, how many moles of M do you have?
     
  4. Aug 12, 2018 #3
    My question is how to calculate the mole of M? because I don't know the molecular mass of M
     
  5. Aug 12, 2018 #4

    Ygggdrasil

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    What does the chemical formula MO tell you about the ratio of moles of oxygen to moles of M?
     
  6. Aug 12, 2018 #5
    If we break MO, we get 1 mole of O and 1 mole of O So O: M = 1:1
     
  7. Aug 12, 2018 #6

    Ygggdrasil

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    Correct Can you use that information along with what you have previously calculated to determine the molar mass of M?
     
  8. Aug 13, 2018 #7
    Yes molar mass of M = (100 -27.6) = 72.4g
    So, 1 mol of M weighs 72.4g
     
  9. Aug 13, 2018 #8
    By that reasoning, molar mass of O is 27.6. Try again.

    Here's a hint. With MO, you have 1 mol of M for EACH MOL of O. For your initial 100g of MO, how many mols of O do you have, how many mols of M do you have, what is the mass of that number of mols, and, therefore, what is the mass of a single mol of M?
     
    Last edited: Aug 13, 2018
  10. Aug 13, 2018 #9
    When O is 27.6%, in 100g MO, M = 1 mole = 72.4g and O = 1.725 mole = 27.6g
    when O is 30%, in 100g MO, M = 1 mole = 70g and O = 1.875 mole = 30g
    but how to calculate 'what is the mass of a single mol of M?'
     
  11. Aug 13, 2018 #10

    symbolipoint

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    I have not yet analyzed the arithmetic carefully.

    If you have TWO DIFFERENT metal oxides of the particular metal M, corresponding to two different percentages of oxygen element in the "molecule", then you should expect that one of your metal oxides may correspond to MO but the other will NOT be a one-to-one mole relationship between the Oxygen and the metal M.

    You are merely looking for a ratio for the second compound which does not use very small whole numbers, but slightly or more larger whole numbers.
     
  12. Aug 13, 2018 #11

    symbolipoint

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    Note, there are two compounds with M and O described. One is MO and the other is of unknown atom ratio of M and O. You found the correct moles oxygen of 100 g sample, for MO compound.

    0.276*100/15.9994=1.725 moles of Oxygen.

    This means, 1.725 moles M for 100 g of MO.
    How many grams of M?
    From 72.4 grams of the 100 g being M,
    72.4/1.725=41.971 grams per mole, M.

    You already know that 15.9994 grams per mole, O.

    You next want to find the mole ratio for the unknown M and O compound which is 30 % Oxygen; and is 70 % M. Consider a sample of 100 grams.
    Of this sample, 30 grams is Oxygen and 70 grams is M.
    How many moles of each?
    Can you then try to find a good whole number ratio for each element to match?

    My values found of each M and O:
    --
    70/41.971=1.667818 moles M
    --
    30/15.9994=1.87507 moles O
    --
    These raw values not yet as whole values for the compound, M1.667818O1.87507
    and you need to try to find a good equivalent of that which uses whole numbers.
     
    Last edited: Aug 13, 2018
  13. Aug 13, 2018 #12

    symbolipoint

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    Review post #11.
    I tried this as a way to find best whole number values:

    1. Divide both values by 1.667818
    2. Multiply both values by 8

    Finding something close to M8O9 .
     
  14. Aug 14, 2018 #13
    I don't understand the point above 'This means, 1.725 moles M for 100 g of MO.' Could you simplify it, please? As I know 1.725 mole of O weighs.276g, so, how did you get 1.725 moles of M? it should be 1 mole of M and 1 mole of M weighs 72.4g. Please explain it. I am confused.
     
  15. Aug 14, 2018 #14

    symbolipoint

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    I reemphasised that the compound MO, in regard to a.m.u.'s, has 1 a.m.u. of M and 1 a.m.u. of O.

    To say this a little differently, 1 mole of MO has 1 mole of M and 1 mole of O.
     
  16. Aug 14, 2018 #15

    symbolipoint

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    This is the key question to handle:
    You would arrange the rest after finding the formula weight for the element M.
     
  17. Aug 14, 2018 #16
    Ya, I understand it that 1 mole of MO has 1 mole of M and 1 mole of O. But still, I don't understand what you mean to say by ' 'This means, 1.725 moles M for 100 g of MO.' Could you simplify your point, please?
     
  18. Aug 14, 2018 #17

    Ygggdrasil

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    Perhaps we can try to rephrase the question.

    A 100 g sample contains an unknonwn number of moles of MO. The sample is 27.6% oxygen. How many moles of oxygen are present in the sample?

    Once you figure that out you then should be able to answer how many moles of MO are present in the sample and how many moles of M are present in the sample.
     
  19. Aug 14, 2018 #18
    You found that 100 grams of MO had 1.725 mol O. But by molecular formula, for each mol of O, you have one mol of M. Right? Formula of MO means one mol of each per molecule. Consider if you had started with 200 grams of MO instead of 100, and and found that you had 3.45 mol O instead of 1.725 mol. Would you expect that it must also have exactly 1 mol M? Molecular weight of M is fixed; as the mass of M changes, the number of mols must also change, and you must determine that number of mols based on the molecular weight.

    If you have 1.725 mol O, you must have, identically, 1.725 mol M. (Also, identically, 1.725 mol of MO).

    You also found that your 100 g MO contained 72.4 g M. Therefore, you have 1.725 mol M with a mass of 72.4 g; the gram-molecular weight is (72.4g/1.725 mol), or 41.971 g/g-mol.
     
    Last edited: Aug 14, 2018
  20. Aug 14, 2018 #19
    1.725 moles of O present in the sample. 1.725 moles of MO present in the solution. So 1.725 moles of M present in the sample
    1.275 M + 1.375 O2 = 1.275 MO
     
  21. Aug 14, 2018 #20
    I got it now.
    Now my new questions are
    1. 27.6g of O = how many atoms of O?
    2. 72.4g M = how many atoms of M?
     
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