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how do i find the moles and molar mass of an unknown solid acid?

A lab team places .0250g of an unknown solid acid in an Erlenmeyer flask. They neutralize the solid acid with 15.0ml of .210 M Na(OH)(aq). One mole of the acid reacts with one mole of the base.
Calculate the molar mass of the unknown solid acid
Calculate the molar mass of the unknown acid.

Comments

Greetings!  You may take the .025g in 15ml, multiply by 66 to get a 1000ml equivalent => 1.65g, then multiply by 5x to get from .21M to 1.0M => about 8g:)

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5 Answers

The formula used for titrations ( see my answer to Brionna's question on  neutralizing H3PO4 with  NaOH ) has general application for complete reactions and can be used here . However, a direct chemical thinking is even simpler. 15 ml of a 0.21M  NaOH solution  contain 15X0.21 mEq ( milliequivalents, see referenced answer above) of NaOH and by definition require the same number of equivalents to react completely with the unknown compound( X ) . Therefore :     Eq (X) = 25/0.21 x 15  = 7.95g
  The equivalent of X is 7.94g and so is is the gram mole since X is monovalent.
 
    A compound with a mole of 7.94? The only possible answer is Lithium  hydride.
 
   LiH is not an acid but it reacts with water with formation of H2.
LiH +  HOH  = Li OH + H2
  NaOH does not  appear to be required in this reaction?
Maybe  Maria from Warrenville Il. can elucidate?
 
Regards.
  Ed C.
 
 

It is good to use the same beginning strategy for all practical problems.  

1. List all facts with proper units, labels and significant figures:
    0.0250 g unknown solid acid
    15.0 ml  NaOH
    0.210 M NaOH
    _____ g/mol unknown solid acid (molar mass is your mass per given moles)
    _____ g/mol unknown acid
    1 mole of acid = 1 mole of base (this does not mean they will be the same mass...only that there will
    be the same number of particles since 1 mole is 6.022x10^23 particles)

2. Relate the information--this part is the test to see if you understand the concept behind the math.
    M is mol/L since Molarity is Moles of solute/liter of solution
    ml can be converted to L
    g can be converted to moles given molar mass of the substance (need name and periodic table)
    1 mole of one will equal 1 mole of the other
    mol can be converted to g given molar mass of the substance

3. Convert units so they are all compatible for your final answer:
        Metric: KHD(base)dcm if you go from left to right on this prefix line,
        so does your decimal and vice versa.
   *ml to L (base)...the decimal should move 3 positions to the left.
     15.0 ml is 0.0150 L Acid (do not drop the last 0...it was measured and therefore, significant)
   *M to moles/L  No work here, just the ability to recognize this relationship.
     0.210 M is 0.210 mol/L NaOH
   *Since 1mole acid is neutralized by one mole of base, the 0.0250 g/MOLE of acid is completely
     neutralized by 15.0L  0.210 mol/L base or 0.0150L(0.210 mol/1L NaOH solution)= 0.00315 mol NaOH
   *Since there was 0.00315 moles Base, there were 0.00315 moles Acid based on the 1:1 ratio stated
   *By converting, you now know that 0.0250 g per 0.00315 moles acid or 0.0250g/0.00315mol or
     7.9365 g/mol  acid----> 7.94 g/mole acid (using 3 as the maximum number of significant figures)

When you divided out the 0.0250 g/0.00315 mol you were converting to ____g/1 mole, thus 7.94g/1mole is further understood to be 7.94g/mole acid the mass per one mole of a substance (molar mass)
                                                                                  
Logic:

If there is a 1:1 ratio of moles of acid and moles of base, then if I have the volume and molar mass of one and the mass of the other, I can convert to answer...

I could elaborate, but based on this question, you are probably far enough along in coursework to understand some of the underlying concepts.  If you are still troubled by those, I would be happy to elaborate...It is those seemingly unimportant details and definitions that may cause gaps in your learning :)

 

Original Question

  • A lab team places .0250g of an unknown solid acid in an Erlenmeyer flask. They neutralize the solid acid with 15.0ml of .210 M Na(OH)(aq). One mole of the acid reacts with one mole of the base.  Calculate the molar mass of the unknown solid acid

 

Answer using my 4 Step Process

Step 1: Find your givens (so you can turn a word problem into a simple list)

  • Mass Acid: 0.0250g
  • Volume Base: 15.0ml or 0.015L   (always put units into base units to avoid issues)
  • Molarity Base: .210 M Na(OH)

Step 2: Find where you're going (this gives you an idea of what formulas to use.

  • Asking for molar mass

Step 3: Find a formula (search for a formula that has your givens and goings in it)

  • molar mass= grams/mole

Step 4: Plug and Chug (use your formula or figure out what additional steps need to be done before you can use the formula)

  • molar mass acid =0.0250g/mole acid
  • We have grams but we don't have moles of acid so we need to do an additional step before we can finish using the formula we identified in step 3.
    • Thought process:
      • The question tells us its a 1:1 ratio of acid to base.  (Conceptually: 1 Acid + 1 Base --> Salt + Water).
      • Need to find how many moles of base we have.
    • To find moles of base, we're need to look at what we're given and see if there is a way to find moles of base.
      • Given: Volume Base: 15.0mL or 0.015L, Molarity Base: 0.210 M Na(OH)
      • Going: Moles of Base
      • Formula: Molarity = moles/Liter
      • Plug: 0.210M = moles/0.015L    
      • Answer: 0.00315 moles Base
    • Thought process: Now I know how many moles of base.  This must be the same number of moles of acid since the acid and base are in a 1:1 ratio.  Now I can solve by going back to step 4 above and plugging in 0.00315 moles.
      • molar mass acid =0.0250g/0.00315mol
      • ANSWER: molar mass acid = 7.936g/mol
      • On your game answer: molar mass acid: 7.94g/mol
        • Thought process: The givens each only had 3 significant figures, so your answer can only have 3 significant figures.

 

 

Hi.  Thanks for asking this question. Before answering, I have a tip that is helpful for chemistry classes as well as for professional jobs like nursing, medicine and engineering: To not lose the decimal point, put a zero in front of it:  

Here's the modified question and this suggestion will help prevent errors.

A lab team places... [0.0250g] ...of an unknown solid acid in an Erlenmeyer flask. They neutralize the solid acid with 15.0ml of [0.210 M Na(OH)(aq)]. One mole of the acid reacts with one mole of the base.

Calculate the molar mass of the unknown solid acid

Calculate the molar mass of the unknown acid."

Now, do you know all the words in the question?  Can you define them:

aq
aqueous
solid
Ehrlenmeyer flask
neutralize
acid
solid acid
mole
base
calculate
molar mass
M
mass
reacts

A lot of the answers in chemistry (and physics, for that matter) come from the definitions, so, lets look at a key definition: 

molar mass 

In chemistry, the molar mass is a physical property. It is defined as the mass of a given substance (chemical element or chemical compound) divided by its amount of substance....molar masses have units (in this case, grams/mole)... The molar mass of a compound is given by the sum of the standard atomic mass of the atoms which form the compound multiplied by the molar mass constant, Mµ:
[Example]
M(NaCl) = [22.989 769 28(2) + 35.453(2)] × 1 g/mol = 58.443(2) g/mol  [http://en.wikipedia.org/wiki/Molar_mass, accessed May 19, 2013]

You see from the definition you need to use g/mol to find your answers.
Now, what about that capital "M?"

molarity - M → moles per liter solution
        molality - m → moles per kilogram solvent

[http://chemistry.about.com/od/chemistryterminology/a/What-Is-The-Difference-Between-Molarity-And-Molality.htm, May 19, 2013]

From the above definitions, you can see tat a, "Concentration of  0.210 M,"tells you you have

(How many) ______ moles per liter, and

15.0ml of [0.210 M Na(OH)(aq)]. One mole of the acid reacts with one mole of the base.  [from the question],

 

which tells you, you've have (how many)_________ milliliters and which means you have (how many) ___"A"____ liters?  

The question further states,

One mole of the acid reacts with one mole of the base.

 

How can you use that information?  (Or can you?)  Aha!  It gives you a ratio.  What ratio?  How do you use it?  One mole of Na(OH) reacts with one mole of the acid, so the two are in a ______:_______ ratio. Therefore, if it is 1:1, or 2:1, or 3:1, or 1:3 you can figure out how many moles you have of each.  What ratio gives you the same number of moles of Na(OH) as you have moles of the acid?

You are given the number of moles of solute and the number of liters of solution and the ratio.

Calculate the number of moles of Na(OH).  Let's see...  

0.21 moles  = (x moles)      or   0.21moles (0.15 liter) = x moles   or  __________moles of NaOH
         liter       0.15 liter                                                 liter   

Hints... Cancel out the units and see if you get the right units for the answers.

            Don't forget "significant digits."

             What does, "aqueous," tell you and do you need to use this information in your calculations?

Can you figure out the empirical formula by calculating it from moles? There are 6.02 x 1023 amu (atomic mass units) in a gram of a substance. See Avogadro's number if you have questions on that. Do you need this information? Why or why not?

You now know that  ___ moles (the, "A," you calculated) of this acid weighs 0.025 grams (you got from the question), but you want to find the molar mass.

Define molar mass:

Definition: The mass of one mole of a substance, usually expressed in grams or kilograms.
Examples:
GMM O2 = 32.0 g or KMM O2 = 0.032 kg [http://chemistry.about.com/od/dictionariesglossaries/g/defmolmas.htm, accessed May 19, 2013]

So, set up a proportion paying attention to units.

    x___g_ = 1 mole                ,    so, x =  _____________  grams, which is the molar mass of the acid. 
  0.025g      0.00315 mole, 

 

Once you have answered the assigned question, you might also want to compare and contrast M with m for your own learning enhancement.  This further study will help you lock what you have learned into your brain so you remember it for tests and for your job.

The molecular mass (m) is the mass of a given molecule: it is measured in [atomic mass unit]]s (u) or daltons (Da), where 1 u = 1 Da = 1.660 538 782(83)×10−27 kg).[6][7] Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The molar mass is a measure of the average molecular mass of all the molecules in a sample, and is usually the more appropriate measure when dealing with macroscopic (weighable) quantities of a substance. [http://en.wikipedia.org/wiki/Molar_mass#Molar_masses_of_compounds, accessed May 19, 2013]

 

Review all the definitions and double check your answers.  Try some similar problems and see if you can get them.  Have fun with it.  Play with the numbers and the units.  Try different ratios.  Let me know how it works for you to use definitions and units in problem solving.  Oh, and practice your times tables.

Note:  If the doctors and nurses working with my grandfather had known that tip, he wouldn't have received a lethal dose of his medicine by mistake.  He was given medicine a factor of 10 times too strong. So, don't think that the details on this question don't matter, they do.  You can prevent medicine errors and other errors.  In so doing, you will save lives.

Start by calculating the number of moles of Na(OH) that you have. You've got a concentration of .210 M, meaning .21 moles per liter, and you've got 15 mL (.015 L). Solve the equation: .21 mol/1 L = x mol/.015 L, and you get .00315 mole of Na(OH). The problem states that each mole of Na(OH) reacts with one mole of the acid, so the two are in a 1:1 ratio. Therefore, you also have .00315 mole of the acid.

You now know that .00315 mole of this acid weighs .025 gram, but you want to find the molar mass, or the mass for one mole. So, set up another proportion: x/.025 g = 1 mol/.00315 mol, and you find that x = 7.94 grams, which is the molar mass of the acid.

Comments

The whole strategy is to frame things at 1.0M, 1000 ml volume.

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