Calculate the molar mass of the metal

  • Thread starter parwana
  • Start date
  • #1
182
0

Main Question or Discussion Point

A metal M reacts with phosphorus ( P4 ) to form a compound having the formula M3P.
13.30 g of the metal produce 16.81 g of the compound. Calculate the molar mass of the metal.


Enter a numeric answer only, no units.
 

Answers and Replies

  • #2
574
2
Have you tried the question? Please show us what you have done. I always approach these problems using unit analysis.
 
  • #3
182
0
I dont understand it, iam new to this, but dont i need the molas mass of one to find the molar mass of the other???? Also I need some grams of P4as well, please tell me how to do this, or i'll fail the exam.
 
  • #4
574
2
Start with the balanced equation:
[tex]12M+P_{4}\longrightarrow4M_{3}P[/tex]
Now unit analysis (remember that the equation expresses mole ratios between the reactants and products, not mass ratios):
[tex]x\frac{g}{mol}M=16.81gM_{3}P\times\frac{1molM_{3}P}{(3x+30.97)gM_{3}P}\times\frac{12molM}{4molM_{3}P}\times13.3gM[/tex]
Do you see how the units cancel to give me the ones I want for the answer? That's unit analysis. Usually, you don't have a variable on both sides of the equation, but in this case you do. That's not a problem; just isolate x, and that is your answer.

PS: normally I don't give away this much, but you have an exam. :smile:
 
Last edited:
  • #5
182
0
I got 45 g/mol, is it right?? This is just too confusing for me, I dont get it.
 
  • #6
182
0
please share the answer with me and show me step by step
 
  • #7
574
2
Because of the way the equation is set up, you need to use the quadratic formula here. You can simplify the equation, dropping the units, to
[tex]x=3(16.81)(13.3)\left(\frac{1}{3x+30.97}\right)[/tex]
which becomes the quadratic equation
[tex]3x^{2}+30.97x-670.719[/itex]
if my calculations are correct. Now apply the quadratic formula to find x.
 
Last edited:
  • #8
182
0
well what do u get please tell fast, i dont have a decent calculator.,
 
  • #9
182
0
ok i got 10.6g/mol and
 
  • #10
574
2
Correct. Do you understand the method?
 
  • #11
182
0
but its wrong, i plugged it in, and it said it was wrong
 
  • #12
chem_tr
Science Advisor
Gold Member
609
2
parwana said:
A metal M reacts with phosphorus ( P4 ) to form a compound having the formula M3P.
13.30 g of the metal produce 16.81 g of the compound. Calculate the molar mass of the metal.
Hello Parwana, Sirus has done much to help you, but maybe I can be of a little more help.

Let me consider that [tex]\displaystyle\frac{13.30}{M}[/tex] moles of metal is reacted with tetraphosphorus to give [tex]\displaystyle\frac{16.81}{3M+P}[/tex] moles of compound. Here, M and P denotes the molar masses of metal and phosphorus, respectively.

We also know that [tex]\displaystyle\frac{3*16.81}{3M+P}=\frac{13.30}{M}[/tex], as you understand from the reaction Sirus wrote. By taking 30.97 grams/mol for phosphorus, we get this:

[tex]\displaystyle\frac{50.43}{3M+30.97}=\frac{13.30}{M}[/tex]

where [tex]50.43M=39.90M+411.901[/tex]. You can find M here. I hope this is settled now.

Take care.
 
Last edited:
  • #13
182
0
thanks so much chem tr and sirus, i understand it much better now.
 
  • #14
574
2
I am curious as to why my method gave a different answer. From what chem_tr did, I get about 39 g/mol, but my method gave about 10.6 g/mol. What was I doing wrong?
 
  • #15
chem_tr
Science Advisor
Gold Member
609
2
Sirus said:
Start with the balanced equation:
[tex]12M+P_{4}\longrightarrow4M_{3}P[/tex]
Now unit analysis (remember that the equation expresses mole ratios between the reactants and products, not mass ratios):
[tex]x\frac{g}{mol}M=16.81gM_{3}P\times\frac{1molM_{3}P}{(3x+30.97)gM_{3}P}\times\frac{12molM}{4molM_{3}P}\times13.3gM[/tex]
I think the error is hidden in 12/4=3 ratio, as in the first fraction of your equation; I did the same error and corrected.
 
  • #16
574
2
Hmm. I now realize one error I made...I should not have multiplied by 13.3 g at the end to get proper units (not g*mol). Therefore the calculations should be as follows:

[tex]xmolM=16.81gM_{3}P\times\frac{1molM_{3}P }{(3x+30.97)gM_{3}P}\times\frac{12molM}{4molM_{3}P}}}[/tex]

To solve for x...

[tex]3x^{2}+30.97x-50.43[/tex]

[tex]x=1.430207329molM[/tex]

Now to find molar mass...

[tex]x\frac{g}{mol}M=\frac{13.30gM}{1.430207329molM}=9.29935103\frac{g}{mol}M[/tex]

Why am I getting a different answer than you? I'm not sure what error you are getting at regarding the 12/4=3 ratio.
 
  • #17
chem_tr
Science Advisor
Gold Member
609
2
It is very likely that there is something wrong with your setup. Please review the logic behind your formula.
 

Related Threads on Calculate the molar mass of the metal

Replies
3
Views
990
Replies
5
Views
8K
Replies
4
Views
2K
Replies
11
Views
10K
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
1
Views
684
Replies
2
Views
1K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
1
Views
3K
Top