# Calculate the molar mass of the metal

## 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.

Have you tried the question? Please show us what you have done. I always approach these problems using unit analysis.

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.

$$12M+P_{4}\longrightarrow4M_{3}P$$
Now unit analysis (remember that the equation expresses mole ratios between the reactants and products, not mass ratios):
$$x\frac{g}{mol}M=16.81gM_{3}P\times\frac{1molM_{3}P}{(3x+30.97)gM_{3}P}\times\frac{12molM}{4molM_{3}P}\times13.3gM$$
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. Last edited:
I got 45 g/mol, is it right?? This is just too confusing for me, I dont get it.

please share the answer with me and show me step by step

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
$$x=3(16.81)(13.3)\left(\frac{1}{3x+30.97}\right)$$
$$3x^{2}+30.97x-670.719[/itex] if my calculations are correct. Now apply the quadratic formula to find x. Last edited: well what do u get please tell fast, i dont have a decent calculator., ok i got 10.6g/mol and Correct. Do you understand the method? but its wrong, i plugged it in, and it said it was wrong chem_tr Science Advisor Gold Member parwana said: A metal M reacts with phosphorus ( P4 ) to form a compound having the formula M3P. 13.30 g of the metal produce 16.81 g of the compound. Calculate the molar mass of the metal. Hello Parwana, Sirus has done much to help you, but maybe I can be of a little more help. Let me consider that [tex]\displaystyle\frac{13.30}{M}$$ moles of metal is reacted with tetraphosphorus to give $$\displaystyle\frac{16.81}{3M+P}$$ moles of compound. Here, M and P denotes the molar masses of metal and phosphorus, respectively.

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

$$\displaystyle\frac{50.43}{3M+30.97}=\frac{13.30}{M}$$

where $$50.43M=39.90M+411.901$$. You can find M here. I hope this is settled now.

Take care.

Last edited:
thanks so much chem tr and sirus, i understand it much better now.

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?

chem_tr
Gold Member
Sirus said:
$$12M+P_{4}\longrightarrow4M_{3}P$$
Now unit analysis (remember that the equation expresses mole ratios between the reactants and products, not mass ratios):
$$x\frac{g}{mol}M=16.81gM_{3}P\times\frac{1molM_{3}P}{(3x+30.97)gM_{3}P}\times\frac{12molM}{4molM_{3}P}\times13.3gM$$
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.

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:

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

To solve for x...

$$3x^{2}+30.97x-50.43$$

$$x=1.430207329molM$$

Now to find molar mass...

$$x\frac{g}{mol}M=\frac{13.30gM}{1.430207329molM}=9.29935103\frac{g}{mol}M$$

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.

chem_tr