[theframes]

 Vanadium and Oxygen form a series of compounds that have the following compositions:

Mass % Vanadium: 

 76.10
 67.98
 61.42
 56.02

Mass % Oxygen:

23.90
32.02
38.58
43.98


What are the relative numbers of atoms of oxygen in the compounds for a given mass of vanadium?

I just haven't seen a solution worked out before, it would help me a lot if someone could just show me how to do this

thank you

[theframes]

please help, I'm sure that this is trivial for most of you

[renge ishyo]

The easiest way to do these mass percent questions is to assume you have 100 g of each substance. Then that means for the first example that you have 76.10 g of Vanadium and 23.90 g of Oxygen. Now you can use the molecular weights on the periodic table to convert the grams of each substance to moles of vanadium atoms and moles of oxygen atoms. In every mole of atoms there are 6.022x10²³ atoms so that's how you get the number of atoms of each.

[theframes]

let me try it...


I didn't know that you could assume an amount of substance.. but this should be okay because according to the law of proportions, the ratios will always be the same?

thanks

[theframes]

 I don't know how to proceed.. I have that 23.90 g of oxygen has 8.99556714375*10^23 number of moles.. then what?



thanks

[cth]

I don't know how to proceed.. I have that 23.90 g of oxygen has 8.99556714375*10^23 number of moles.. then what?

No, 8.99556714375*10²³ would be the number of oxygen atoms you have, because you multiplied by the Avogadro constant.
But, no need to carry such huge numbers! Moles exist so that you don't have to get into numbers with 10²³.


Let's take this problem backwards:
You are looking for compounds with the formula V_xO_y. So you need to determine the x and y numbers.
1 mole of V_xO_y contains x moles of vanadium and y moles of oxygen.
But, percentages you have are in mass, not in mole. So, just convert them into moles using the atomic weight of V and O. Then, it is just a percentage calculation.


Let's take an example:
Imagine you have a compound C₃₆O₃₂ with M_C=12 and M_O=16.
The 34 moles of carbon have a mass of m_C=36/12=3g.
The 32 moles of oxygen have a mass of m_O=32/16=2g.
Therefore the weight percentages are: %C=3/(3+2)=0.6=60%
                                                     %O=2/(3+2)=0.4=40%
Do you understand how it is calculated? 
Now, your problem is equivalent to: calculate the C_xO_y from %C=60% and %O=40%. You just need to revert back from mass to moles.

[theframes]

 thank you for your post.

 
 I see how you can do this now, but I'm not sure how you can convert the percentages into moles, could you show me please?

[theframes]

 I think I got the answer through another way.. the method seems right but the answer is not:

av = atomic mass of vanadium
ao = atomic mass of oxygen
mv = molar mass of vanadium
mo = molar mass of oxygen

 mass% of vanadium = av*mv / (av*mv + ao*mo)
 first question :

 0.7610 = 50.94*mv/(50.94*mv+16*mo)

 1/0.7610 =  (50.94*mv+16*mo) / 50.94*mv = 1 + (16*mo/50.94*mv)

mo/mv = (1/0.7610 - 1)* 50.94/16

which is equal to 1.. but it should be 2 :S

what is wrong? and I still need to look over that other method

thank you

[renge ishyo]

Imagine you have a compound C36O32 with MC=12 and MO=16.
The 34 moles of carbon have a mass of mC=36/12=3g.
The 32 moles of oxygen have a mass of mO=32/16=2g.

I think there was a calculation error made in here cth. 36 moles of carbon should not have a mass of 3g (it should be 36*12g = 432g of carbon). Other than that, the point of the argument seems right.

theframes, that last attempt was so painful I think I will break from tradition here and just work the first one out for you as a sample:

1. Convert mass percents into grams by assuming 100g of substance (you can always do this with mass percents to find the molar ratio regardless of what the "actual mass" of your sample is).

76.10% Vanadium = 76.10 g Vanadium

23.90% Oxygen = 23.90 g Oxygen

2. Next convert the grams of each substance into moles.

For Vanadium, 76.10 g * 50.9415 g/mol = 3876.6481 moles
For Oxygen, 23.90 g * 15.9994 g/mol = 382.38566 moles

3. Write this as a molecular formula.

V_3876.6481O_382.38566

4. Divide all the atoms by the lowest number to get the lowest molar ratio, and then round to the nearest whole number (if the rough answer was close to a whole number).

V_{3876.6481/382.38566}O_{382.38566/382.38566}

= V_10.14O₁ ~ V₁₀O

5. If in step 4 you have a formula where the answer is not near a whole number such as V_2.3O₁ then multiply by some constant to make it closer:

V_2.3*3O_1*3 = V_6.9O₃ ~ V₇O₃

[theframes]

 ah that looks great, thank you so much. the worked out example really helps.

could I ask you what was wrong with my attempt though? and the answer should be 2 :S how come it isn't 2 in your answer?
thanks a lot

EDIT: Ohhh is it because 1 molecule of oxygen has 2 oxygen atoms?

[cth]

I think I got the answer through another way.. the method seems right but the answer is not:

av = atomic mass of vanadium
ao = atomic mass of oxygen
mv = molar mass of vanadium
mo = molar mass of oxygen

 mass% of vanadium = av*mv / (av*mv + ao*mo)
 first question :

 0.7610 = 50.94*mv/(50.94*mv+16*mo)

 1/0.7610 =  (50.94*mv+16*mo) / 50.94*mv = 1 + (16*mo/50.94*mv)

mo/mv = (1/0.7610 - 1)* 50.94/16

which is equal to 1.. but it should be 2 :S

what is wrong? and I still need to look over that other method

thank you

There is nothing wrong with your result. The ratio is 1.

OK, let's try this same example a slightly different way:
%_mV=76.10, %_mO=23.90
Those percentages are in mass. So, we need to convert them to mole using atomic weights:
nV = 76.10/50.94 = 1.494 ~ 1.5
nO = 23.90/16 = 1.494 ~ 1.5
Now, you can write your compound formula: V_1.5O_1.5. It is nearly finished.
All you need now is to get the stoichiometric coefficients integer:
V_1.5O_1.5  V₁O₁
The ratio is 1, as you had found. 

[renge ishyo]

For Vanadium, 76.10 g * 50.9415 g/mol = 3876.6481 moles
For Oxygen, 23.90 g * 15.9994 g/mol = 382.38566 moles

What's humorous here is I had just told cth that he got the ratio upside down in his example and then I do the very same thing. Yay! I should have divided here, not multiplied.

[theframes]

thanks for the help guys, it really helped me