Finding mole and mass fractions?

[cherrymilk]

Homework Statement

Ti-6Al-4V is a metal alloy used to make biomaterials. Its composition is 90% Ti; 6% Al and 4% V (mass percentages).

(a) What are the mass fractions of Ti, Al and V?

(b) What are the mole fractions of Ti, Al and V?

Homework Equations

Mass fraction = m/mtotal
Mole fraction = n/ntotal

The Attempt at a Solution

The first thing I did was find the molar mass of Ti-6Al-4V, which came out to be 413.527g. Then, using this information, I found the masses of Ti, Al and V using the following method:

Mass of Ti: (90%)(413.527) = 372.174g
Mass of Al: (6%)(413.527) = 24.812g
Mass of V: (4%)(413.527) = 16.541g

I then started to find the mass fractions by dividing the masses I had found by the molar mass like so:

Mass fraction of Ti: (327.174)/(413.527) = 0.9

I found the mass fractions of Al and of V in a similar fashion, getting 0.06 and 0.04 respectively.

My question is: was this the correct approach to the problem? When I started part (b), I realized that the 'mass fractions' I had found in part (a) used the equation n = m/M and that's why I'm a bit confused. Say that 0.9 is the number of moles of Ti, 0.06 is the number of moles of Al and 0.04 is the number of moles of V, that would yield a total number of 1, meaning that the mass and mole fractions would be equal, which doesn't make much sense to me.

Any help would be much appreciated!

 

[Borek]

First of all - there is no such thing as a molar mass of an alloy. You can calculate weighted average of the molar masses of elements involved, but it is not a molar mass.

If you have 100g of the alloy, how much of each element does it contain? Mass? Moles?

Interestingly, incorrect approaches sometimes accidentally lead to correct answers.

 

[cherrymilk]

Homework Statement

Ti-6Al-4V is a metal alloy used to make biomaterials. Its composition is 90% Ti; 6% Al and 4% V (mass percentages).

(a) What are the mass fractions of Ti, Al and V?

(b) What are the mole fractions of Ti, Al and V?

Homework Equations

Mass fraction = m/mtotal
Mole fraction = n/ntotal

The Attempt at a Solution

The first thing I did was find the molar mass of Ti-6Al-4V, which came out to be 413.527g. Then, using this information, I found the masses of Ti, Al and V using the following method:

Mass of Ti: (90%)(413.527) = 372.174g
Mass of Al: (6%)(413.527) = 24.812g
Mass of V: (4%)(413.527) = 16.541g

I then started to find the mass fractions by dividing the masses I had found by the molar mass like so:

Mass fraction of Ti: (327.174)/(413.527) = 0.9

I found the mass fractions of Al and of V in a similar fashion, getting 0.06 and 0.04 respectively.

My question is: was this the correct approach to the problem? When I started part (b), I realized that the 'mass fractions' I had found in part (a) used the equation n = m/M and that's why I'm a bit confused. Say that 0.9 is the number of moles of Ti, 0.06 is the number of moles of Al and 0.04 is the number of moles of V, that would yield a total number of 1, meaning that the mass and mole fractions would be equal, which doesn't make much sense to me.

Any help would be much appreciated!

So I think I've figured out what I was doing wrong. This time, I supposed that the compound was in 100g of water.

So, the mass fraction of Ti was 90/100 = 0.9
Mass fraction of Al = 6/100 = 0.6
Mass fraction of V = 4/100 = 0.4


So:

Number of moles of Ti = 90/413.52 = 0.22 moles
Number of moles of Al = 6/413.52 = 0.015 moles
Number of moles of V = 4/413.52 = 0.0097 moles

The total number of moles came out to be 0.24 moles.

With that calculated:

Mole fraction of Ti = 0.22/0.24 = 0.92
Mole fraction of Al = 0.015/0.24 = 0.063
Mole fraction of V = 0.0097/0.24 = 0.040

This seems more logical to me. Is this method correct?

Edit: Borek, I read your reply just as I posted mine! Thanks for the hint!

 

[Borek]

This time, I supposed that the compound was in 100g of water.

There is no compound (an alloy is not a compound) and there is no need for water.

What is the definition of the percentage composition?

How many grams/moles of Ti in 100 g sample of an alloy containing 90% of Ti?

 

[cherrymilk]

There is no compound (an alloy is not a compound) and there is no need for water.

What is the definition of the percentage composition?

How many grams/moles of Ti in 100 g sample of an alloy containing 90% of Ti?

So since I've been given mass percentages, I'm considering a 100g sample of Ti-6Al-4V. That wouldn't change the answer, though, would it?

Thank you for being patient with me - I've never taken a thing about alloys!

 

[Borek]

So since I've been given mass percentages, I'm considering a 100g sample of Ti-6Al-4V. That wouldn't change the answer, though, would it?

Your molar fractions are incorrect.

Please try to answer questions I posted twice. They should point you in the right direction.