[kriggy]

I was helping my GF with this and we cant figure it out. so:
From 50t or iron ore containing Fe2O3 and Fe3O4 is made 35,7t of Fe. How many tonnes of Fe₂O₃ and) Fe₃O₄ are in ore (their ratio)?

We are assuming that the ore contains no impurities and the process of smelting ore is has 100% yield.
So the book say that its 29t of Fe₃O₄ and 21t of Fe₂O₃.(which doesnt even make the amount of pure iron which is in the written in the task)
But I counted something totaly different, im not sure if Its correct:

mass fraction of Fe in  Fe₂O₃ is 0,6994, in Fe₃O₄ is 0,723
W1 is mass fraction of  Fe₂O₃ in 50t of ore, W2 is same for  Fe₃O₄

w1+w2=1   -> w1=1-w2
50*0,6994*w1 + 50*0,723*w2 = 35,7
34,97*(1-w2) + 36,15w2 = 35,7
36,15w2 - 34,97w2 = 35,7 - 34,97
1,18w2 = 0,73
w2=0,686

m( Fe₃O₄) = 0,686*50=30,93t
m( Fe₂O₃)= 50-30,93 = 19,067t

So did I counted right or made some mistake somewhere ? thanks

[magician4]

(which doesnt even make the amount of pure iron which is in the written in the task)

don't know what you've been calculating to reach this statement, but in my calculation I'll get ~ 35,67 t of pure iron from the named substances: close enough to 35,7 tons

asides from that: there is nothing wrong with the structure of your calculation, you did everything ok

the problem lies within the numbers and how you're forced to process them ( in computing it's called "numeric instability"), i.e. the degree of abbreviation in the decimals.

to put it into picture: the structure of the task asks you to calculate the weight of a captain, by once weighting his ship with him, and once without him.

  use more precise molecular weights (i.e. 3 decimals or more), more precise intermediary results (like 5 decimals or more) and see for yourself, how suddenly the distribution of tons inbetween the ores will change drastically  (esp. due to the division step involved)


regards

Ingo

[kriggy]

Thanks, I got something like 35,4 when I tried to use their result, gotta do it again, probably wanted to be too precise.