a hydrated sulphate of a metal contained 8.1% of the metal and 43.2% of SO4 2- by weight . assuming the specific heat of the metal to be 0.242 ,determine the formula of hydrated sulphate
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You thus have 48.7/18.015 (=2.7033) moles of water.
You have 43.2/96.0576 (=.44973) moles of sulfate.
Note that since we know the number of moles of sulfate, we can predict the number of moles of metal present depending on its oxidation state (or charge) of the metal. If the metal is +1, then the 8.1 grams of metal will represent twice the moles of sulfate (which has a -2 charge). Since we know the mass and the numbers of moles present, we can calculate its atomic weight. We will do the same for charges of +2 (1:1 mole ratio) and +3 (2:3 mole ratio), and, if those don't work, we will go on to +4, +5, etc.
We will start with the easiest calculation:
If the metal is divalent (+2 charge), then you will have 0.44973 moles of the metal. That would give an atomic weight of 8.1 g/.44973 moles or 18. Hmmm... no such metal.
If the metal were monovalent (+1 charge) then you would have 2 x 0.44973 moles of metal. That gives an atomic weight of 9. Again, no such metal.
However, if the metal is trivalent (+3 charge), or, if you prefer, 2 metal atoms per three sulfate anions, then you would have an atomic weight of 8.1/(2*0.44973/3) or 27 g/mol. Bingo! Aluminum! (and by the way, we can check the +4 and +5 cations and none of those fit, but if this is an examination you probably will want to save the "what-if?" checking for later!)
You thus have 8.1/26.9815 (=.3002) moles aluminum.
The mole ratio of aluminum to sulfate to water is: .3002:.44973:2.7033
or: 1: 1.5: 9.
Multiply by 2 to get rid of the 1.5: 2: 3: 18
Formula: Al2(SO4)3*18H2O.
You have 43.2/96.0576 (=.44973) moles of sulfate.
Note that since we know the number of moles of sulfate, we can predict the number of moles of metal present depending on its oxidation state (or charge) of the metal. If the metal is +1, then the 8.1 grams of metal will represent twice the moles of sulfate (which has a -2 charge). Since we know the mass and the numbers of moles present, we can calculate its atomic weight. We will do the same for charges of +2 (1:1 mole ratio) and +3 (2:3 mole ratio), and, if those don't work, we will go on to +4, +5, etc.
We will start with the easiest calculation:
If the metal is divalent (+2 charge), then you will have 0.44973 moles of the metal. That would give an atomic weight of 8.1 g/.44973 moles or 18. Hmmm... no such metal.
If the metal were monovalent (+1 charge) then you would have 2 x 0.44973 moles of metal. That gives an atomic weight of 9. Again, no such metal.
However, if the metal is trivalent (+3 charge), or, if you prefer, 2 metal atoms per three sulfate anions, then you would have an atomic weight of 8.1/(2*0.44973/3) or 27 g/mol. Bingo! Aluminum! (and by the way, we can check the +4 and +5 cations and none of those fit, but if this is an examination you probably will want to save the "what-if?" checking for later!)
You thus have 8.1/26.9815 (=.3002) moles aluminum.
The mole ratio of aluminum to sulfate to water is: .3002:.44973:2.7033
or: 1: 1.5: 9.
Multiply by 2 to get rid of the 1.5: 2: 3: 18
Formula: Al2(SO4)3*18H2O.
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Answer:
molecular formula=M2(SO4)3. 18 H2O
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