A metal M forms the sulphate M2(SO4)3 . A 0.596 gram sample of the sulphate reacts with excess BaCl2 to give 1.220 g BaSO4. What is the atomic weight of M?

(Atomic weights : S = 32, Ba = 137.3)

.....M2(SO4)3 + 3BaCl2 ==> 3BaSO4 + 2MCl3

.....0.596g.................1.220g

Convert 1.220g BaSO4 to mols. mol = g/molar mass = estimated 0.005
Convert to mols M2(SO4)3. That's estd 0.005 x (1 mol M2(SO4)3/3 mol BaSO4) = 0.005*1/3 = about 0.00174 but you need to sharpen the numbers.
Then mols = g/molar mass. You know mols and g, solve for molar mass. That's an estimated 342 and the 342 must be 2*M + 3*SO4. You know S and O, solve for M. I obtained approximately 27.

To find the atomic weight of M, we need to follow a few steps:

Step 1: Calculate the molar mass of BaSO4:
The molar mass of BaSO4 is equal to the sum of the atomic masses of its constituent elements:
Ba = 137.3 g/mol
S = 32 g/mol
O = 16 g/mol (since there are 4 oxygen atoms in BaSO4)

So, the molar mass of BaSO4 is:
(1 × Ba) + (1 × S) + (4 × O) = 137.3 + 32 + (4 × 16) = 233.3 g/mol

Step 2: Calculate the number of moles of BaSO4 formed:
We can use the equation:
moles = mass / molar mass

The mass of BaSO4 is given as 1.220 g, so the number of moles of BaSO4 is:
moles = 1.220 g / 233.3 g/mol = 0.00523 mol

Step 3: Determine the molar ratio between M2(SO4)3 and BaSO4:
From the balanced chemical equation of the reaction between M2(SO4)3 and BaCl2, we can see that the molar ratio between M2(SO4)3 and BaSO4 is 1:3.
This means that for every 1 mole of M2(SO4)3 that reacts, 3 moles of BaSO4 are formed.

Step 4: Calculate the moles of M2(SO4)3:
Since we know the moles of BaSO4, we can use the molar ratio to determine the moles of M2(SO4)3:
moles of M2(SO4)3 = moles of BaSO4 × (1 mole of M2(SO4)3 / 3 moles of BaSO4)
= 0.00523 mol × (1/3)
= 0.00174 mol

Step 5: Calculate the mass of M2(SO4)3:
The mass of M2(SO4)3 is given as 0.596 g, so the molar mass can be calculated using the equation:
molar mass = mass / moles

molar mass = 0.596 g / 0.00174 mol = 342.53 g/mol

Step 6: Determine the atomic weight of M:
The atomic weight of M is equal to the molar mass of M2(SO4)3 divided by the formula unit of M2(SO4)3.
From the formula M2(SO4)3, we can determine that the formula unit is 2 moles of M.

Therefore, the atomic weight of M is:
atomic weight of M = molar mass of M2(SO4)3 / formula unit of M2(SO4)3
= 342.53 g/mol / 2
= 171.27 g/mol

So, the atomic weight of M is 171.27 g/mol.

Nice question. Try to solve it by yourself. Not that difficult really. Go ahead.

It should be clear not understanding