A hydrate of zinc chlorate, Zn(ClO3)2 .xH2O(s) contains 21.5% zinc by mass. Find the value of x.

Question

What I've done:
Molar mass of Zn: 65.409 g/mol
Molar mass of Cl: 2*35.453 =70.906 g/mol
Molar mass of O: 6*15.9994 =95.9964 g/mol
Total molar mass of Zn(ClO3)2: 232.3114 g/mol

21% of molar mass = 232.3114 g/mol
100% of mass = 1106.244762 g/mol

Molar mass of H2O: 18.01528 g/mol

232.3114 g/mol + 18.01528 g/mol = 250.32668 g/mol

250.32668 = 1106.244762
1106.244762 g/mol divided by 232.3114 g/mol
x = 4.419

But how can x be a decimal number? Would I have to multiply it?

Thanks in advance!

Answer 1

I'm not sure I understand what you did. Here is what I would do.
% anything = (g/total mass)*100 = ?
Atomic mass Zn = 65.4 from your post.
molar mass Zn(ClO3)2 from your post = 232.3
molar mass H2O = 18
The 21.5% Zn is (note you used 21%) percent Zn in the hydrate so
%Zn = [(65.4)/(232.3 + x*18)]*100 = 21.5%
Solve for x and I obtained 3.99 which rounds to 4.00. Let me know if you don't understand any part.

Answer 2

You would just round it down to 4 you are right

Answer 3

How is X equivalent to 4? After my calculation, I got a surprising
x=1677.03
This, of course, isn't right so can you show your steps as this is tricky for me and friends.

Answer 4

21.5%= 65.4 / (232.4 + x18) * 100%
0= 65.4 / (232.4 + x18) * 100%-21.5%
0= 65.4 / (232.4 + x18) * 78.5%
0= 65.4 / (232.4 + x18) * 0.785 - In this line, you first divide 65.4 by 232.4, but leave the remainder divided by x18.
0= 0.28 / x18 * 0.785
0= 0.28 * (0.785 * x18) - In this line, you multiply x18 to 0.28 / x18 and 0.785, which leaves 0.28 * (0.785 * x18).
0= 0.28 * x14.13 - In this line, I simplified 0.785 * x18.
x= 0.28 * 14.13- In this line, I got rid of the x and moved it to the other side of the equation.
x= 3.9
x=4
Therefore, Zn(ClO3)2 . 4H2O