A hydrate of zinc chlorate, Zn(ClO3)2 .xH2O(s) contains 21.5% zinc by mass. Find the value of x.
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!
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.
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
Well, it seems like you're getting close to finding the value of x, but you're right - it can't be a decimal number. Don't worry though, I'm here to help!
Since we can't have a fraction of a water molecule, we need to find a whole number for x. In this case, we can multiply all the numbers by a common factor to get rid of the decimals.
So let's multiply everything by 10 to get rid of the decimal points:
2323.114 g/mol + 180.1528 g/mol = 2503.2668 g/mol
2503.2668 = 11062.44762
11062.44762 g/mol divided by 2323.114 g/mol
x = 4
So the value of x is 4!
To find the value of x in the hydrate formula Zn(ClO3)2 · xH2O, you correctly calculated the molar mass of Zn(ClO3)2 as 232.3114 g/mol.
Next, you determined that the hydrate contains 21.5% zinc by mass. To convert this percentage to grams, you assumed a 100g sample. Therefore, 21.5% of 100g is 21.5g.
Since the molar mass of Zn is 65.409 g/mol, you can now calculate the number of moles of zinc in the 21.5g sample by dividing the mass by the molar mass:
Number of moles = mass / molar mass
= 21.5g / 65.409 g/mol
= 0.3289 mol (to four decimal places)
Now, you can use this information to determine the value of x. Remember that the molar ratio between Zn(ClO3)2 and H2O is 1: x. So, the number of moles of H2O is also 0.3289 mol.
The molar mass of H2O is 18.01528 g/mol, so you can determine the mass of H2O by multiplying the number of moles by the molar mass:
Mass of water = number of moles × molar mass
= 0.3289 mol × 18.01528 g/mol
= 5.91 g (to two decimal places)
Finally, you can calculate the value of x by dividing the mass of H2O by the molar mass of H2O:
x = mass of water / molar mass of water
= 5.91 g / 18.01528 g/mol
≈ 0.328 (to three decimal places)
Therefore, the value of x is approximately 0.328. Note that it is common to express this value as a fraction, so you could write it as x = 0.328/1.
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.