Calculations involving water of crystallization

 Hello everyone! Welcome to the month of August. Just like I announced yesterday, we are going to look at a couple of mathematical problems that involve water of crystallization of a salt. In all these problems, we can see that the hydrated salt is heated to produce the anhydrous salt.


Example 1;

Find x in the formula MgSO4.xH2O if 5.0 g of magnesium sulfate was dehydrated and 2.44 g remained.


Solution;

Molar mass of hydrated salt = 24 + 32 + 3(16) + x[2(1) + 16]

= 104 + 18x g/mol

Molar mass of anhydrous salt = 24 + 32 + 3(16)

= 104 g/mol


We know that;

Number of moles of hydrated salt = Number of moles of anhydrous salt

But number of moles = mass/molar mass

Number of moles of hydrated salt = 5 g/104 + 18x g/mol

Number of moles of anhydrous salt = 2.44 g/104

Hence;

5 /104 + 18x = 2.44/104

5 * 104 = 2.44(104 + 18x)

520 = 253.76 + 43.92x

X = 520 – 253.76/43.92

= 6

The formula of the hydrated salt is MgSO4.6H2O


Example 2;

A 0.970 g sample of a hydrated copper II salt, CuX2.6H2O was heated to give 0.538 g of the anhydrous salt. What is X?


Solution;

Molar mass of CuX2.6H2O = 63.5 + 2(x) + 6[2(1) + 16]

= 171.5 + 2x g/mol

Molar mass of the anhydrous salt = 63.5 + 2(x)

= 63.5 + 2x g/mol


Number of moles of hydrated salt = Number of moles of anhydrous salt

0.970/171.5 + 2x = 0.538/63.5 + 2x

0.970(63.5 + 2x) = 0.538(171.5 + 2x)

61.6 + 1.94x = 92.3 + 1.11x

Collect like terms;

61.6 – 92.3 = 1.11x – 1.94x

-30.7 = -0.83x

X = 37

X is an isotope of chlorine.

The formula of the salt is; CuCl2.6H2O


Self test problems;

1) Determine the value of X in the formula of washing soda crystals given the equation below;

Na2CO3.xH2O -> Na2CO3 + xH2O

28.6g                         10.6 g

2) A 46.1 g sample of hydrated potassium dichromate K2Cr2O7.xH2O was heated to give 35.3 g of anhydrous salt. What is the value of x?


You can solve the problems on a paper, snap the solution and attach the solution in the comments box.


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