Question

The formula for hydrated copper(ii) nitrate is Cu(NO3)2.xH2O. It contains 36.5% water crystallization by mass.

What is the value of x?

[Ar= H: 1 ; N: 14; O: 16; Cu: 64]

A) 4
B) 5
C) 6
D) 7
​

Answer 1

6

Step-by-step explanation:

The percent mass is equal to the ratio between the mass of the component of interest and the total mass of the compound, multiplied by 100 % in case we need to express it as a percentage.

We may apply this knowledge to write the formula for copper(II) nitrate x-hydrate. Let's assume that we take 1 mole of the compound. Then we will divide x molar masses of water by the molar mass of the overall compound and multiply by 100 % to get the mass percent of water:

`\omega = (xM_(H_2O))/(M_(total))\cdot 100\%`

Here:

`M_(H_2O) = 18.016 g/mol`

`M_(total) = M_(Cu(NO_3)_2) + xM_(H_2O) = (187.56 + 18.016x) g/mol`

Substitute into the formula:

`(18.016x)/(187.56 + 18.016x) = 0.365`

Solve for x:

`18.016x = 0.365(187.56 + 18.016x)`

`18.016x = 68.46 + 6.58x`

`11.44x = 68.46\therefore x = 6`