1 mole of Cu(NO2)2.xH2O forms 1 mole of CuO. 7.26g of a hydrate, Cu (NO3)2.xH2O formed 2.4g copper (II) oxide.

Question

number of moles of CuO formed =_____

number of moles Cu (NO3)2.xH2O in 7.62g =_____

mass of 1 mole of Cu(NO3)2.xH2O =_____g

mass of 1 mole of Cu (NO3)2 is 188g

the value of x in this hydrate = _______

Answer 1

Hello, Chloe,

There are too many steps involved to fit all the details into this reply box, but I'll do my best to demonstrate the process.

We are told that one mole of the hydrate produced 1 mole of CuO. The balanced equation is for this is not given, which makes it a little more challenging. One is tempted to say the nitrate groups simply come off the copper and then the copper reacts with water to produce CuO. That's eventually true, but there are two heating steps involved: one to remove the water molecules and a second, hotter step, to form the CuO, which results in O₂ formation from the water. Luckily, we don't need the full balanced equation, if we make some assumptions. I'll use this unbalanced equation to illustrate that one mole of the copper nitrate produces one mole of CuO:

Cu(NO₃)₂ *xH₂O = CuO + 2HNO₃ + H₂O

We need the molar masses of CuO (79.5 g/mole), Cu(NO₃)₂ (187.5g/mole - not the hydrate) and H₂O (18g/mole).

To find moles of CuO, divide 2.4 grams by it's molar mass to get 0.030 moles (2 sig figs). That means we started with 0.030 moles of the hydrate, but more importantly, we also have 0.030 moles of just the Cu(NO₃)₂ molecule. Find the mass of this 0.030 mole by multiplying the moles times the molar mass of Cu(NO₃)₂ It's mass is 7.62 grams, so then it's molar mass is (7.62g)*(187,5g/mole), or 5.66 grams Cu(NO₃)₂.

The total mass of the hydrate minus the mass of Cu(NO₃)₂ is the mass of the water molecules attached to it. That is 1.60 grams. Divide by water's molar mass to find moles of water (1.60 g/18g/mole) = 0.089 moles H₂O in 0.030 moles of hydrate. We want a whole number ratio of these two (0.090/0.030) = 2.94, or 3, since we need a whole number.

The value of x in this problem is therefore 3.

I hope this helps,

Bob