Question

Cobalt (II) nitrate (Co(NO3)2) exists as a hydrate with the composition of 37.1% water and 62.9% cobalt nitrate by mass. Determine the molecular formula for this hydrate.

Answer 1

Co(NO₃)₂·6H₂O

Step-by-step explanation:

Assume that you have 100 g of the hydrate.

Then you have 62.9 g Co(NO₃)₂ and 37.1 g H₂O.

1. You will need a chemical equation with masses and molar masses, so let’s gather all the information in one place.

`M_(r)`: 182.94 18.02

Co(NO₃)₂·xH₂O ⟶ Co(NO₃)₂ + xH₂O

Mass/g: 62.9 37.1

2. Use the molar masses of each compound to calculate its number of moles.

`\text{Moles of Co(NO}_(3))_(2) = \text{62.9 g} * \frac{\text{1 mol} }{\text{182.94 g}} = \text{0.3438 mol}`

`\text{Moles of H}_(2)\text{O} = \text{37.1 g} * \frac{\text{1 mol} }{\text{18.02 g}} = \text{ 2.059 mol}`

3. Calculate the molar ratio of the two products.

Divide each number by the smaller number of moles (0.3438 mol).

`\text{Moles of Co(NO}_(3))_(2):\text{Moles of H}_(2)\text{O} = \frac{\text{0.3438 mol}}{\text{0.3438 mol}}:\frac{\text{2.059 mol}}{\text{0.3438 mol}} = 1: 5.988`

4. Round off each number to the closest integer.

`\text{Moles of Co(NO}_(3))_(2):\text{Moles of H}_(2)\text{O} \approx 1:6`

1 mol of Co(NO₃)₂ combines with 6 mol H₂O, so x = 6.

The formula of the hydrate is Co(NO₃)₂·6H₂O.