An unknown hydrate of calcium nitrate,Ca(NO₃)2 • XH₂O,is heated to give 30.5% water.What is the water of crystallization (X)for the hydrate?

Question

Quizplus · Accepted Answer

To solve this problem, we need to use the concept of percent composition.

1. Assume that we have 100 g of the hydrate. 
2. According to the problem, when heated, the hydrate loses 30.5% of its weight as water. This means that 100 - 30.5 = 69.5 g of the original hydrate remains after heating. 
3. The remaining substance after heating is calcium nitrate, Ca(NO₃)2. We can calculate the molar mass of Ca(NO₃)2 as follows:

- M(Ca(NO₃)2) = 1 x M(Ca) + 2 x M(N) + 6 x M(O) 
- M(Ca(NO₃)2) = 1 x 40.08 g/mol + 2 x 14.01 g/mol + 6 x 16.00 g/mol 
- M(Ca(NO₃)2) = 164.08 g/mol

4. We know that the remaining substance (69.5 g) contains 164.08 g/mol of Ca(NO₃)2. Using this information, we can calculate the number of moles of Ca(NO₃)2:

- n(Ca(NO₃)2) = 69.5 g / 164.08 g/mol 
- n(Ca(NO₃)2) ≈ 0.423 moles

5. Finally, we can calculate the number of moles of water that were present in the original hydrate by subtracting the moles of Ca(NO₃)2 from the total moles of the hydrate:

- n(H₂O) = n(total hydrate) - n(Ca(NO₃)2) 
- n(H₂O) = X mol / 18.02 g/mol - 0.423 mol 
- n(H₂O) = (X - 9.61) / 18.02 mol

(Note: We used the molar mass of water, 18.02 g/mol, to convert from grams to moles.)

6. According to the problem, the hydrate contained X moles of water. We can set up an equation using the information we have calculated:

- X / (X + 1) = (X - 9.61) / 18.02 
- Solving for X gives X ≈ 4

Therefore, the water of crystallization (X) for the hydrate is 4. The correct choice is (C).

An Unknown Hydrate of Calcium Nitrate,Ca(NO₃)2 • XH₂O,is Heated to Give