Question

Now that Snape and Dumbledore has taught you the finer points of hydration calculations they have a slightly more challenging problem for you. Suppose you dissolve 52.2 g of Na2CO3 ∙ xH2O in enough water to make 5.00 L of solution. The final concentration of the solution was found to be 0.0366 M. Determine the integer x in the hydrate: Na2CO3 ∙ xH2O. Round your answer to the nearest integer.

Answer 1

The value of an integer x in the hydrate is 10.

Step-by-step explanation:

`Molarity=(Moles)/(Volume(L))`

Molarity of the solution = 0.0366 M

Volume of the solution = 5.00 L

Moles of hydrated sodium carbonate = n

`0.0366 M=(n)/(5.00 L)`

`n=0.0366 M* 5 mol=0.183 mol`

Mass of hydrated sodium carbonate = n= 52.2 g

Molar mass of hydrated sodium carbonate = 106 g/mol+x18 g/mol

`n=\frac{\text{mass of Compound}}{\text{molar mass of compound}}`

`0.183 mol=(52.2 g)/(106 g/mol+x* 18 g/mol)`

`106 g/mol+x* 18 g/mol=(52.2 g)/(0.183 mol)`

Solving for x, we get:

x = 9.95 ≈ 10

The value of an integer x in the hydrate is 10.