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

Answer:

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

Explanation:

$Molarity=\frac{Moles}{Volume(L)}$

Molarity of the solution = 0.0366 M

Volume of the solution = 5.00 L

Moles of hydrated sodium carbonate = n

$0.0366 M=\frac{n}{5.00 L}$

$n=0.0366 M\times 5 mol=0.183 mol$

Mass of hydrated sodium carbonate = n= 52.2 g

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

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

$0.183 mol=\frac{52.2 g}{106 g/mol+x\times 18 g/mol}$

$106 g/mol+x\times 18 g/mol=\frac{52.2 g}{0.183 mol}$

Solving for x, we get:

x = 9.95 ≈ 10

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