Question

Dumbledore decides to gives a surprise demonstration. He starts with a hydrate of Na2CO3 which has a mass of 4.31 g before heating. After he heats it he finds the mass of the anhydrous compound is found to be 3.22 g. He asks everyone in class to determine the integer x in the hydrate: Na2CO3·xH2O; you should do this also. Round your answer to the nearest integer.

Answer 1

Answer : The integer 'x' in the hydrate is, 2

Explanation : Given,

Mass of hydrate $Na_2CO_3$ = 4.31 g

Mass of anhydrous $Na_2CO_3$ = 3.22 g

First we have to calculate the mass of water.

Mass of water = Mass of hydrate $Na_2CO_3$ - Mass of anhydrous $Na_2CO_3$

Mass of water = 4.31 g - 3.22 g

Mass of water = 1.09 g

Now we have to calculate the moles of $H_2O$ and $Na_2CO_3$

$\text{Moles of }H_2O=\frac{\text{Mass of }H_2O}{\text{Molar mass of }H_2O}$

Molar mass of $H_2O$ = 18 g/mol

$\text{Moles of }H_2O=\frac{1.09g}{18g/mol}=0.0605mol$

and,

$\text{Moles of }Na_2CO_3=\frac{\text{Mass of }Na_2CO_3}{\text{Molar mass of }Na_2CO_3}$

Molar mass of $Na_2CO_3$ = 106 g/mol

$\text{Moles of }Na_2CO_3=\frac{3.22g}{106g/mol}=0.0303mol$

Now we have to calculate the ratio of $H_2O$ and $Na_2CO_3$

$\frac{H_2O}{Na_2CO_3}=\frac{0.0605mol}{0.0303mol}=1.99\approx 2$

The formula of compound is, $Na_2CO_3.xH_2O$

The value of 'x' is, 2

So, the formula of compound is, $Na_2CO_3.2H_2O$

Thus, the integer 'x' in the hydrate is, 2