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.

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Alleei Alleei · Answer 1 · 2020-03-11T07:31:12+01:00

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

Explanation : Given,

Mass of hydrate [tex]Na_2CO_3[/tex] = 4.31 g

Mass of anhydrous [tex]Na_2CO_3[/tex] = 3.22 g

First we have to calculate the mass of water.

Mass of water = Mass of hydrate [tex]Na_2CO_3[/tex] - Mass of anhydrous [tex]Na_2CO_3[/tex]

Mass of water = 4.31 g - 3.22 g

Mass of water = 1.09 g

Now we have to calculate the moles of [tex]H_2O[/tex] and [tex]Na_2CO_3[/tex]

[tex]\text{Moles of }H_2O=\frac{\text{Mass of }H_2O}{\text{Molar mass of }H_2O}[/tex]

Molar mass of [tex]H_2O[/tex] = 18 g/mol

[tex]\text{Moles of }H_2O=\frac{1.09g}{18g/mol}=0.0605mol[/tex]

and,

[tex]\text{Moles of }Na_2CO_3=\frac{\text{Mass of }Na_2CO_3}{\text{Molar mass of }Na_2CO_3}[/tex]

Molar mass of [tex]Na_2CO_3[/tex] = 106 g/mol

[tex]\text{Moles of }Na_2CO_3=\frac{3.22g}{106g/mol}=0.0303mol[/tex]

Now we have to calculate the ratio of [tex]H_2O[/tex] and [tex]Na_2CO_3[/tex]

[tex]\frac{H_2O}{Na_2CO_3}=\frac{0.0605mol}{0.0303mol}=1.99\approx 2[/tex]

The formula of compound is, [tex]Na_2CO_3.xH_2O[/tex]

The value of 'x' is, 2

So, the formula of compound is, [tex]Na_2CO_3.2H_2O[/tex]

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