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Zorluk: ZorWater of Crystallization, Efflorescence, Deliquescence, and Hygroscopy

A sample of hydrated sodium trioxocarbonate(IV), Na2CO3xH2O\text{Na}_2\text{CO}_3 \cdot x\text{H}_2\text{O}, is heated strongly in a crucible until a constant mass is reached. If the salt loses 62.94%62.94\% of its initial mass as water vapor during heating, what is the integer value of xx?

[Relative atomic masses: Na=23\text{Na} = 23, C=12\text{C} = 12, O=16\text{O} = 16, H=1\text{H} = 1]

Cevap: 10

Cevap

The integer value of xx is 10.
Heating hydrated sodium trioxocarbonate(IV) drives off all water of crystallization as steam. Since 62.94%62.94\% of the total mass is lost, water accounts for 62.94%62.94\% of the molar mass of Na2CO3xH2O\text{Na}_2\text{CO}_3 \cdot x\text{H}_2\text{O}. Solving 18x106+18x=0.6294\frac{18x}{106 + 18x} = 0.6294 yields x=10x = 10, representing decahydrate crystals, Na2CO310H2O\text{Na}_2\text{CO}_3 \cdot 10\text{H}_2\text{O}.

Adım Adım Çözüm

1
Calculate the formula masses of the anhydrous salt Na2CO3\text{Na}_2\text{CO}_3 and water H2O\text{H}_2\text{O}.
Molar mass of Na2CO3=106 g/mol\text{Na}_2\text{CO}_3 = 106\text{ g/mol} and molar mass of H2O=18 g/mol\text{H}_2\text{O} = 18\text{ g/mol}.
Establishing the molar component masses is required to determine the percentage ratio of water of crystallization to the total mass of the hydrated salt.
2
Set up an algebraic ratio relating the mass of water lost to the total hydrated mass using the given percentage.
18x106+18x=0.6294\frac{18x}{106 + 18x} = 0.6294.
Heating to constant mass removes all water of crystallization, meaning the mass lost corresponds to the xH2Ox\text{H}_2\text{O} component of the hydrated crystal.
3
Solve the algebraic equation for xx.
x=10x = 10.
Isolating xx yields the exact stoichiometric coefficient of water molecules per mole of hydrated salt.

Anahtar Kavram

Quantitative determination of water of crystallization using percentage mass loss.
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