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Chapter 3: Problem 72

Anhydrous sodium sulfate, \(\mathrm{Na}_{2} \mathrm{SO}_{4},\) absorbs water vapor and is converted to the decahydrate, \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O} .\) How much would the mass of \(24.05 \mathrm{g}\) of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) increase if converted completely to the decahydrate?

Short Answer

Expert verified
The mass of anhydrous sodium sulfate would increase by approximately 30.4 g if completely converted to the decahydrate.

Step by step solution

01

Calculate the Molar Masses

Start by calculating the molar mass of both anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and its decahydrate form \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\). The molar mass of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is approx. 142.04 g/mol, derived by adding the molar masses of: 2 Sodium atoms (2*23.0 g/mol), 1 Sulfur atom (32.1 g/mol), and 4 Oxygen atoms (4*16.0 g/mol). On the other hand, the molar mass of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) is approx. 322.20 g/mol, obtained by adding: molar mass of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (142.04 g/mol) and 10 times the molar mass of water (10*18.02 g/mol).
02

Calculate Moles of Anhydrous Sodium Sulfate

Next, calculate the number of moles of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) in the given 24.05g. This can be done using the formula: moles = mass / molar mass. Plug in the values to get: moles of \(\mathrm{Na}_{2} \mathrm{SO}_{4}=\) 24.05g / 142.04 g/mol = 0.169 mol.
03

Calculate Mass Increase

Using stoichiometry, the same number of moles of decahydrate will be formed from anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\). Therefore, calculate the mass of decahydrate produced using the formula: mass = moles * molar mass. Substitute the values to get: mass of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}=\) 0.169 mol * 322.20 g/mol = 54.45g. Finally, subtract the initial mass of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) from the final mass of the decahydrate to find the increase in mass. That is: 54.45g - 24.05g = 30.4g. So, the mass increases by 30.4g when all the anhydrous sodium sulfate is converted to the decahydrate.

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Most popular questions from this chapter

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