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Chapter 3: Problem 107

A thoroughly dried 1.271 g sample of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is exposed to the atmosphere and found to gain \(0.387 \mathrm{g}\) in mass. What is the percent, by mass, of \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) in the resulting mixture of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and the decahydrate?

Short Answer

Expert verified
The percent, by mass, of \( \mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O} \) in the resulting mixture is approximately 76.68%.

Step by step solution

01

Calculate Mass of Hydrate

First calculate the mass of the resulting hydrate. To do this, add the mass of the anhydrous compound (\(1.271 \, g\)) to the gain in mass caused by the absorption of water (\(0.387 \, g\)).
02

Calculate Molecular Weight

Calculate the molar mass of anhydrous \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) and of \(\mathrm{H}_{2} \mathrm{O}\). The molar mass of \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) is approximately 142.04 g/mol and that of \(\mathrm{H}_{2} \mathrm{O}\) is approximately 18.015 g/mol. Therefore, the molar mass of the hydrate \(\mathrm{Na}_{2} \mathrm{SO}_{4} \cdot 10 \mathrm{H}_{2} \mathrm{O}\) is \(142.04 \, g/mol + 10 \times 18.015 \, g/mol = 322.19 \, g/mol\).
03

Calculate Mass Percentage

To find the mass percentage of the hydrate, divide the mass of the anhydrous compound by the mass of the hydrate and multiply by 100. The mass percentage of the hydrate is then \(\frac{1.271 \, g}{1.658 \, g} \times 100 = 76.68\%\).

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Most popular questions from this chapter

A \(1.562 \mathrm{g}\) sample of the alcohol \(\mathrm{CH}_{3} \mathrm{CHOHCH}_{2} \mathrm{CH}_{3}\) is burned in an excess of oxygen. What masses of \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\) should be obtained?

Write the condensed structural formulas for the organic compounds: (a) octane (b) heptanoic acid (c) 3-hexanol (d) 2 -chlorobutane

Name these compounds: (a) \(\mathrm{Ba}\left(\mathrm{NO}_{3}\right)_{2} ;\) (b) \(\mathrm{HNO}_{2}\); (c) \(\operatorname{Cr} \mathrm{O}_{2} ;\) (d) \(\mathrm{KIO}_{3} ;\) (e) \(\mathrm{LiCN} ;\) (f) \(\mathrm{KIO} ;\) (g) \(\mathrm{Fe}(\mathrm{OH})_{2}\) (h) \(\mathrm{Ca}\left(\mathrm{H}_{2} \mathrm{PO}_{4}\right)_{2} ;\) (i) \(\mathrm{H}_{3} \mathrm{PO}_{4} ;\) (j) \(\mathrm{NaHSO}_{4} ;\) (k) \(\mathrm{Na}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\); (l) \(\mathrm{NH}_{4} \mathrm{C}_{2} \mathrm{H}_{3} \mathrm{O}_{2} ;(\mathrm{m}) \mathrm{MgC}_{2} \mathrm{O}_{4} ;\) (n) \(\mathrm{Na}_{2} \mathrm{C}_{2} \mathrm{O}_{4}\)

Determine the mass percent \(\mathrm{H}_{2} \mathrm{O}\) in the hydrate \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O}\)

Name the following compounds and specify which ones are best described as ionic: (a) \(\mathrm{KNO}_{2} ;\) (b) \(\mathrm{Br} \mathrm{F}_{3}\) (c) \(\mathrm{S}_{2} \mathrm{Cl}_{2} ;\) (d) \(\mathrm{Mg}(\mathrm{ClO})_{2} ;\) (e) \(\mathrm{Cl}_{2} \mathrm{O}\)
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