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Chapter 3: Problem 127

A hydrate of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) contains almost exactly \(50 \% \mathrm{H}_{2} \mathrm{O}\) by mass. What is the formula of this hydrate?

Short Answer

Expert verified
The formula of the sodium sulfite hydrate containing exactly 50% water by mass is \(\mathrm{Na}_{2} \mathrm{SO}_{3} \cdot 7 \mathrm{H}_{2} \mathrm{O}\).

Step by step solution

01

Calculate Molar Masses

Calculate the molar masses of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) and \( \mathrm{H}_{2} \mathrm{O}\). The molar mass of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) is \(2 * 23\)(Na) + \(32\)(S) + \(3 * 16\)(O) = 126 g/mol. The molar mass of water \( \mathrm{H}_{2} \mathrm{O}\) is \(2 * 1\)(H) + \(16\)(O) = 18 g/mol.
02

Compare the Ratios

As the mass percentage of water is exactly 50%, the mass ratio of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) to \( \mathrm{H}_{2} \mathrm{O}\) is 1:1. Therefore, they also have the same weight in grams. Let's take 126g of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) and 126g of \( \mathrm{H}_{2} \mathrm{O}\).
03

Calculate the Proportions

Convert mass into moles to find the ratio between \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) and \( \mathrm{H}_{2} \mathrm{O}\). The amount of \(\mathrm{Na}_{2} \mathrm{SO}_{3}\) and \( \mathrm{H}_{2} \mathrm{O}\) in moles is 126g / 126g/mol = 1 mol and 126g / 18g/mol = 7 mol respectively. Thus, the formula of the hydrate is \(\mathrm{Na}_{2} \mathrm{SO}_{3} \cdot 7 \mathrm{H}_{2} \mathrm{O}\).

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Most popular questions from this chapter

The food flavor enhancer monosodium glutamate (MSG) has the composition \(13.6 \%\) Na, \(35.5 \%\) C. \(4.8 \% \mathrm{H}, 8.3 \% \mathrm{N}, 37.8 \% \mathrm{O},\) by mass. What is the empirical formula of MSG?

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