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Chapter 3: Problem 22

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

Short Answer

Expert verified
After calculating the mass percent of water in the given compound using the equation and observations made in Step 4, write down the obtained value which indicates the mass percent of water in \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} . 9 \mathrm{H}_{2}\mathrm{O}\).

Step by step solution

01

- Find molar masses

First, look up the molar masses of all elements involved. Hydrogen (H) has a molar mass of 1.00794 g/mol, oxygen (O) is 15.9994 g/mol, nitrogen (N) is 14.00674 g/mol, chromium (Cr) is 51.9961 g/mol, and lastly, oxygen (O) is again 15.9994 g/mol. Keep in mind that Nitrate (NO3) has one nitrogen atom and three oxygen atoms.
02

- Calculate molar mass of the hydrate

Next, calculate the molar mass of the entire hydrate. The formula \(\mathrm{Cr}\left(\mathrm{NO}_{3}\right)_{3} . 9 \mathrm{H}_{2}\mathrm{O}\) includes 1 atom of chromium, 3 nitrate groups (each containing 1 nitrogen atom and 3 oxygen atoms), and 9 water molecules (each containing 2 hydrogen atoms and 1 oxygen atom). Thus, the molar mass of the entire compound is calculated as follows: \(1 * 51.9961 \, g/mol + 3 * (1 * 14.00674 \, g/mol + 3 * 15.9994 \, g/mol) + 9 * (2 * 1.00794 \, g/mol + 15.9994 \, g/mol)\).
03

- Calculate molar mass of the water in the hydrate

Now, calculate the molar mass of only the water part in the hydrate. As there are 9 water molecules in the compound, the molar mass of water only is \(9 * (2 * 1.00794 \, g/mol + 15.9994 \, g/mol)\).
04

- Determine mass percent of water

The mass percent of a component in a compound is the mass of that component divided by the total mass of the compound, all multiplied by 100%. Hence, mass percent of water in the compound is \(\frac{{molar \, mass \, of \, water}}{{total \, molar \, mass \, of \, hydrate}} * 100%\). Calculate this using the values determined in steps 2 and 3.

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Most popular questions from this chapter

The mineral spodumene has the empirical formula \(\mathrm{LiAlSi}_{2} \mathrm{O}_{6} .\) Given that the percentage of lithium- 6 atoms in naturally occuring lithium is \(7.40 \%,\) how many lithium- 6 atoms are present in a 518 g sample of spodumene?

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?

Explain each term as it applies to the element nitrogen. (a) atomic mass; (b) molecular mass; (c) molar mass.

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