Question

Determine the water of hydration for the following hydrates and write the chemical formula: (a) \(\mathrm{NiCl}_{2} \cdot \mathrm{XH}_{2} \mathrm{O}\) is found to contain \(21.7 \%\) water. (b) \(\mathrm{Sr}\left(\mathrm{NO}_{3}\right)_{2} \cdot \mathrm{XH}_{2} \mathrm{O}\) is found to contain \(33.8 \%\) water. (c) \(\mathrm{CrI}_{3} \cdot \mathrm{XH}_{2} \mathrm{O}\) is found to contain \(27.2 \%\) water. (d) \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2} \cdot \mathrm{XH}_{2} \mathrm{O}\) is found to contain \(30.5 \%\) water.

Short answer

(a) \( \mathrm{NiCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O} \); (b) \( \mathrm{Sr(NO}_{3})_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O} \); (c) \( \mathrm{CrI}_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O} \); (d) \( \mathrm{Ca(NO}_{3})_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O} \).

Step-by-step solution

Calculate Molar Mass of Anhydrous Salt

For each compound, calculate the molar mass of the anhydrous part. (a) For \( \mathrm{NiCl}_{2} \):- Nickel (Ni): 58.69 g/mol- Chlorine (Cl): 35.45 g/mol each, so \( 35.45 \times 2 \)Molar mass of \( \mathrm{NiCl}_{2} = 58.69 + 2 \times 35.45 = 129.59 \) g/mol.(b) For \( \mathrm{Sr(NO}_{3})_{2} \):- Strontium (Sr): 87.62 g/mol- Nitrogen (N): 14.01 g/mol each, Oxygen (O): 16.00 g/mol each (nitrate has 3 oxygen atoms), so \( 2 \times (14.01 + 3 \times 16.00) \)Molar mass of \( \mathrm{Sr(NO}_{3})_{2} = 87.62 + 2 \times (14.01 + 48.00) = 211.63 \) g/mol.(c) For \( \mathrm{CrI}_{3} \):- Chromium (Cr): 51.996 g/mol- Iodine (I): 126.90 g/mol each, so \( 126.90 \times 3 \)Molar mass of \( \mathrm{CrI}_{3} = 51.996 + 3 \times 126.90 = 432.70 \) g/mol.(d) For \( \mathrm{Ca(NO}_{3})_{2} \):- Calcium (Ca): 40.08 g/mol- Nitrogen (N) and Oxygen (O) as in (b):Molar mass of \( \mathrm{Ca(NO}_{3})_{2} = 40.08 + 2 \times (14.01 + 48.00) = 164.10 \) g/mol.

Calculate Mass of Water in 100g of Hydrate

Given the percentage of water, we can calculate the mass of water in 100 g of each hydrate.(a) Water mass in \( \mathrm{NiCl}_{2} \cdot \mathrm{XH}_{2} \mathrm{O} \) = 21.7 g.(b) Water mass in \( \mathrm{Sr(NO}_{3})_{2} \cdot \mathrm{XH}_{2} \mathrm{O} \) = 33.8 g.(c) Water mass in \( \mathrm{CrI}_{3} \cdot \mathrm{XH}_{2} \mathrm{O} \) = 27.2 g.(d) Water mass in \( \mathrm{Ca(NO}_{3})_{2} \cdot \mathrm{XH}_{2} \mathrm{O} \) = 30.5 g.

Calculate Mass of Anhydrous Salt in 100g of Hydrate

Subtract the mass of the water calculated in Step 2 from 100 g to find the mass of the anhydrous salt in each hydrate.(a) \( \mathrm{NiCl}_{2} \): 100 g - 21.7 g = 78.3 g.(b) \( \mathrm{Sr(NO}_{3})_{2} \): 100 g - 33.8 g = 66.2 g.(c) \( \mathrm{CrI}_{3} \): 100 g - 27.2 g = 72.8 g.(d) \( \mathrm{Ca(NO}_{3})_{2} \): 100 g - 30.5 g = 69.5 g.

Determine Moles of Anhydrous Salt and Water

Divide the mass of the anhydrous salt from Step 3 by its molar mass from Step 1 to find the moles of anhydrous salt, and divide the mass of water from Step 2 by the molar mass of water (18.02 g/mol).(a) \( \mathrm{NiCl}_{2} \): Moles of anhydrous salt = \( \frac{78.3}{129.59} \approx 0.604 \); Moles of water = \( \frac{21.7}{18.02} \approx 1.204 \).(b) \( \mathrm{Sr(NO}_{3})_{2} \): Moles of anhydrous salt = \( \frac{66.2}{211.63} \approx 0.313 \); Moles of water = \( \frac{33.8}{18.02} \approx 1.876 \).(c) \( \mathrm{CrI}_{3} \): Moles of anhydrous salt = \( \frac{72.8}{432.70} \approx 0.168 \); Moles of water = \( \frac{27.2}{18.02} \approx 1.510 \).(d) \( \mathrm{Ca(NO}_{3})_{2} \): Moles of anhydrous salt = \( \frac{69.5}{164.10} \approx 0.424 \); Moles of water = \( \frac{30.5}{18.02} \approx 1.693 \).

Calculate Water of Hydration

Divide the moles of water by the moles of anhydrous salt for each compound to find the number of moles of water per mole of salt, rounding to the nearest whole number.(a) \( \mathrm{NiCl}_{2} \): \( \frac{1.204}{0.604} \approx 2 \); hence, the formula is \( \mathrm{NiCl}_{2} \cdot 2 \mathrm{H}_{2} \mathrm{O} \).(b) \( \mathrm{Sr(NO}_{3})_{2} \): \( \frac{1.876}{0.313} \approx 6 \); hence, the formula is \( \mathrm{Sr(NO}_{3})_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O} \).(c) \( \mathrm{CrI}_{3} \): \( \frac{1.510}{0.168} \approx 9 \); hence, the formula is \( \mathrm{CrI}_{3} \cdot 9 \mathrm{H}_{2} \mathrm{O} \).(d) \( \mathrm{Ca(NO}_{3})_{2} \): \( \frac{1.693}{0.424} \approx 4 \); hence, the formula is \( \mathrm{Ca(NO}_{3})_{2} \cdot 4 \mathrm{H}_{2} \mathrm{O} \).

Key concepts

hydrates

Hydrates are fascinating compounds commonly encountered in chemistry. They consist of a salt and water molecules integrated into their crystal structure. These water molecules are called "water of hydration," and they are incorporated in fixed proportions relative to the salt.

For instance, if you see a chemical formula like \( \mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O} \), this means there are 5 water molecules for every \( \mathrm{CuSO}_4 \) unit. The "dot" connecting the two parts of the formula indicates they are part of the same crystalline matrix but distinct entities within it.

Hydrates are notable for several properties:

• **Color Change**: Many hydrates have characteristic colors. When they lose water (becoming anhydrous), their color can dramatically change.
• **Humidity Sensitivity**: Some hydrates can absorb or lose water depending on the humidity of their environment, showcasing their dynamic nature.
• **Applications**: Many industrial processes and laboratory techniques utilize specific hydrates for their reversible hydration and dehydration properties.

Understanding hydrates is crucial, as they are widely present in both natural and industrial contexts.

molar mass calculation

Calculating the molar mass of a compound is fundamental to understanding many aspects of chemistry. Molar mass is the mass of one mole of a given substance and is expressed in grams per mole (g/mol). Determining it requires knowing the atomic masses of the constituent elements.

Here's how you can calculate molar mass step by step:

• **Identify Each Element**: First, breakdown the compound's formula to list all its elements and how many atoms of each are present.
• **Atomic Mass**: Use a periodic table to find the atomic mass of each element. This mass reflects the average mass of one mole of atoms of that element.
• **Multiply and Sum**: Multiply the atomic mass of each element by the number of times the element appears in the compound, and add all these values together to get the total molar mass.

For example, in \( \mathrm{NiCl}_2 \), you'd find the atomic masses: Nickel (Ni) is 58.69 g/mol, and Chlorine (Cl), which appears twice, is 35.45 g/mol. Thus, the molar mass calculation would look like this: \( 58.69 + (2 \times 35.45) = 129.59 \) g/mol.

Efficient molar mass calculation is crucial for stoichiometry, reaction yields, and many other areas in chemistry.

chemical formula

A chemical formula is a concise way to represent the composition of a compound. It indicates the types and numbers of atoms present. Understanding chemical formulas is crucial for everything from predicting the behavior of molecules to synthesizing new ones.

Here are some tips for reading chemical formulas:

• **Atoms and Elements**: Each element in a chemical formula is represented by its chemical symbol, such as \(\mathrm{H}\) for hydrogen or \(\mathrm{O}\) for oxygen.
• **Subscripts**: These small numbers next to symbols indicate the number of atoms of an element in the molecule. For instance, in \(\mathrm{H}_2\mathrm{O}\), the subscript '2' tells us there are two hydrogen atoms.
• **Charges and States**: Sometimes, chemical formulas may include ionic charges or states, especially in formulas for ions or compounds in specific states of matter.

When it comes to hydrates, the formula also includes water molecules as a distinct part of the compound's structure. This is why formulas like \(\mathrm{Sr(NO}_3)_2 \cdot 6 \mathrm{H}_2\mathrm{O}\) are written, showing us that the hydrate consists of both the ionic compound and the water of hydration.

Successfully interpreting chemical formulas is essential for executing laboratory work, understanding chemical literature, and much more.