Question

Cobalt(II) chloride hexahydrate, \(\mathrm{CoCl}_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\), is often used as a humidity indicator. This is due to the fact that the hydrate is a deep magenta color while the anhydrous form is a pale blue. As the humidity level changes, the color changes as well. What is the mass percent water in cobalt(II) hexahydrate?

Short answer

The mass percent water in cobalt(II) chloride hexahydrate is 45.45%.

Step-by-step solution

Determine the molar mass of cobalt(II) chloride hexahydrate

First, compute the molar mass of \(\text{CoCl}_{2} \cdot 6 \text{H}_{2} \text{O}\). Find the atomic masses: Co = 58.93 g/mol, Cl = 35.45 g/mol, H = 1.01 g/mol, O = 16.00 g/mol. \(\text{Molar mass of} \ \text{CoCl}_{2} = 58.93 \ \text{g/mol} + 2 \times 35.45 \ \text{g/mol} = 129.83 \ \text{g/mol}\). The molar mass of \(\text{6} \ \text{H}_{2} \text{O} = 6 \times (2 \times 1.01 + 16.00) = 108.12 \ \text{g/mol}\).

Calculate the total molar mass

Add the molar masses calculated in Step 1 to obtain the molar mass of \(\text{CoCl}_{2} \cdot 6 \text{H}_{2} \text{O}\). \(\text{Total molar mass} = 129.83 \ \text{g/mol} + 108.12 \ \text{g/mol} = 237.95 \ \text{g/mol}\).

Compute the mass percent of water

Use the mass percent formula: \(\text{mass percent water} = \frac{(\text{mass of } \text{H}_{2} \text{O})}{\text{total molar mass}} \times 100\)\. \(\frac{108.12 \ \text{g/mol}}{237.95 \ \text{g/mol}} \times 100 = 45.45\%\).

Key concepts

Molar Mass

The molar mass of a compound is the weight of one mole of its molecules, expressed in grams per mole (g/mol). To calculate the molar mass, add up the atomic masses of all the atoms in the molecule. For example, in cobalt(II) chloride hexahydrate, \(\text{CoCl}_{2} \times 6 \text{H}_{2} \text{O}\), the molar mass is calculated by summing the masses of each element present in the molecule.
Let's break it down:
- Cobalt (Co): 58.93 g/mol
- Chlorine (Cl): 35.45 g/mol (but there's 2 chlorine atoms in \(\text{CoCl}_{2}\))
- Hydrogen (H): 1.01 g/mol
- Oxygen (O): 16.00 g/mol

So, the molar mass of \(\text{CoCl}_{2}\) is:
\(\text{58.93 g/mol (Co)} + 2 \times \text{35.45 g/mol (Cl)} = 129.83 \text{g/mol}}\)
And for 6 molecules of water (H₂O):
\(\text{6} \times (2 \times 1.01 \text{(H)} + 16.00 \text{(O)}) = 108.12 \text{g/mol}\)

Finally, add them together to get the molar mass of cobalt(II) chloride hexahydrate: \(129.83 + 108.12 = 237.95 \text{g/mol}\)

Hydrated Compounds

Hydrated compounds are chemicals that include water molecules within their crystalline structure. These water molecules are known as water of hydration. They play a significant role in the compound's properties and reactions.
When writing the chemical formula of a hydrated compound, the water molecules are typically shown after a dot. For instance, in \(\text{CoCl}_{2} \times 6 \text{H}_{2} \text{O}\), the '6 \(\text{H}_{2} \text{O}\)' indicates that there are six water molecules for every cobalt(II) chloride molecule. These attached water molecules can affect color, weight, and other chemical properties.
Hydrated compounds are often used in applications such as:

• Humidity indicators
• Desiccants (to keep environments dry)
• In various chemical reactions

Cobalt(II) Chloride Hexahydrate

Cobalt(II) chloride hexahydrate, \(\text{CoCl}_{2} \times 6 \text{H}_{2} \text{O}\), is an example of a hydrated compound. It's commonly used as a humidity indicator due to its observable color change.
- In its hydrated form, it appears deep magenta.
- When anhydrous (water is removed), it turns pale blue.
The dramatic color change helps in monitoring moisture levels. This makes it valuable in devices that detect humidity. This compound's distinctive color properties come from the water of hydration and the transition metal cobalt. Transition metals are known for having colored ions, especially when they form complexes with water.

In practical uses, such as commercial humidity indicators or chemical laboratories, this property aids in quickly determining moisture presence. Handling cobalt(II) chloride with care is necessary due to its toxic nature if ingested or inhaled.

Chemical Composition Analysis

Chemical composition analysis is the process of identifying and quantifying the elements or compounds within a sample. It is essential for understanding a substance's makeup.
When calculating the mass percent of a component in a compound, follow these steps:

• Determine the molar mass of the entire compound.
• Calculate the total mass of the component of interest (e.g., water in a hydrate).
• Use the mass percent formula.

The mass percent formula is:
\( \text{mass \, percent \, of \, component} = \frac{\text{mass \, of \, component}}{\text{total \, molar \, mass}} \times 100 \)

In our example with cobalt(II) chloride hexahydrate:
Total molar mass = 237.95 g/mol
Mass of water = 108.12 g/mol
Using the formula:
\( \frac{108.12}{237.95} \times 100 = 45.45\text{\text{%}} \)
So, the mass percent of water in cobalt(II) chloride hexahydrate is 45.45\text{\text{%}}. Understanding this helps in analyzing the compound's properties and potential uses.