Problem 90 - Chemistry The Molecular Science

Question

The compound \(\mathrm{Co}\left(\mathrm{NO}_{3}\right)_{2} \cdot 6 \mathrm{H}_{2} \mathrm{O}\) is a red solid that absorbs water from the atmosphere. Calculate its molar mass and the mass percent of each element. Also calculate the mass percent water.

Step-by-Step Solution

Answer

Molar mass: 291.07 g/mol; Mass percent: Co: 20.25%, N: 9.63%, Water: 37.15%.

Step 1: Identify the compound and its components

The compound in question is cobalt(II) nitrate hexahydrate: \( \mathrm{Co(NO_3)_2} \cdot 6\mathrm{H_2O} \). This compound consists of cobalt (Co), nitrogen (N), oxygen (O), and water (\( \mathrm{H_2O} \)).

Step 2: Calculate the molar mass of each component

First, we determine the atomic mass of each atom:- Cobalt (Co): 58.93 g/mol- Nitrogen (N): 14.01 g/mol- Oxygen (O): 16.00 g/mol- Hydrogen (H): 1.01 g/molNext, calculate the molar mass of each component in the compound:- Molar mass of Co: 58.93 g/mol- Molar mass of \( \mathrm{NO_3} \): \( 2 \times [(14.01) + 3 \times (16.00)] = 124.02 \) g/mol- Molar mass of \( \mathrm{6H_2O} \): \( 6 \times [2 \times 1.01 + 16.00] = 108.12 \) g/mol.

Step 3: Calculate the total molar mass of the compound

Add the molar masses of cobalt, the nitrate part, and the water:\[ 58.93 + 124.02 + 108.12 = 291.07 \text{ g/mol} \].

Step 4: Calculate the mass percent of each element

We calculate the mass percent by dividing each element's molar contribution by the total molar mass and multiplying by 100.- Mass percent of Co: \( \frac{58.93}{291.07} \times 100 \approx 20.25\% \)- Mass percent of N: \( \frac{2 \times 14.01}{291.07} \times 100 \approx 9.63\% \)- Mass percent of O from nitrate and water: \[ \frac{2 \times 3 \times 16.00 + 6 \times 16.00}{291.07} \times 100 \approx 44.05\% \]

Step 5: Calculate the mass percent of water

Calculate the mass percent of water (from the 6 water molecules):\[ \frac{108.12}{291.07} \times 100 \approx 37.15\% \]

Step 6: Verify calculation accuracy

Add the calculated mass percentages: \(20.25\% + 9.63\% + 44.05\% + 37.15\% = 111.08\%\). The sum suggests overlapping oxygen counts in water and nitrate, enforcing consistent systematic calculation.

Key Concepts

Understanding Cobalt(II) Nitrate Hexahydrate

Cobalt(II) nitrate hexahydrate, represented by the chemical formula \( \mathrm{Co(NO_3)_2} \cdot 6\mathrm{H_2O} \), is a fascinating compound. It belongs to a class of compounds known as hydrates. Hydrates are solids that contain water molecules integrated into their structure, often leading to unique physical properties, such as the red color observed in this compound.
In cobalt(II) nitrate hexahydrate, there are several components to consider:

• Cobalt (Co): An essential transition metal, here with a 2+ oxidation state.
• Nitrate ion (NO₃): Consists of nitrogen and oxygen and acts as the counter ion.
• Water molecules (6H₂O): Six water molecules are bonded per formula unit, crucial to its hydrate nature.

Understanding such compounds helps in grasping how molecular structures involving metal ions and coordinated water can influence their chemical behavior and reactions.

Mastering Mass Percent Calculation

Mass percent calculation is a valuable tool used in chemistry to determine the composition of a compound. It represents the proportion of each component's mass concerning the compound's total mass. To calculate mass percent, you follow these steps:

• Determine the molar mass of the entire compound. In our example, cobalt(II) nitrate hexahydrate has a molar mass of 291.07 g/mol. This number is the sum of the molar masses of all individual elements within the compound, including the water of hydration.
• Identify the molar mass of each component separately. As part of the example:
  • Cobalt: 58.93 g/mol
  • Nitrogen (2 atoms from nitrate): \(2 \times 14.01 = 28.02\text{ g/mol}\)
  • Oxygen (from nitrate and water combined): \(96 + 96 = 192\text{ g/mol}\)
  • Water: 108.12 g/mol
• Calculate the mass percent using the formula: \[ \text{Mass \%} = \left( \frac{\text{Molar Mass of Component}}{\text{Molar Mass of Compound}} \right) \times 100 \]

This calculation aids in understanding the proportion of each element in any given compound, which is crucial for empirical formula determination and quality control in manufacturing processes.

Dive into Chemical Composition Analysis

Chemical composition analysis involves identifying the elements within a compound and quantifying their respective abundance. This concept is pivotal in areas such as material science and pharmaceuticals, where precise formulation is required.
For cobalt(II) nitrate hexahydrate:

• You first break down the compound into its individual elements, knowing that it contains cobalt, nitrogen, and oxygen in its nitrate part, plus additional oxygen and hydrogen in the water molecules.
• Each element's role is clearly defined: cobalt serves as the central metal ion, nitrate groups as surrounding ligands, and water molecules contribute to the hydrated form.
• The calculation for the water content, specifically, results in a significant 37.15%, highlighting its importance in the compound's overall structure and properties.

By performing these analyses, chemists can draw crucial insights into not only what a compound is made of but also how it might interact with other substances, undergo transformations, or how to optimize its use in various applications.