Problem 200 - Introductory Chemistry Atoms First

Question

What is the mass in grams of the nitrogen atoms in \(100.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}\) solution?

Step-by-Step Solution

Answer

The mass of nitrogen atoms in \(100.0 \mathrm{~mL}\) of \(1.00 \mathrm{M} \mathrm{Ca}(\mathrm{NO}_{3})_{2}\) solution is 2.802 grams.

Step 1: Calculate the moles of Ca(NO3)2

To calculate the number of moles of Ca(NO3)2 in solution, we will use the given molarity and volume of the solution: Moles of Ca(NO3)2 = Molarity × Volume Given, Molarity = 1.00 M Volume = 100.0 mL (Converted to liters, 0.100 L) Moles of Ca(NO3)2 = 1.00 M × 0.100 L = 0.100 mol

Step 2: Determine the moles of nitrogen atoms

In the formula for calcium nitrate, Ca(NO3)2, there are 2 nitrate (NO3) ions per formula unit. Since there is one nitrogen atom in each nitrate, this means there are 2 nitrogen atoms per formula unit of Ca(NO3)2. Therefore, the number of moles of nitrogen atoms will be twice the number of moles of Ca(NO3)2. Moles of nitrogen atoms = Moles of Ca(NO3)₂ × 2 Moles of nitrogen atoms = 0.100 mol × 2 = 0.200 mol

Step 3: Convert moles of nitrogen atoms into grams

Finally, to find the mass of nitrogen atoms in grams, we will use the molar mass of nitrogen and the number of moles calculated in step 2: Mass = Moles × Molar Mass Molar Mass of nitrogen = 14.01 g/mol (from the periodic table) Mass of nitrogen atoms = 0.200 mol × 14.01 g/mol = 2.802 g So, the mass of nitrogen atoms in 100.0 mL of 1.00 M Ca(NO3)2 solution is 2.802 grams.

Key Concepts

Molarity

Molarity is a fundamental concept in chemistry that helps us understand the concentration of a solution. It is defined as the number of moles of solute (the substance being dissolved) per liter of solution. The formula for molarity is given by:

• Molarity (M) = Moles of solute / Volume of solution in liters

In our exercise, we have a calcium nitrate solution with a molarity of 1.00 M. This indicates that there is 1 mole of calcium nitrate in every liter of this solution. To perform calculations involving solutions, converting volumes from milliliters to liters is essential, as molarity uses liters as the unit for volume. Once this conversion is done, we can easily calculate the number of moles of solute present in a given volume of solution.

Moles and Molar Mass

Understanding the relationship between moles and molar mass is crucial for performing stoichiometric calculations. A mole is a unit used to measure the amount of substance, similar to how we use dozens to measure quantities. One mole contains precisely Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\).

The molar mass is the mass of one mole of a substance and is expressed in grams per mole (g/mol). You can find the molar mass of an element by looking at the periodic table. For nitrogen, the molar mass is about 14.01 g/mol. In stoichiometry, understanding how to convert between moles and mass using the molar mass allows us to calculate the actual amount of a substance in grams.

Calcium Nitrate Solution

Calcium nitrate, with the formula \( ext{Ca(NO}_3 ext{)}_2\), is a compound consisting of calcium and nitrate ions. When dissolved in water, it dissociates to form calcium ions \( ext{Ca}^{2+}\) and nitrate ions \( ext{NO}_3^-\).

In the context of the exercise, knowing the composition of calcium nitrate helps us track the number of specific atoms, like nitrogen, within the solution. Each calcium nitrate molecule provides two nitrate ions, and therefore, two nitrogen atoms. By understanding this stoichiometric relationship, we can calculate specific amounts of atoms present in a solution, aiding in further computations like mass calculations.

Mass Conversion Calculations

Mass conversion calculations are a common task in chemistry, where we transform moles of a substance into mass in grams, or vice versa. These calculations are based on the molar mass of the element or compound involved.

• To calculate the mass, use the formula: Mass = Moles \(\times\) Molar Mass
• To find moles from mass, use: Moles = Mass / Molar Mass

In the given exercise, we initially found the number of moles of nitrogen atoms derived from our calcium nitrate solution. By using the molar mass of nitrogen, we multiplied this with the moles of nitrogen atoms to get their total mass in grams. Mastering these conversions is key for understanding how amounts of substances are related between moles and measurable quantities like grams.