Question

If \(10 . \mathrm{g}\) of \(\mathrm{AgNO}_{3}\) is available, what volume of \(0.25 \mathrm{MAgNO}_{3}\) solution can be prepared?

Short answer

The volume of \(0.25 M\) AgNO\(_3\) solution that can be prepared using \(10 g\) of AgNO\(_3\) is \(235.2 mL\).

Step-by-step solution

Find the molar mass of AgNO3

To find the number of moles of AgNO3, we first need to determine its molar mass. Molar mass of AgNO3 = Molar mass of Ag + Molar mass of N + 3 * Molar mass of O = 107.87 g/mol + 14.01 g/mol + 3 * 16.00 g/mol = 107.87 g/mol + 14.01 g/mol + 48.00 g/mol = 169.88 g/mol

Calculate the number of moles of AgNO3

Now we will find the number of moles of AgNO3 by dividing the given mass by its molar mass: Number of moles = (mass of AgNO3) / (molar mass of AgNO3) = (10 g) / (169.88 g/mol) = 0.0588 mol

Calculate the volume of the solution

Since we know the desired concentration and the number of moles of AgNO3, we can now calculate the volume of the solution prepared: Volume = (number of moles) / (concentration) = (0.0588 mol) / (0.25 M) = 0.2352 L To convert that to milliliters: Volume = 0.2352 L * 1000 mL/L = 235.2 mL So, the volume of the 0.25 M AgNO3 solution that can be prepared using 10 g of AgNO3 is 235.2 mL.

Key concepts

Molar Mass Calculation

Understanding how to calculate the molar mass of a compound is fundamental in chemistry. The molar mass is the mass of one mole of that substance, essentially the sum of the mass of each atom in a single molecule multiplied by the Avogadro's number, \(6.022 \times 10^{23}\) atoms, ions, or molecules.

Molar Mass of AgNO3

Let's break down the molar mass calculation as in the original exercise. AgNO3 comprises one silver (Ag) atom, one nitrogen (N) atom, and three oxygen (O) atoms. We sum the individual atomic masses, taken from the periodic table, to find the total molar mass of AgNO3: \(107.87 \, \text{g/mol} + 14.01 \, \text{g/mol} + 3 \times 16.00 \, \text{g/mol} = 169.88 \, \text{g/mol}\).
This value is pivotal for many calculations in chemistry, particularly in stoichiometry and solution concentration, because it is used to convert between grams and moles.

Moles Calculation

A mole is simply a unit to count a specific number of particles, atoms, molecules, ions, or other entities. In chemistry, moles bridge the gap between the microscopic world of atoms and the real world scales.

From Mass to Moles

To calculate the number of moles, divide the given mass by the molar mass: \(\text{moles} = \frac{\text{mass}}{\text{molar mass}}\). For the exercise, we take the 10 grams of AgNO3 and divide it by its molar mass (169.88 g/mol) to find 0.0588 moles.
Calculating moles allows us to determine how many particles we have, which is a crucial step for reacting them with other substances or diluting them to a certain concentration in solution.

Solution Concentration

Solution concentration is a measure of the amount of solute present in a given quantity of solvent or solution. It's a vital concept when preparing solutions in a lab setting.

Understanding Molarity

Molar concentration, or molarity, is defined as the number of moles of solute per liter of solution (mol/L). It is usually expressed as 'M.' In the context of the exercise, the goal is to prepare a 0.25 M solution of AgNO3. To find the volume for the available moles, the equation \(\text{Volume} = \frac{\text{moles}}{\text{concentration}}\) is used. With the calculated moles (0.0588 mol) the volume of the solution can be determined. This calculation is critical for accurately creating solutions with the desired chemical characteristics.

Stoichiometry

Stoichiometry is the study of quantitative relationships in chemical reactions. It uses the concept of moles and molar ratios from the balanced chemical equations to predict the amounts of reactants needed or products formed.

Applying Stoichiometry to Solutions

In the exercise, we use stoichiometry to create a solution with a particular concentration. The calculated number of moles, method for determining molar mass, and the intended concentration are all integrated to find the final volume of solution. Here, we connected the amount of AgNO3 (in moles) with the desired solution concentration to find how much solvent (typically water) is needed. This highlights stoichiometry's role in practical applications such as solution preparation, where precise ratios are essential for successful reactions and desired outcomes.