A laboratory procedure calls for making 400.0 mL of a 1.1 M NaNO3 solution. What mass of NaNO3 (in g) do you need?

Molarity is a measure of the concentration of a solution and is expressed in moles of solute per liter of solution, abbreviated as M. When preparing a chemical solution, understanding molarity is crucial as it dictates the proportion of the solute in relation to the solvent. For instance, a 1.1 M solution of NaNO3 means that for every liter of solution, there are 1.1 moles of sodium nitrate.

To determine the amount of substance needed to prepare a particular molar solution, we start by identifying the desired concentration and volume. The molarity formula, which is the cornerstone of this process, is given by:
\[ \text{Molarity (M)} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \].
From there, we can manipulate this formula to solve for the quantity we are after, be it the number of moles, volume, or ultimately the mass of solute needed.

The mole is a fundamental unit in chemistry that quantifies the amount of a substance. When calculating moles, we use Avogadro's number (approximately \(6.022 \times 10^{23}\)), which represents the number of units—atoms, molecules, ions, or particles—in one mole of substance.

For solving problems involving molar solutions, it's critical to convert the given molarity and volume of the solution to moles. As seen in the step-by-step solution for the exercise, moles calculation is straightforward with the formula:
\[ \text{moles} = \text{molarity} \times \text{volume (in liters)} \].
Knowing the moles, we then use this amount along with the molar mass to find the mass of the solute required to create our solution. This conversion is particularly important for accurately measuring out reagents for a laboratory procedure or experiment.

Volume conversions are frequently necessary in chemistry to align with the standard units used in formulas. Since molarity is expressed in terms of liters, when volumes are provided in milliliters (mL), a conversion is needed. There are 1000 milliliters in a liter, which is a fixed ratio that simplifies the conversion process.

To convert milliliters to liters, we divide the milliliters by 1000 because:
\[ 1 \text{ L} = 1000 \text{ mL} \].
For instance, converting 400.0 mL of solution to liters would involve the following calculation:
\[ 400.0 \text{ mL} \div 1000 = 0.4 \text{ L} \].
This step is essential because all further calculations—involving molarity, for example—need to be done using liters to ensure accuracy and consistency.

Molar mass serves as a bridge between the microscopic scale of atoms and molecules and the macroscopic scale that we can measure in the lab. It is defined as the mass in grams of one mole of a given substance. By knowing the molar mass, we can convert between the number of moles of a substance and its mass in grams—a key step in preparing solutions.

The molar mass is found using the periodic table where the atomic mass of each element, given in atomic mass units (amu), is equivalent to the molar mass in grams per mole. For a compound like NaNO3, you would add the molar masses of its constituent elements: sodium (Na), nitrogen (N), and oxygen (O).
\[ \text{Molar mass of NaNO3} = (1 \times \text{Molar mass of Na}) + (1 \times \text{Molar mass of N}) + (3 \times \text{Molar mass of O}) \].
The result gives us the molar mass to use in our calculations for converting moles to grams when determining the amount we need to weigh to prepare the desired solution.