Problem 12 - Chemistry An Atoms First Approach

Question

Which of the following must be known to calculate the molarity of a salt solution (there may be more than one answer)? a. the mass of salt added b. the molar mass of the salt c. the volume of water added d. the total volume of the solution Explain.

Step-by-Step Solution

Answer

To calculate the molarity of a salt solution, we must know the mass of salt added (a), the molar mass of the salt (b), and the total volume of the solution (d). Molarity can be determined using the formula: \( molarity = \frac{moles~of~solute}{volume~of~the~solution~in~liters}\), where the moles of solute can be calculated by dividing the mass of salt by its molar mass.

Step 1: Identify the mass of salt added and the molar mass of the salt

The mass of salt added to the solution (option a) and the molar mass of the salt (option b) are both required to calculate the moles of solute present. Make note of these values.

Step 2: Calculate moles of solute

Divide the mass of salt added by the molar mass of the salt to find the number of moles of solute. Use the following formula: moles of solute = (mass of salt added) / (molar mass of the salt)

Step 3: Identify the total volume of the solution

Option d states that we need the total volume of the solution. This is the final volume of the mixture of salt and water. Make note of this value.

Step 4: Convert the total volume of the solution to liters

If the volume of the solution is not already in liters, convert the volume to liters (1 L = 1000 mL).

Step 5: Calculate the molarity of the salt solution

Divide the moles of solute (from Step 2) by the volume of the solution in liters (from Step 4) to find the molarity of the salt solution. Use the following formula: molarity = (moles of solute) / (volume of the solution in liters) Hence, to calculate the molarity of a salt solution, we must know the mass of salt added (a), the molar mass of the salt (b), and the total volume of the solution (d).

Key Concepts

Molarity of a Solution

Molarity, often denoted by the symbol M, is a unit of concentration that exemplifies the number of moles of a solute per liter of solution. This measurement is a way to express the strength or concentration of a solution in a uniform way. To calculate molarity, one must simply divide the moles of solute by the volume of the solution in liters. The formula looks like this: \[\begin{equation}Molarity (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}\end{equation}\]Understanding molarity is crucial in fields such as chemistry and biology where solutions are regularly used in experiments and reactions.

For example, let's calculate the molarity of a solution where 58.5 grams of NaCl (table salt) is dissolved in enough water to make 1 liter of solution. Assuming the molar mass of NaCl is 58.45 g/mol, the calculation would entail determining the moles of NaCl using the mass and molar mass and then dividing it by the volume of the solution.

Molar Mass

Molar mass is the weight of one mole of a substance, usually expressed in grams per mole (g/mol). It corresponds to the atomic or molecular weight of a substance taken from the periodic table based on the number and type of atoms in a single molecule of the substance.

To find the molar mass of a compound, like salt (NaCl), simply add together the atomic masses of sodium (Na), around 22.99 g/mol, and chlorine (Cl), approximately 35.45 g/mol. This would give us:\[\begin{equation}Molar\;Mass\;of\;NaCl = 22.99\;g/mol\; + 35.45\;g/mol\; = 58.44\;g/mol\end{equation}\]Knowing the molar mass is essential when converting from the mass of a substance to the number of moles, which is a key step in calculating the molarity of a solution.

Moles of Solute

Moles of solute is a measure of the number of moles of a substance that is present in a given volume of solution. A mole represents Avogadro's number \(6.022 \times 10^{23}\) of entities, such as atoms, ions, or molecules. Calculating the moles of solute is essential for determining molarity and requires the mass of the solute and its molar mass.

Using the formula\[\begin{equation}Moles\;of\;solute = \frac{Mass\;of\;solute}{Molar\;mass\;of\;solute}\end{equation}\]we can establish the connection between the tangible mass of a substance and the theoretical concept of moles, which is pivotal for understanding chemical reactions and solution dynamics.

Solution Volume

Solution volume is the total space occupied by the solution, which includes both the solute and the solvent. It is typically measured in liters (L) or milliliters (mL), but for the purpose of calculating molarity, it is essential to use liters. To convert milliliters to liters, one simply divides the volume in milliliters by 1000, since 1 liter equals 1000 milliliters.

The formula for converting is:\[\begin{equation}Volume\;in\;liters = \frac{Volume\;in\;milliliters}{1000}\end{equation}\]Having the precise volume of the solution is crucial, as molarity is defined per liter of solution. Therefore, accurate volume measurements are integral to achieving correct molarity calculations.