Question

For each of the following solutions, the mass of solute is given, followed by the total volume of the solution prepared. Calculate the molarity of each solution. a. \(3.51 \mathrm{~g} \mathrm{NaCl} ; 25 \mathrm{~mL}\) b. 3.51 g \(\mathrm{NaCl} ; 50 . \mathrm{mL}\) c. \(3.51 \mathrm{~g} \mathrm{NaCl} ; 75 \mathrm{~mL}\) d. \(3.51 \mathrm{~g} \mathrm{NaCl} ; 1.00 \mathrm{~L}\)

Short answer

The molarities of the given NaCl solutions are: a. 2.4 M b. 1.2 M c. 0.8 M d. 0.06 M

Step-by-step solution

Step 1. Calculate the moles of solute (NaCl)

In each solution, the mass of solute (NaCl) is given as 3.51 g. We need to find out the number of moles of NaCl in each solution. The molar mass of NaCl is approximately 58.44 g/mol, which we can calculate by adding the molar masses of sodium (Na) and chlorine (Cl). To calculate the moles, use the formula: Moles of solute (NaCl) = \(\frac{Mass of solute (NaCl)}{Molar mass of NaCl}\) Moles of NaCl = \(\frac{3.51 g}{58.44 g/mol}\) Moles of NaCl ≈ 0.06 mol

Step 2. Convert the volume of the solution from mL to L

The volumes given for each of the solutions are in milliliters (mL). We need to convert them to liters (L) to calculate the molarity, as the unit of molarity is moles per liter (moles/L). Conversion factor: 1 L = 1000 mL For each solution: a. Volume = \(25 mL \times \frac{1 L}{1000 mL} = 0.025 L\) b. Volume = \(50 mL \times \frac{1 L}{1000 mL} = 0.05 L\) c. Volume = \(75 mL \times \frac{1 L}{1000 mL} = 0.075 L\) d. Volume = 1.00 L

Step 3. Calculate the molarity of each solution

Molarity (M) = \(\frac{Moles of solute}{Volume of solution (L)}\) For each solution: a. \(M_a = \frac{0.06 mol}{0.025 L} = 2.4 M\) b. \(M_b = \frac{0.06 mol}{0.05 L} = 1.2 M\) c. \(M_c = \frac{0.06 mol}{0.075 L} = 0.8 M\) d. \(M_d = \frac{0.06 mol}{1.00 L} = 0.06 M\) Molarities of the given solutions are: a. 2.4 M b. 1.2 M c. 0.8 M d. 0.06 M

Key concepts

Solute Mass

Understanding the solute mass is fundamental when calculating molarity. The mass of a solute is the weight of the substance that is being dissolved in the solvent to create a solution. It is typically measured in grams (g) and is an integral part of the molarity calculation formula.

For instance, if you have 3.51 g of NaCl (table salt), this is the solute mass that will interact with the solvent to form a solution. It's crucial to measure this mass accurately since it directly affects the concentration of the final solution, which is expressed in molarity (moles of solute per liter of solution).

Solution Volume

The solution volume is the total space that the solution occupies, usually measured in liters (L) or milliliters (mL). For molarity calculations, we often need the volume in liters. Since in many practical situations volumes are measured in milliliters, you may need to convert from mL to L.

Remember that 1 liter is equivalent to 1000 milliliters. Hence, to convert milliliters to liters, you would divide the volume in milliliters by 1000. This conversion is essential for calculating molarity since molarity is defined as moles of solute per liter of solution.

Moles of Solute

The moles of solute in a solution represent the amount of substance present. One mole is 6.022 x 10^23 particles (Avogadro's number) of the substance.

To find the moles of solute, we use the formula:
\[\text{Moles of solute} = \frac{\text{Mass of solute (g)}}{\text{Molar mass of solute (g/mol)}}\]
Calculating the moles of solute is a critical step because molarity is based on how many moles of solute are in one liter of solution. An accurate count of moles is necessary to determine the exact concentration of the solution.

Molar Mass

Molar mass is the mass of one mole of a substance. It is the sum of the masses of all the atoms in a molecule and is expressed in grams per mole (g/mol).

For NaCl, for example, we calculate the molar mass by adding the atomic mass of sodium (Na) to the atomic mass of chlorine (Cl), giving us approximately 58.44 g/mol. This value is critical in converting the measured solute mass (in grams) into moles, a necessary step in molarity calculations.

It's essential to use the correct molar mass for the substance you're evaluating to ensure the precision of the calculation. Any discrepancy here can significantly alter the calculation's outcome.