91Ó°ÊÓ

Molarity is a key concept in chemistry, representing the concentration of a solute in a solution. It’s expressed in moles of solute per liter of solution (mol/L or M). To calculate molarity, you need to know two main things: the number of moles of solute and the volume of the solution in liters.

For instance, in the example of preparing a potassium dichromate (\(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\)) solution, we had 89.3 grams of solute. The molar mass of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\) helps us calculate the number of moles:

• Potassium (K): 39.10 g/mol \(\times\) 2 = 78.20 g/mol
• Chromium (Cr): 51.9961 g/mol \(\times\) 2 = 103.9922 g/mol
• Oxygen (O): 15.999 g/mol \(\times\) 7 = 111.993 g/mol

Adding these up, we find a total molar mass of 294.1852 g/mol.

Converting grams to moles, you divide the mass by the molar mass. So, \(\frac{89.3 \, \text{g}}{294.1852 \, \text{g/mol}} = 0.3033 \, \text{moles}\).

Molarity is then found by dividing moles by the volume of the solution in liters, yielding a concentration of 0.3033 M for the stock solution.

The dilution formula is a handy tool when you need to prepare a solution of desired concentration from a more concentrated stock solution. It incorporates the concept of molarity and helps maintain the same amount of solute in different volumes of solution.

The formula \(M_1 \times V_1 = M_2 \times V_2\) relates the initial concentration and volume to the final concentration and volume. Here's what the terms mean:

• \(M_1\) is the molarity of the initial concentrated solution.
• \(V_1\) is the volume of the initial solution.
• \(M_2\) is the molarity of the diluted solution.
• \(V_2\) is the final volume of the diluted solution.

Using the dilution formula, you can solve for an unknown volume or molarity if the other three variables are known.

In our case, we wanted to create a 0.100 M solution from a 0.3033 M stock solution. Plugging into the formula, we found the needed volume \(V_1\) as follows:
\[V_1 = \frac{M_2 \times V_2}{M_1} = \frac{0.100 \times 1.00}{0.3033} = 0.3297 \, \text{L}\]
This calculation tells us that to make the desired 1.00 L of 0.100 M solution, 0.3297 L of the stock solution is needed. Converting to milliliters, we find \(329.7 \, \text{mL}\).

Molar mass is essential for converting between the mass of a compound and the number of moles. It is the mass of one mole of a substance, usually given in grams per mole (g/mol). Calculating molar mass involves adding up the atomic masses of all the atoms in a molecule.

For the compound potassium dichromate, \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\), you sum up the atomic masses for all the constituent atoms:

• Potassium (K): 39.10 g/mol. Since there are two potassium atoms, multiply by 2.
• Chromium (Cr): 51.9961 g/mol. With two chromium atoms, multiply by 2.
• Oxygen (O): 15.999 g/mol. With seven oxygen atoms, multiply by 7.

By calculating these, the total molar mass comes out to 294.1852 g/mol.

Knowing the molar mass allows chemists to convert between the mass of a substance to the amount in moles. This conversion is crucial for correctly calculating concentrations and for measuring out reactants in stoichiometry.