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Molarity is a fundamental concept in chemistry that describes the concentration of a solute in a solution. It's expressed as the number of moles of solute per liter of solution (mol/L). Understanding molarity is crucial when preparing solutions since it directly affects the reactions and properties of the solution.
To calculate molarity, use the formula:

• \( \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \)

For instance, if you need to prepare a 1.50 L solution with a molarity of 0.110 M of \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\), start by determining the moles of solute required by multiplying the desired molarity by the volume in liters. In this case: \(1.50 \, \text{L} \times 0.110 \, \mathrm{M} = 0.165 \, \text{mol}\).

• Next, calculate the molar mass of the solute to find out how much of the solid you need. For \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\), the molar mass is 132.14 g/mol.
• This means you need 0.165 mol \(\times\) 132.14 g/mol = 21.8 g of \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\) to achieve the desired concentration.

Finally, dissolve this amount of the solute in enough water to make up the total volume of the solution, which is 1.50 L in this example.

Mass percent is a way to express the concentration of a solution. It indicates how many grams of solute are present per 100 grams of solution. This can be particularly helpful in industrial and laboratory settings where precise measurements are crucial.
Calculate mass percent using the formula:

• \( \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{mass of solution}} \right) \times 100 \% \)

For example, if you need to prepare 1.20 L of a solution that is 15.0% \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) by mass, you'll need the total mass of the solution. Knowing the density of the solution (1.16 g/mL), you can calculate the total mass by multiplying the volume by the density.

• Total mass = 1.20 L \(\times\) 1000 mL/L \(\times\) 1.16 g/mL = 1392 g.
• With a 15.0% mass percentage, the mass of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) needed is 0.15 \(\times\) 1392 g = 208.8 g.

Dissolve this amount of \(\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}\) in water to make up the total volume of 1.20 L.

Neutralization reactions occur when an acid and a base react to form water and a salt. These reactions are important in a variety of fields, including chemistry and biology, as they can be applied in titration and chemical synthesis.
The balanced chemical equation for a neutralization reaction that involves hydrochloric acid and barium hydroxide is:

• \(\mathrm{Ba}(\mathrm{OH})_{2} + 2 \mathrm{HCl} \rightarrow \mathrm{BaCl}_{2} + 2 \mathrm{H}_{2}\text{O}\)

To neutralize 5.5 g of \(\mathrm{Ba}(\mathrm{OH})_{2}\), calculate its moles using the molar mass (171.35 g/mol). The moles of \(\mathrm{Ba}(\mathrm{OH})_{2}\) are given by: 5.5 g \(\div\) 171.35 g/mol = 0.0321 mol.

• Since the stoichiometry of the reaction requires two moles of HCl for every mole of \(\mathrm{Ba}(\mathrm{OH})_{2}\), you will need 2 \(\times\) 0.0321 mol = 0.0642 mol of HCl.
• Using a 0.50 M solution, determine the volume needed: 0.0642 mol \(\div\) 0.50 M = 0.128 L. This is equivalent to 128 mL of the 0.50 M solution.

Prepare this 128 mL by diluting a more concentrated 6.0 M HCl solution to achieve the desired molarity.