Calculate the number of moles of solute in each of the following solutions: (a) \(1.5 \mathrm{~L}\) of \(1.20 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (b) \(25.0 \mathrm{~mL}\) of \(0.0015 \mathrm{M} \mathrm{BaCl}\) (c) \(125 \mathrm{~mL}\) of \(0.35 \mathrm{M} \mathrm{K}_{3} \mathrm{PO}_{4}\)

Molarity (M) is a measurement of the concentration of a solution. It tells you how many moles of solute are present in one liter of solution.

To calculate molarity, you need to know two things:

• The amount of solute (in moles).
• The volume of the solution (in liters).

Simplified, the formula for molarity is:
\[ M = \frac{n}{V} \]
where:

• \( M \) = molarity
• \( n \) = moles of solute
• \( V \) = volume of the solution in liters

Understanding molarity is essential for calculating the quantity of solute in a given solution, a common task in chemistry problems.

Volume conversion is often necessary in chemistry to ensure that the units match, especially when dealing with molarity, which requires volume in liters. Many times, volumes are given in milliliters (mL), which need to be converted to liters (L).

The conversion is straightforward: 1 liter = 1000 milliliters. Therefore, to convert from milliliters to liters, you divide by 1000.

• Example: Convert 25.0 mL to liters: 25.0 mL ÷ 1000 = 0.025 L
• Example: Convert 125 mL to liters: 125 mL ÷ 1000 = 0.125 L

Converting volumes accurately ensures that you can correctly apply formulas involving molarity, which is crucial for solving related problems.

Applying the formula to calculate the number of moles of solute in a solution is an important skill. The formula used is:

\[ n = M \times V \]
where:

• \( n \) = number of moles of solute
• \( M \) = molarity of the solution
• \( V \) = volume of the solution in liters

Let's look at the examples from the problem:

(a) For 1.5 L of 1.20 M H\(_2\)SO\(_4\):
\( n = 1.20 \times 1.5 = 1.80 \) moles of H\(_2\)SO\(_4\)

(b) For 25.0 mL of 0.0015 M BaCl:
First, convert 25.0 mL to liters: 25.0 mL ÷ 1000 = 0.025 L

Then, apply the formula:\( n = 0.0015 \times 0.025 = 0.0000375 \) moles of BaCl

(c) For 125 mL of 0.35 M K\(_3\)PO\(_4\):
First, convert 125 mL to liters: 125 mL ÷ 1000 = 0.125 L

Then, apply the formula:
\( n = 0.35 \times 0.125 = 0.04375 \) moles of K\(_3\)PO\(_4\)

By converting volumes to liters and using the correct formula, you can easily find the number of moles of a solute given the molarity and volume of the solution.