Question

Calculate the moles and the mass of solute in each of the following solutions. (a) \(150.0 \mathrm{~mL}\) of \(0.245 \mathrm{MCl}_{2}\) (b) \(1450 \mathrm{~mL}\) of \(0.00187 M \mathrm{H}_{2} \mathrm{SO}_{4}\)

Short answer

(a) Moles of MCl2 = 0.03675 moles and Mass of MCl2 = 3.50g. (b) Moles of H2SO4 = 0.0027115 moles and Mass of H2SO4 = 0.26g.

Step-by-step solution

Calculate moles of MCl2

First, the volume of the solution needs to be converted from milliliters to liters since molarity is defined as moles/liter. Hence, 150 ml = 0.15 liters. Using the formula Moles = Molarity x Volume. So, moles of MCl2 = 0.245M x 0.15L = 0.03675 moles.

Calculate the mass of MCl2

The mass can be calculated by using the formula Mass = Moles x Molar mass. So, the mass of MCl2 = 0.03675 moles x 95.21 g/mol = 3.50g.

Calculate moles of H2SO4

Similar to step 1, first convert the volume from milliliters to liters: 1450 ml = 1.45 liters. Then use the formula Moles = Molarity x Volume. Moles of H2SO4 = 0.00187M x 1.45L = 0.0027115 moles.

Calculate the mass of H2SO4

Using the formula Mass = Moles x Molar mass. So, the mass of H2SO4 = 0.0027115 moles x 98.09 g/mol = 0.26g.

Key concepts

Understanding Solution Chemistry

Solution chemistry is an essential part of chemistry that deals with how substances, known as solutes, dissolve in solvents to form solutions. In this context, molarity plays a crucial role. Molarity is a way of expressing the concentration of a solution and is defined as the number of moles of solute per liter of solution.
Think of a solution as a mixture where its concentration tells you how much solute is present in a given volume of solvent. Whether it's mixing salt water or creating a medicinal compound, molarity helps determine the appropriate proportions.
When calculating molarity, it's important to ensure all measurements are in standard units, such as converting milliliters to liters when necessary. This helps in accurately determining how many moles of solute exist in your solution, aiding in various chemical calculations.

Exploring Moles and Mass

Moles and mass are foundational concepts in chemistry that connect measurements to the number of particles present in a substance. The mole is a unit of measurement that allows chemists to count atoms, molecules, or ions in a sample without handling astronomically small numbers. One mole equals Avogadro's number, which is approximately 6.022 x 10²³ particles.
Using the mole concept, you connect the quantity of substance to its mass via the molar mass, which is the mass of one mole of a substance expressed in grams per mole. To find the mass of a substance dissolved in a solution, use the formula:

• Mass = Moles × Molar Mass

For example, in solution examples like MCl₂ and H₂SO₄, knowing the molar mass allows us to convert moles of the substance directly into its mass using this formula.

Conversion of Units in Chemistry

Understanding conversion of units is crucial in chemistry because it ensures calculations are accurate and meaningful. Oftentimes, we're given quantities in inconvenient units or measures that don't directly fit into common chemical formulas.
In solution chemistry, for instance, converting milliliters to liters is typical. This is because molarity calculations require volumes to be in liters. Here's a simple way to handle such conversions: 1 milliliter (mL) is equal to 0.001 liters (L). Thus, to convert from mL to L, multiply the volume in mL by 0.001.
Practicing these conversions ensures that all variables align properly in equations like those used to find moles from molarity, which are based on volumes being expressed in liters. Consistent and correct unit conversion is key to mastering both basic and complex chemistry problems.