Question

Calculate what volume of the following solutions is required to obtain \(0.250 \mathrm{~mol}\) of each solute. (a) \(1.50 \mathrm{M} \mathrm{H}_{2} \mathrm{SO}_{4}\) (b) \(0.750 \mathrm{M} \mathrm{NaCl}\)

Short answer

The volumes of the solutions required to obtain 0.250 mol of solute are 0.167 liters of 1.50 M \( \mathrm{H}_2\mathrm{SO}_4 \) and 0.333 liters of 0.750 M \( \mathrm{NaCl} \).

Step-by-step solution

Understand the Problem

We need to find the volume (in liters) of two solutions required to obtain 0.250 mol of each solute. The solutions have different molarities.

Formula Setup

The formula used for this problem is the molarity formula, rearranged to solve for `V (volume, in litres)`: Volume (V) = moles of solute / molarity (M). We will apply this formula to each part of the problem.

Solve part (a) for \( \mathrm{H}_2\mathrm{SO}_4 \)

We need to find the volume of a solution with a molarity of 1.50 M that will contain 0.250 mol of \( \mathrm{H}_2\mathrm{SO}_4 \). Using the formula, we get: Volume (V) = 0.250 mol / 1.50 M = 0.167 liters.

Solve part (b) for \( \mathrm{NaCl} \)

We need to find the volume of a solution with a molarity of 0.750 M that will contain 0.250 mol of \( \mathrm{NaCl} \). Using the formula, we get: Volume (V) = 0.250 mol / 0.750 M = 0.333 liters.

Key concepts

Molar Solutions

Understanding molar solutions is a fundamental aspect of chemistry that involves the concentration of a solute within a given volume of solvent. Molarity, symbolized by 'M', is a measure of concentration that represents the number of moles of a solute per liter of solution. To express it mathematically, the molarity formula is:
\[ M = \frac{{\text{{moles of solute}}}}{{\text{{volume of solution in liters}}}} \]
When working with molar solutions, it's important to be familiar with the concept of the mole, which is a standard unit of measurement in chemistry. One mole corresponds to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) entities (atoms, ions, or molecules), similar to how a dozen represents 12 items.
For example, to make a 1 M solution of sodium chloride (NaCl), one would dissolve 1 mole of NaCl in enough water to make 1 liter of solution. When solving problems involving molar solutions, it's crucial to use this relationship between moles, volume, and molarity to determine the unknown quantity based on the information provided.

Chemistry Problem Solving

Chemistry problem solving often involves a step-by-step approach where understanding the question is the first and most critical step. Once the objective is clear—to find the volume required to obtain a certain amount of solute in this case—the next steps involve setting up the relevant chemistry equations and then performing the necessary calculations.
For intuitive problem-solving in chemistry, consider the following steps:

• Clearly identify the known variables and the unknown variable.
• Choose the appropriate formula to connect these variables.
• Rearrange the formula if necessary to solve for the unknown.
• Carefully substitute the known values into the equation.
• Carry out the calculation while paying attention to units.
• Check your answer to ensure it makes sense both mathematically and chemically.

It's beneficial to have a strong grasp of conversions, for example, between milliliters and liters, and moles and grams, as these skills are often needed in problem solving. Additionally, understanding the concepts behind the formulas—like why molarity expresses concentration—helps in applying them correctly and with comprehension, not just memorization.

Stoichiometry

Stoichiometry is a section of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. In the context of molar solutions, stoichiometry is used to calculate the amounts of substances involved in chemical reactions, taking into account the laws of conservation of mass and the proportions as described by balanced chemical equations.
In the given exercise, stoichiometry is simplified to involve just the relationship between the volume of solution and the amount of solute. This simple stoichiometric calculation is foundational for understanding more complex reactions where ratios between multiple reactants and products must be considered.
The basic principle is that the amounts of reactants and products in a chemical reaction are related to one another through their molar ratios as determined by the balanced chemical equation. For instance, if you know the amount of one reactant, you can calculate the required or resulting amount of another substance using their stoichiometric relationship. This principle extends beyond just chemical reactions—it's also applicable in preparing solutions, where the 'recipe' is defined by the molarity formula.