Question

What mass of oxalic acid, \(\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4},\) is required to prepare \(250 .\) mL of a solution that has a concentration of \(0.15 \mathrm{M} \mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4} ?\)

Short answer

3.375 g of oxalic acid is required.

Step-by-step solution

Understand the Problem

We need to determine the mass of oxalic acid (\(\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4\)) required to make a 250 mL solution with a molarity of 0.15 M. Molarity (M) is defined as moles of solute per liter of solution.

Convert Volume to Liters

The solution volume given is 250 mL. Convert this to liters by dividing by 1000 because there are 1000 mL in a liter: \[ 250 \, \text{mL} = \frac{250}{1000} \, \text{L} = 0.25 \, \text{L} \]

Calculate Moles of Oxalic Acid

Use the formula for molarity: \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \). Rearrange to find moles of solute: \( \text{moles of solute} = M \times \text{liters of solution} \). Substitute the given values: \[ \text{moles of } \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 = 0.15 \, \text{M} \times 0.25 \, \text{L} = 0.0375 \, \text{moles} \]

Find Molar Mass of Oxalic Acid

Calculate the molar mass of oxalic acid (\(\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4\)). The atomic masses are approximately H = 1 g/mol, C = 12 g/mol, O = 16 g/mol: \[ \text{Molar mass} = (2 \times 1) + (2 \times 12) + (4 \times 16) = 90 \, \text{g/mol} \]

Calculate Mass of Oxalic Acid

Use the formula: \[ \text{mass} = \text{moles} \times \text{molar mass} \]. Substitute in the values to find the mass: \[ \text{mass of } \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 = 0.0375 \, \text{moles} \times 90 \, \text{g/mol} = 3.375 \, \text{g} \]

Key concepts

Molarity

Molarity is a way to express the concentration of a solution. It describes how many moles of a solute are present in one liter of solution. By definition, molarity is the number of moles of solute divided by the volume of the solution in liters. This is often expressed as \[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \].
This measure is important because it allows chemists to compare concentrations and to predict the outcomes of reactions. For example, a 0.15 M oxalic acid solution means that there are 0.15 moles of \( \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \) per liter of solution.

• Simply put, it tells you how 'crowded' the solute molecules are in the solution.
• The concept of molarity makes it easier to create precise and repeatable chemical reactions and studies.

Moles of Solute

The term 'moles of solute' refers to the actual number of molecules or atomic entities present in a solution. A mole is a unit used to count particles, similar to a dozen, but instead of 12, a mole represents approximately \(6.022 \times 10^{23} \) entities (known as Avogadro's number).
In our example, we calculate the moles of oxalic acid required for the solution by using the molarity formula and the volume of the solution in liters. The equation to find the moles is \( ext{moles of solute} = ext{M} \times ext{liters of solution} \).

• For a given molarity, the volume of your solution directly determines how many moles you will have.
• In practice, moles help us to handle large numbers of molecules in manageable amounts for reaction measurement and analysis.

Molar Mass

Molar mass is the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol). To find the molar mass, sum up the atomic masses of all atoms in the molecular formula.
In the case of oxalic acid,\( \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \), you calculate the molar mass by adding the atomic mass of hydrogen (H), carbon (C), and oxygen (O):

• 2 hydrogen atoms each with atomic mass 1 g/mol = 2 g/mol
• 2 carbon atoms each with atomic mass 12 g/mol = 24 g/mol
• 4 oxygen atoms each with atomic mass 16 g/mol = 64 g/mol

Adding these together gives a total molar mass of 90 g/mol for oxalic acid. Understanding molar mass is crucial for converting between the mass of substances and the number of moles, particularly in solution preparation.

Solution Preparation

Preparing a solution involves dissolving a specific amount of solute in a solvent. The ultimate goal is to achieve a desired molarity for the solution. To prepare a solution of oxalic acid with a concentration of 0.15 M, we must calculate how much solid \( \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \) is needed using the equation:\[ ext{mass of solute} = ext{moles} \times ext{molar mass} \].
Using the moles calculated from the desired molarity and the solution volume provided, we find the mass needed. This process is crucial for creating solutions for experiments and ensuring their chemical reactions proceed correctly.

• The accurate preparation of solutions requires precise measurements to ensure the correct concentration of solutes.
• Understanding how to calculate and measure these quantities is essential for any chemist or lab technician.