Question

Strong acid solutions may have their concentration determined by reaction with measured quantities of standard sodium carbonate solution. What mass of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is needed to prepare \(250 . \mathrm{mL}\) of \(0.0500 \mathrm{M}\) \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) solution?

Short answer

To prepare 250 mL of 0.0500 M Na2CO3 solution, 1.32 g of Na2CO3 is needed. This is calculated using the relationship between molarity, volume, and mass, and converting moles of Na2CO3 into mass using its molar mass (105.99 g/mol).

Step-by-step solution

Calculate the moles of Na2CO3

To find the moles of Na2CO3, we will use the formula: moles = molarity × volume (L). Given that we want to prepare 250 mL of 0.0500 M Na2CO3 solution, we first need to convert the volume from mL to L. Volume (L) = 250 mL × (1 L / 1000 mL) = 0.250 L Now, we will calculate the moles of Na2CO3: moles = molarity × volume moles = 0.0500 mol/L × 0.250 L

Solve for the moles of Na2CO3

Now, let's calculate the moles of Na2CO3: moles = 0.0500 mol/L × 0.250 L = 0.0125 mol

Calculate the molar mass of Na2CO3

To convert moles of Na2CO3 into mass, we need to find the molar mass of Na2CO3 by adding the molar masses of its constituent elements: 2 sodium (Na), 1 carbon (C), and 3 oxygen (O). The molar masses are 22.99 g/mol for Na, 12.01 g/mol for C, and 16.00 g/mol for O. Molar mass of Na2CO3 = (2 × 22.99) + 12.01 + (3 × 16.00) = 105.99 g/mol

Calculate the mass of Na2CO3 required

Now, having the molar mass and the moles of Na2CO3, we will calculate its mass using the formula: mass = moles × molar mass. mass = 0.0125 mol × 105.99 g/mol

Solve for the mass of Na2CO3

Finally, let's calculate the mass of Na2CO3 required for preparing the 0.0500 M solution: mass = 0.0125 mol × 105.99 g/mol = 1.32 g (rounded to two decimal places) Therefore, 1.32 g of Na2CO3 is needed to prepare 250 mL of 0.0500 M Na2CO3 solution.

Key concepts

Molarity Calculation

Understanding molarity is crucial in chemistry, as it is a measure of concentration that tells us how many moles of a solute are in a liter of solution. To calculate the molarity, use the formula:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \].
In the context of our problem, the molarity is already given as 0.0500 M for the Na2CO3 solution. When we prepare this solution, we aim to have 0.0500 moles of Na2CO3 in every liter of solution. Since we're preparing 250 mL (or 0.250 L), we adjust our moles calculation accordingly to maintain the desired concentration. This step is crucial because it sets the stage for all subsequent stoichiometric calculations.

Moles to Mass Conversion

Once we know the number of moles needed to achieve a particular molarity, the next step is converting these moles to mass. This is essential for practical laboratory situations where substances are weighed, not counted by moles.
Use the formula:
\[ \text{Mass (g)} = \text{moles} \times \text{molar mass (g/mol)} \].
Make sure to have the molar mass ready for this step. In our case study, we find that 0.0125 moles of Na2CO3 have a specific mass that we will calculate using its molar mass. This moles to mass conversion is a key aspect of stoichiometry, bridging the gap between theoretical calculations and practical measurements.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves calculating the amounts of substances produced or consumed in a chemical reaction. This process requires a balanced chemical equation and a thorough understanding of mole ratios.
In our exercise, although there isn’t a reaction to balance, the principle of stoichiometry is used to deduce the amount of reactant (in this case, Na2CO3) required. Importantly, stoichiometry not only considers the quantities but also the concentration of chemical solutions as part of the calculations. This ensures that the right proportions of substances are used to achieve the desired product concentration.

Molar Mass Calculation

The molar mass of a compound is the mass of one mole of that substance and is expressed in grams per mole (g/mol). It's the sum of the molar masses of its constituent atoms. Finding the molar mass of Na2CO3 requires adding together the molar masses of 2 sodium (Na) atoms, 1 carbon (C) atom, and 3 oxygen (O) atoms.
Calculating the molar mass accurately is vital because it directly impacts the moles to mass conversion. For students, the best approach is to always confirm the atomic masses from a reliable periodic table and pay attention to the number of each atom in the chemical formula. This exercise demonstrates a practical example of how molar mass calculations are fundamental in determining how much of a compound is needed to prepare a particular solution.