Problem 87 - Chemistry and Chemical Reactivity

Question

You have a bottle of solid \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) and a \(500.0-\mathrm{mL}\). volumetric flask. Explain how you would make a \(0.20 \mathrm{M}\) solution of sodium carbonate.

Step-by-Step Solution

Answer

Weigh 10.6 g of \(\text{Na}_2\text{CO}_3\), dissolve in water and dilute to 500 mL.

Step 1: Determine Moles Needed

To make a 0.20 M solution of sodium carbonate (\(\text{Na}_2\text{CO}_3\)) in 500.0 mL, we need to calculate the required moles of solute. The formula for molarity is:\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]Thus, we have:\[ 0.20 = \frac{\text{moles of } \text{Na}_2\text{CO}_3}{0.500} \]Solving for moles, you'll find:\[ \text{moles of } \text{Na}_2\text{CO}_3 = 0.20 \times 0.500 = 0.10 \text{ moles} \]

Step 2: Calculate Mass Needed

Next, we calculate the mass (in grams) of \(\text{Na}_2\text{CO}_3\) required. The molar mass (MW) of \(\text{Na}_2\text{CO}_3\) is calculated as follows:\[ MW = 2(23.0) + 12.0 + 3(16.0) = 106.0 \text{ g/mol} \]So the mass needed is:\[ 0.10 \text{ moles} \times 106.0 \text{ g/mol} = 10.6 \text{ g} \]

Step 3: Dissolve in Volumetric Flask

Weigh out 10.6 g of solid \(\text{Na}_2\text{CO}_3\) using a balance. Transfer the solid into a 500.0-mL volumetric flask. Add distilled water to the flask, but do not fill to the 500 mL mark initially. Swirl the flask until the \(\text{Na}_2\text{CO}_3\) is completely dissolved.

Step 4: Fill to the Mark

Once dissolved, carefully add additional distilled water to the 500 mL mark on the volumetric flask. Ensure the bottom of the meniscus is on the mark when viewed at eye level. Secure the stopper, and mix the solution by inverting the flask several times.

Key Concepts

Molarity Calculation

To make a desired solution, the concept of molarity is key. Molarity indicates how concentrated a solution is and is denoted by the symbol 'M'. It is defined as the number of moles of solute per liter of solution. The formula is:\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]This formula helps in determining how many moles are needed when preparing solutions of specific molarity.

• For instance, if we need a 0.20 M sodium carbonate solution in 500 mL, first convert the volume into liters by dividing 500 mL by 1000, which equals 0.5 L.
• Next, rearrange the molarity formula to find moles: \[ \text{moles} = M \times V \]
• Plug in the numbers: \[ \text{moles of } \text{Na}_2\text{CO}_3 = 0.20 \times 0.5 = 0.10 \text{ moles} \]

This calculation ensures you use the correct amount of solute for your desired solution molarity.

Sodium Carbonate

Sodium carbonate, noted chemically as \(\text{Na}_2\text{CO}_3\), is a versatile salt used in many applications, from cleaning agents to buffering solutions. When preparing a solution with it, you must know its molar mass, which helps in calculating the required grams for a given number of moles.
Sodium carbonate has a molar mass of 106.0 g/mol, calculated by adding:

• Two sodium atoms \((2 \times 23.0)\)
• One carbon atom \((12.0)\)
• Three oxygen atoms \((3 \times 16.0)\)

This gives a sum of 106.0 g/mol. Once you know the moles needed for your solution, you multiply it by the molar mass to find the mass required. For a 0.10 mole need, you will use:\[ 0.10 \times 106.0 = 10.6 \text{ grams} \]This precise measurement ensures the solution has the exact concentration you desire.

Volumetric Flask

The volumetric flask is an essential piece of laboratory glassware when precision is required in solution preparation. It is used primarily for creating solutions of accurate and exact concentrations. These flasks come with a precise calibration mark showing where the liquid should come up to.

• Begin by weighing the amount of solid sodium carbonate calculated earlier and placing it into the flask.
• Add distilled water to partially fill the flask.
• Swirl or gently shake the flask until all the solute dissolves.
• Once dissolved, continue adding water until the bottom of the meniscus touches the calibration mark.

It is crucial to fill to this line when making a solution. Otherwise, the concentration won't be correct. Once filled correctly, secure the stopper and invert the flask to ensure thorough mixing. This guarantees the solution is homogeneous and fits the intended molarity.