Question

How would you prepare \(2.00 \mathrm{~kg}\) of an \(\mathrm{NaCl}\) solution that is \(30.0\) mass \(\% \mathrm{NaCl} ?\)

Short answer

To prepare a 2.00 kg NaCl solution with a 30.0% mass concentration, you will need 600 g of NaCl and 1400 g of water. Weigh the NaCl and water separately, then slowly add the NaCl to the water while stirring continuously until it dissolves completely, forming a homogeneous solution.

Step-by-step solution

Calculate the mass of NaCl required

To determine the mass of NaCl needed, we first need to find how much 30.0% of the total solution mass is. Since the total mass is 2.00 kg, which is equal to 2000 g, we can find the mass of NaCl needed by multiplying the total mass by the mass percent (in decimal form): Mass of NaCl = Total mass × Mass percent of NaCl = 2000 g × 0.30 = 600 g So, 600 g of NaCl is needed.

Calculate the mass of water required

To determine the mass of water needed to make the NaCl solution, we will subtract the mass of NaCl from the total mass of the solution: Mass of water = Total mass - Mass of NaCl = 2000 g - 600 g = 1400 g So, 1400 g of water is needed.

Combine the masses to prepare the solution

Now that we have the masses of NaCl and water needed, we can prepare the 2.00 kg NaCl solution at 30.0% mass concentration by combining the two components: 1. Weigh 600 g of NaCl and 1400 g of water separately. 2. Slowly add the NaCl to the water while stirring continuously to help dissolve the NaCl. 3. Continue stirring until the NaCl is completely dissolved in the water, forming a homogeneous solution. The final result is a 2.00 kg NaCl solution with a 30.0% mass concentration of NaCl.

Key concepts

Mass Percent Concentration

Understanding the mass percent concentration is crucial when preparing solutions in chemistry. It expresses the mass of a solute (in this case, NaCl or table salt) as a percentage of the total mass of the solution. For the given exercise, a 30.0% mass percent concentration means that 30.0 grams of NaCl are present in every 100 grams of the solution.

The formula to calculate the mass of the NaCl needed is given by:
\[ \text{Mass of NaCl} = \text{Total mass} \times \text{Mass percent of NaCl} \]
To convert the percentage to a decimal, 30.0% becomes 0.30. This conversion is important because percentages must be expressed as decimal values in calculations. Using this information, when a solution is said to be 30.0% NaCl, it implies that for every 100 grams of this solution, 30 grams are NaCl and the remaining 70 grams are usually the solvent, typically water.

Understanding this concept helps ensure that we mix the correct proportions of solute and solvent to achieve the desired concentration for various applications, such as laboratory experiments, medical formulations, or culinary recipes.

Solution Preparation

The preparation of a solution requires precise measurement and mixing of the solute and solvent. In the solution preparation process outlined in the exercise, NaCl is the solute (the substance to be dissolved), and water is the solvent (the substance that dissolves the solute).

When preparing a 2.00 kg NaCl solution at 30.0% mass concentration, it's crucial to follow these steps:

• Accurately weigh out 600 g of NaCl using a balance.
• Measure 1400 g of water, which will act as the solvent.
• Gradually add the NaCl to the water while continuously stirring to promote dissolution.
• Ensure that the NaCl is entirely dissolved into the water, forming a homogeneous solution.

Stirring is a vital part of the process as it helps to break up the NaCl and distribute it evenly throughout the water. This method ensures all the NaCl is dissolved, which is necessary for a uniform solution where the concentration of salt is the same throughout. Skipping or rushing these steps can lead to an improperly mixed solution with varying concentrations of solute.

Stoichiometry

Stoichiometry plays an integral role in chemistry, including solution preparation, as it involves the calculation of the quantitative relationships or ratios between reactants and products in a chemical reaction. In the context of preparing solutions, stoichiometry helps us determine the exact amounts of solute and solvent needed to create a solution of a specific concentration.

In our exercise, we use stoichiometric calculations to relate the mass percent concentration to the masses of NaCl and water required. The exercise doesn't involve a chemical reaction per se, but stoichiometry is still applicable as it deals with the ratios and relationships in the mixture.

To perform a stoichiometric calculation, follow these steps:

• Identify the required concentration and total mass of the solution.
• Calculate the mass of the solute (NaCl) using the given mass percent concentration.
• Deduct the mass of the solute from the total mass to find the mass of the solvent (water) required.

By meticulously applying stoichiometric principles, we can precisely measure the components needed to create a solution with the desired properties, ensuring accuracy in scientific and practical applications.