Mass Percent Calculation: 1.50 M NaCl Solution

by Alex Johnson 47 views

Understanding solution concentration is a fundamental concept in chemistry. Molarity, density, and mass percent are common ways to express the amount of solute dissolved in a solvent. This article will walk you through calculating the mass percent concentration of a 1.50 M NaCl (sodium chloride) solution with a density of 1.06 g/mL. We'll break down the steps, explain the underlying principles, and ensure you grasp the dimensional analysis involved.

Understanding the Concepts

Before we dive into the calculation, let's clarify the key concepts:

  • Molarity (M): Molarity is defined as the number of moles of solute per liter of solution (mol/L). A 1.50 M NaCl solution contains 1.50 moles of NaCl in every liter of solution.
  • Density: Density is the mass per unit volume (g/mL or g/cm³). A density of 1.06 g/mL means that 1 milliliter of the solution has a mass of 1.06 grams.
  • Mass Percent (% by mass): Mass percent is the mass of the solute divided by the total mass of the solution, multiplied by 100. It represents the concentration of the solute as a percentage of the total mass.

These concepts are interconnected, and understanding them is crucial for solving concentration-related problems. In this case, we'll use molarity and density to find the mass percent, demonstrating how different concentration units can be interconverted using appropriate conversion factors.

Step-by-Step Calculation

Now, let's break down the calculation into manageable steps:

1. Consider a Specific Volume

To begin, it's helpful to consider a specific volume of the solution. Let's assume we have 1 liter (1000 mL) of the 1.50 M NaCl solution. This assumption simplifies the initial calculations and provides a concrete basis for further conversions.

2. Calculate the Mass of the Solution

Using the density, we can find the mass of 1 liter of the solution:

Mass of solution = Density × Volume
Mass of solution = 1.06 g/mL × 1000 mL
Mass of solution = 1060 g

So, 1 liter of the solution has a mass of 1060 grams. This value represents the total mass of both the solute (NaCl) and the solvent (water).

3. Calculate the Mass of NaCl

Next, we need to determine the mass of NaCl present in the solution. We know the molarity is 1.50 M, which means there are 1.50 moles of NaCl in 1 liter of solution. To convert moles to grams, we use the molar mass of NaCl:

  • The molar mass of Na (Sodium) is approximately 22.99 g/mol.
  • The molar mass of Cl (Chlorine) is approximately 35.45 g/mol.
  • The molar mass of NaCl is 22.99 g/mol + 35.45 g/mol = 58.44 g/mol.

Now we can calculate the mass of NaCl:

Mass of NaCl = Moles of NaCl × Molar mass of NaCl
Mass of NaCl = 1.50 mol × 58.44 g/mol
Mass of NaCl = 87.66 g

Thus, there are 87.66 grams of NaCl in 1 liter of the solution.

4. Calculate the Mass Percent

Finally, we can calculate the mass percent using the following formula:

Mass percent = (Mass of solute / Mass of solution) × 100
Mass percent = (87.66 g / 1060 g) × 100
Mass percent ≈ 8.27%

Therefore, the concentration of the NaCl solution is approximately 8.27% by mass. This means that 8.27% of the solution's mass is due to NaCl, while the remainder is due to the solvent (water).

Dimensional Analysis

Dimensional analysis is a critical tool for ensuring the accuracy of calculations in chemistry. It involves tracking the units of each value and ensuring they cancel out appropriately to yield the desired units. Let's apply dimensional analysis to our calculation.

1. Initial Values and Conversions

We started with the following information:

  • Molarity: 1.50 mol NaCl / 1 L solution
  • Density: 1.06 g solution / 1 mL solution
  • Volume: 1 L solution (assumed)
  • Molar mass of NaCl: 58.44 g NaCl / 1 mol NaCl

2. Steps with Units

Let's outline the steps with their respective units:

  • Step 1: Convert Volume to mL

    1 L solution × (1000 mL / 1 L) = 1000 mL solution

  • Step 2: Calculate Mass of Solution

    1000 mL solution × (1.06 g solution / 1 mL solution) = 1060 g solution

  • Step 3: Calculate Moles of NaCl

    1 L solution × (1.50 mol NaCl / 1 L solution) = 1.50 mol NaCl

  • Step 4: Calculate Mass of NaCl

    1.50 mol NaCl × (58.44 g NaCl / 1 mol NaCl) = 87.66 g NaCl

  • Step 5: Calculate Mass Percent

    (87.66 g NaCl / 1060 g solution) × 100 = 8.27% NaCl

3. Ensuring Unit Cancellation

Notice how in each step, the units cancel out to leave us with the desired units. For instance, in Step 2, mL solution cancels out, leaving us with g solution. This methodical approach helps prevent errors and ensures the final answer has the correct units.

Common Mistakes and How to Avoid Them

When calculating mass percent concentration, several common mistakes can occur. Being aware of these pitfalls can help you avoid them:

1. Incorrect Unit Conversions

One frequent error is failing to convert units correctly. For example, using liters instead of milliliters or forgetting to convert moles to grams. Always double-check your units and use dimensional analysis to ensure proper conversions.

2. Misunderstanding Molarity

Misinterpreting molarity can lead to incorrect calculations. Remember that molarity is moles of solute per liter of solution, not per liter of solvent. This distinction is crucial when calculating the mass of the solution.

3. Forgetting to Multiply by 100

The final step in calculating mass percent is multiplying the ratio of solute mass to solution mass by 100. Forgetting this step will give you a decimal value instead of a percentage.

4. Using the Wrong Molar Mass

Using the incorrect molar mass for the solute will lead to significant errors. Ensure you calculate or look up the correct molar mass from the periodic table and use it in your calculations.

5. Not Considering Significant Figures

Pay attention to significant figures throughout the calculation. Your final answer should reflect the precision of the initial measurements. Rounding errors can accumulate if significant figures are not properly considered.

To avoid these mistakes, practice the following:

  • Write down all given values with their units.
  • Use dimensional analysis to guide your calculations.
  • Double-check your unit conversions.
  • Ensure you are using the correct formulas and molar masses.
  • Pay attention to significant figures at each step.

Practical Applications

The ability to calculate mass percent concentration has numerous practical applications in various fields:

1. Chemistry Labs

In chemistry labs, preparing solutions of specific concentrations is a daily task. Accurately calculating mass percent is essential for experiments, titrations, and other analytical procedures. For example, preparing a standard solution for titration requires precise knowledge of the solute's mass and the solution's volume.

2. Pharmaceuticals

The pharmaceutical industry relies heavily on accurate concentration calculations. Medications must be formulated with precise amounts of active ingredients to ensure efficacy and safety. Mass percent is used to express the concentration of drugs in various formulations, such as creams, ointments, and liquid solutions.

3. Environmental Science

Environmental scientists use concentration calculations to assess pollution levels in water and soil samples. Mass percent can be used to express the concentration of contaminants, such as heavy metals or organic pollutants, in environmental samples. This information is crucial for monitoring and remediating environmental pollution.

4. Food Industry

The food industry uses concentration calculations to control the amount of additives, preservatives, and nutrients in food products. For example, the concentration of salt in a brine solution or the sugar content in a beverage can be expressed as a mass percent. This ensures consistent product quality and adherence to regulatory standards.

5. Chemical Manufacturing

In chemical manufacturing, precise concentration control is vital for producing chemicals and materials with desired properties. Mass percent is used to monitor and adjust the concentration of reactants in chemical processes, ensuring efficient and consistent production.

Conclusion

Calculating the mass percent concentration of a solution is a fundamental skill in chemistry and has wide-ranging applications in various fields. By understanding the concepts of molarity, density, and mass percent, and by following a systematic approach with dimensional analysis, you can accurately determine the concentration of solutions. Avoiding common mistakes and practicing these calculations will build your confidence and competence in this essential area of chemistry. Remember, attention to detail and a solid grasp of the underlying principles are key to success in quantitative chemistry.

For further reading and more detailed explanations on solution concentrations, you might find resources on websites like Khan Academy Chemistry very helpful. They offer comprehensive lessons and practice problems to enhance your understanding.