Question

What mass of each solute is present in \(285 \mathrm{g}\) of a solution that contains \(5.00 \%\) by mass \(\mathrm{NaCl}\) and \(7.50 \%\) by mass \(\mathrm{Na}_{2} \mathrm{CO}_{3} ?\)

Short answer

In a 285 g solution containing 5.00% NaCl and 7.50% Na₂CO₃ by mass, there are approximately 14.25 g of NaCl and 21.38 g of Na₂CO₃.

Step-by-step solution

Understanding the problem and the given information

We are given that 5.00% of the solution's mass is NaCl and 7.50% of the solution's mass is Na₂CO₃. The percentage by mass of a solute in a solution refers to the mass of that solute divided by the total mass of the solution, multiplied by 100.

Calculate the mass of NaCl in the solution

To find the mass of NaCl in the solution, use the percentage by mass formula: Mass of NaCl (in grams) = (Percentage by mass of NaCl / 100) × Mass of the solution (in grams) \(Mass\, of\, NaCl\, (in\, grams) = (\frac{5.00}{100}) × 285\, g\)

Calculate the mass of Na₂CO₃ in the solution

To find the mass of Na₂CO₃ in the solution, use the same percentage by mass formula: Mass of Na₂CO₃ (in grams) = (Percentage by mass of Na₂CO₃ / 100) × Mass of the solution (in grams) \(Mass\, of\, Na_2CO_3\, (in\, grams) = (\frac{7.50}{100}) × 285\, g\)

Solve for the mass of NaCl and Na₂CO₃

Solve for the masses of NaCl and Na₂CO₃ in the solution. For NaCl: \(Mass\, of\, NaCl\, = (\frac{5.00}{100}) × 285\, g \approx 14.25\, g\) For Na₂CO₃: \(Mass\, of\, Na_2CO_3\, = (\frac{7.50}{100}) × 285\, g \approx 21.38\, g\)

Present the final answer

The mass of NaCl present in the 285 g solution is approximately 14.25 g, and the mass of Na₂CO₃ present in the solution is approximately 21.38 g.

Key concepts

Mass Percent

Mass percent is a way to express the concentration of a component in a mixture. It is calculated by taking the mass of the solute and dividing it by the total mass of the solution, then multiplying the result by 100 to get a percentage.
This method is particularly useful when dealing with solid and solid-liquid solutions, providing a clear understanding of the solute concentration.

This form of concentration expression has its importance in chemistry and industry, as it allows chemists to know exactly how much of each component is present in a given solution.

• For example, if a solution contains 5% NaCl, every 100 g of the solution would have 5 g of NaCl.
• Suddenly dealing with larger or other specific amounts is easily possible because of the percentage rule.

Overall, mass percent is a practical way to quantify how much solute is present among all solution components, making it easier to prepare mixes with precise properties.

Sodium Chloride (NaCl)

Sodium Chloride, commonly known as table salt, is an odorless crystalline compound widely used in various industries including food, cleaning, and de-icing. Its chemical symbol is NaCl.
In chemistry, NaCl is often studied for its ability to dissolve in water, becoming a major component of saline solutions.

Here are some key properties and usages:

• Highly soluble in water, forming an essential part of saline solutions.
• Used in medical settings for intravenous fluids to help maintain fluid balance in patients.
• Commonly utilized in laboratories for chemical experiments and demonstrations due to its non-toxic, harmless nature in moderate quantities.

Understanding NaCl's role in solutions and how its concentrations like mass percent affect solution properties helps in various practical applications from cooking to scientific research.

Sodium Carbonate (Na₂CO₃)

Sodium Carbonate, often known as soda ash or washing soda, is a significant industrial chemical with various applications. Its chemical formula is Na₂CO₃.
This compound is known for its strong alkalinity and ability to absorb moisture, making it vital in glass manufacturing and as a water softener.

Main characteristics and uses include:

• Plays a crucial role in the glass-making industry as it reduces the melting point of silica.
• Serves as a popular cleaning agent and detergent booster due to its ability to soften hard water.
• In laboratories, Na₂CO₃ is used to neutralize acidic solutions and as a primary standard for acid-base titrations due to its non-hygroscopic nature, meaning it doesn't absorb moisture from the air.

Understanding the use and impact of sodium carbonate concentrations in solutions supports efficient industrial processes and experimental accuracy.