Question

What is the percent by mass of \(\mathrm{NaHCO}_{3}\) in a solution containing 20.0 \(\mathrm{g}\) of \(\mathrm{NaHCO}_{3}\) dissolved in 600.0 \(\mathrm{mL}\) of \(\mathrm{H}_{2} \mathrm{O}\) ?

Short answer

The percent by mass of \(\mathrm{NaHCO}_{3}\) in the solution is approximately 3.226%.

Step-by-step solution

Convert the volume of water to mass

Since the problem gives the volume of water in milliliters, we'll need to convert it to mass. We know that the density of water is approximately 1 \(\mathrm{g/mL}\). So, the mass of water can be found by multiplying its volume by its density: Mass of water = Volume of water × Density of water Mass of water = 600.0 \(\mathrm{mL}\) × 1 \(\mathrm{g/mL}\) = 600.0 \(\mathrm{g}\)

Calculating total mass of the solution

Now that we know the mass of water (600.0 \(\mathrm{g}\)), we can find the total mass of the solution by adding the mass of water to the mass of dissolved \(\mathrm{NaHCO}_{3}\) (20.0 \(\mathrm{g}\)): Total mass of solution = Mass of water + Mass of \(\mathrm{NaHCO}_{3}\) Total mass of solution = 600.0 \(\mathrm{g}\) + 20.0 \(\mathrm{g}\) = 620.0 \(\mathrm{g}\)

Calculating the percent by mass of \(\mathrm{NaHCO}_{3}\)

To find the percent by mass of \(\mathrm{NaHCO}_{3}\) in the solution, we'll use the following formula: Percent by mass = \(\frac{\text{Mass of solute}}{\text{Total mass of solution}}\) × 100% In this problem, the mass of solute is the mass of \(\mathrm{NaHCO}_{3}\) (20.0 \(\mathrm{g}\)), and the total mass of the solution is 620.0 \(\mathrm{g}\). Plugging these values into the formula, we get: Percent by mass = \(\frac{20.0\ \mathrm{g}}{620.0\ \mathrm{g}}\) × 100% = 0.03226 × 100% ≈ 3.226% The percent by mass of \(\mathrm{NaHCO}_{3}\) in the solution is approximately 3.226%.

Key concepts

Understanding Stoichiometry

Stoichiometry is a branch of chemistry that quantitatively relates the amounts of reactants and products in a chemical reaction. It involves calculations to determine the optimal ratios of these substances, ensuring a reaction proceeds efficiently and completely. In our exercise, stoichiometry isn't involved in the direct sense of a reaction, but it helps us understand the concept of proportions and how to relate different substances in a mixture. When we calculate the percent by mass of sodium bicarbonate (\textbf{NaHCO}\(_3\)) in a solution, we're assessing the ratio of the mass of the compound to the mass of the entire solution, which is a foundational concept in stoichiometry.

Deciphering Molarity

Molarity is a measure of the concentration of a solution, specifically defined as the number of moles of solute per liter of solution. While the textbook problem doesn't directly ask for molarity, understanding this concept is essential when dealing with solution concentrations in chemistry. To calculate molarity, you would divide the number of moles of the solute (\textbf{NaHCO}\(_3\)) by the volume of the solution in liters. If the problem had also provided the molar mass of \textbf{NaHCO}\(_3\), you could calculate moles from the given mass and then find the molarity based on the volume of water. Molarity is a more common unit in chemistry compared to percent by mass but both are important for understanding the composition of solutions.

Solution Concentration Essentials

The term 'solution concentration' can refer to several different ways of expressing the amount of solute in a solvent. Percent by mass, which our exercise focuses on, is one of the simplest forms. It gives us the ratio of solute mass to the total mass of the solution, expressed as a percentage. This is particularly useful in everyday solutions where the precise number of moles isn't required. Percent by mass is calculated by dividing the mass of the solute by the total mass of the solution and multiplying by 100%. In the context of our problem, the solution concentration tells us how much \textbf{NaHCO}\(_3\) there is in a water-based solution. Different concentrations are used for various applications, and choosing the right one is key in fields ranging from medicine to manufacturing.

An understanding of solution concentration is not just academically relevant but also practical, as it dictates how substances will behave and react in different settings.