Problem 46 - Chemistry: Atoms First

Question

What mass of solid NaOH (97.0\% NaOH by mass) is required to prepare 1.00 L of a 10.0\% solution of NaOH by mass? The density of the 10.0\% solution is 1.109 g/mL.

Step-by-Step Solution

Answer

To prepare 1.00 L of a 10.0% NaOH solution, 113.1 g of 97.0% pure NaOH solid is required.

Step 1: Calculate the mass of the 10% NaOH solution

First, determine the mass of the 10% NaOH solution needed for 1.00 L (1000 mL). Using the density of the solution (1.109 g/mL), calculate the mass by multiplying the volume by the density: Mass = Volume × Density.

Step 2: Calculate the mass of NaOH in the solution

Calculate the mass of NaOH that needs to be in the 1.00 L of 10% solution. Since it is 10% by mass, multiply the total mass of the solution by 0.10 to find the mass of NaOH.

Step 3: Adjust for purity of solid NaOH

Since the solid NaOH is 97% pure, not all the mass is NaOH. Calculate the required mass of the solid NaOH by dividing the mass of NaOH needed by the percent purity (in decimal form): Required mass of solid NaOH = Mass of NaOH / 0.97.

Key Concepts

Molar Concentration

Molar concentration, often referred to as molarity, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute divided by the volume of the solution in liters. The units for molar concentration are moles per liter ((mol/L) or M). Molarity is critical for stoichiometric calculations in chemistry, as it enables chemists to measure the exact quantities involved in chemical reactions.

For instance, if we need to find the molarity of a 10.0% NaOH solution given its mass and density, we would start by calculating the mass of NaOH in grams using the percent solution by mass and the density of the solution. Once we have the mass of NaOH, we would divide this by the molar mass of NaOH to find the number of moles, and then divide by the volume of the solution in liters to find the molarity.

Percent Solution by Mass

Percent solution by mass is a common way to express the concentration of a component in a mixture. It is calculated as the mass of the solute (in this case, NaOH) divided by the total mass of the solution, then multiplied by 100 to get a percentage. For the 10% NaOH solution in our exercise, for every 100 grams of the solution, 10 grams are NaOH and the remaining 90 grams are water or other components of the solution.

To calculate the mass of NaOH required to make a specific volume of solution at a given percent concentration, we can use the formula:\[ \text{Mass of Solute} = (\text{Percent by Mass} \times \text{Total Mass of Solution}) \div 100 \]

Incorporating the density allows us to first find the total mass of the solution needed, and from there, the required mass of the solute can be determined. Understanding this concept is crucial when preparing solutions in laboratories or industries, where precision is essential.

Solution Preparation

The preparation of solutions with precise concentrations is a fundamental practice in chemistry. When working with percent solutions by mass, you need to account not only for the desired concentration but also for the purity of the chemicals used. In the given exercise, we are working with solid NaOH that has a purity of 97.0%. This means that not all the solid mass contributes to the NaOH concentration in the solution.

To prepare the desired solution, we first determine the mass of the entire solution, and then calculate how much pure NaOH is needed. Since the solid NaOH is not 100% pure, we adjust for this by dividing by the percentage purity (converted to a decimal). This tells us how much of the impure solid we must use to get the necessary amount of NaOH in our solution.

In a laboratory setting, this would involve weighing the calculated mass of NaOH on a balance, and then dissolving it in a solvent, usually water, to make up the specified volume. It is important to mix the solution thoroughly to ensure uniform distribution of the solute.