Question

A potato peeling solution was found to be \(2.56 \mathrm{M}\) in \(\mathrm{NaOH}\) (formula weight \(=40.0 \mathrm{~g} /\) mole \()\) at the end of the day. To operate, the solution must be at least \(10 \% \mathrm{NaOH}\) by weight (100 g \(\mathrm{NaOH}\) per \(1000 \mathrm{~g}\) of solution). What weight percent corresponds to \(2.56 \mathrm{M} ?\) The density of a \(2.56 \mathrm{M}\) solution of \(\mathrm{NaOH}\) is about \(1.10 \mathrm{~g} / \mathrm{ml}\)

Short answer

The weight percent corresponding to a 2.56 M solution of NaOH is approximately 9.31%.

Step-by-step solution

Calculate the mass of NaOH in 1 L of solution.

Use the molarity of NaOH, which is 2.56 M, to calculate the mass of NaOH present in 1 L of the solution. Recall that Molarity = moles of solute (NaOH) / volume of solution (in L). Moles of solute = Molarity x volume = 2.56 moles/L x 1 L = 2.56 moles of NaOH Now, use the formula weight of NaOH to determine the mass of NaOH in the 1 L of solution: Mass of NaOH = moles of solute x formula weight = 2.56 moles x 40.0 g/mol = 102.4 g

Calculate the total mass of 1 L of solution.

We know the density of the solution (1.10 g/mL) and that there are 1000 mL in 1 L. Use this information to calculate the total mass of 1 L of solution: Total mass of 1 L of solution = density x volume = 1.10 g/mL x 1000 mL = 1100 g

Calculate the weight percent of NaOH in the solution.

Use the calculated mass of NaOH and the total mass of the solution from Steps 1 and 2 to find the weight percent of NaOH in the solution: Weight Percent = (Mass of NaOH / Total mass of the solution) * 100 = (102.4 g / 1100 g) * 100 = 9.31% So, the weight percent corresponding to a 2.56 M solution of NaOH is approximately 9.31%.

Key concepts

Molarity

Molarity is a measure of concentration. It tells us how many moles of solute, like sodium hydroxide (NaOH), are in one liter of a solution. This is an important concept because it allows us to express how concentrated a solution is in a straightforward manner. A molarity of 2.56 M means there are 2.56 moles of NaOH in every liter of the solution. When working with molarity:

• A higher molarity indicates a more concentrated solution.
• We can use molarity to calculate the amount of solute needed for reactions.
• It is essential for preparing solutions with precise concentrations for laboratory work.

In the exercise, this measurement helps us find how much NaOH is in 1 L of solution.

Mass Calculation

Mass calculation involves determining the mass of the substance dissolved in a solution. Here, we need to calculate how much NaOH is present in the 2.56 M solution.To find the mass:

• First, calculate the moles of NaOH using the formula: \[ \text{moles = molarity} \times \text{volume (L)} \]
• Next, multiply the number of moles by the molar mass of NaOH: \[ \text{mass = moles} \times \text{formula weight} \]

In this instance, we have 2.56 moles of NaOH. With a formula weight of 40.0 g/mol, the total mass is 102.4 grams.

Density

Density describes how much mass is in a given volume of a substance. It's important as it allows us to transition between the volume and mass of solutions. In the problem, the density of the NaOH solution is given as 1.10 g/mL, which translates to:

• In 1 mL of this solution, there is 1.10 grams of total mass.
• So, for 1000 mL (or 1 liter), the total mass becomes 1100 grams.

Density helps us understand the solution's behavior and properties, especially in industrial applications.

Weight Percent

Weight percent is another way to represent concentration. It tells us how much solute there is as a percentage of the total solution's weight. To calculate weight percent:

• Take the mass of the solute (e.g., NaOH) and divide it by the total mass of the solution.
• Multiply the result by 100 to get the percentage.

In our example, with 102.4 grams of NaOH in a 1100 gram solution, the weight percent is approximately 9.31%. This figure is crucial for processes like manufacturing and food preparation, where concentration impacts safety and quality.