Question

\(4.28 \mathrm{~g}\) of \(\mathrm{NaOH}\) is dissolved in water and the solution is made to \(250 \mathrm{cc}\). What will be the molarity of the solution? (a) \(0.615 \mathrm{~mol} \mathrm{~L}^{-1}\) (b) \(0.428 \mathrm{~mol} \mathrm{~L}^{-1}\) (c) \(0.99 \mathrm{~mol} \mathrm{~L}^{-1}\) (d) \(0.301 \mathrm{~mol} \mathrm{~L}^{-1}\)

Short answer

The molarity of the solution is 0.428 mol/L.

Step-by-step solution

Find the molar mass of NaOH

To calculate the molarity, we need to know the number of moles of NaOH. The molar mass of NaOH (sodium hydroxide) can be calculated by summing the atomic masses of sodium (Na), oxygen (O), and hydrogen (H): 22.99 grams/mol for Na, 16.00 grams/mol for O, and 1.01 grams/mol for H. Thus, the molar mass of NaOH is 22.99 + 16.00 + 1.01 = 40.00 grams/mol.

Calculate the number of moles of NaOH

Using the molar mass of NaOH, we can calculate the moles of NaOH by dividing the mass of the NaOH used by its molar mass. Thus, the number of moles of NaOH is calculated by \[\begin{equation} \frac{4.28 \text{ g}}{40.00 \text{ g/mol}} = 0.107 \text{ moles} \end{equation}\]

Convert volume from cc to liters

To find the molarity, we need the volume in liters. Since 1 cc (cubic centimeter) is equivalent to 1 mL, and there are 1000 mL in 1 L, we can convert 250 cc to liters by dividing by 1000: \[\begin{equation} 250 \text{ cc} = 250 \text{ mL} = 0.250 \text{ L} \end{equation}\]

Calculate the molarity of the solution

Molarity is defined as the number of moles of solute per liter of solution. Using the number of moles and the volume in liters, we can calculate the molarity: \[\begin{equation} \text{Molarity} = \frac{\text{moles of NaOH}}{\text{Volume in liters}} = \frac{0.107 \text{ moles}}{0.250 \text{ L}} = 0.428 \text{ mol/L} \end{equation}\]

Key concepts

NaOH Molarity

Molarity is a vital concept in chemistry, representing the concentration of a solution. When we talk about the molarity of a solution, we refer to the number of moles of a solute (such as NaOH) present in one liter of the solution. It is expressed as moles per liter (mol/L). Understanding how to determine the molarity is particularly important when preparing solutions for various experiments or industrial processes.

In the provided exercise, we need to find out the molarity of an NaOH solution. Clear steps are essential for students to successfully calculate this: after determining the moles of NaOH and converting the volume from cc to liters, the molarity is simply the ratio of these two values. It is also crucial to remember the conversion factor between milliliters (mL) and liters (L) as errors in this step will directly affect the final calculation of molarity.

Molar Mass of NaOH

To get started with the calculation of molarity, it's necessary to comprehend the concept of molar mass, which is the mass of one mole of any substance. The molar mass of NaOH, or sodium hydroxide, is a constant value that can be computed by adding the atomic masses of its constituent elements - sodium (Na), oxygen (O), and hydrogen (H).

For NaOH:

• The molar mass of sodium is approximately 22.99 g/mol.
• Oxygen contributes about 16.00 g/mol.
• Hydrogen adds another 1.01 g/mol.

By summing these up, we arrive at the molar mass of NaOH, which is 40.00 g/mol. This figure is fundamental to all subsequent calculations involving the substance. It helps translate mass, an easily measurable quantity, into moles, facilitating the determination of concentration through molarity.

Moles of Solute

Moles represent a fundamental concept in chemistry called 'amount of substance,' and knowing the moles of solute in a solution is paramount when calculating molarity. One mole of any substance contains Avogadro's number of entities (atoms, molecules, ions, etc.), which is roughly 6.022 x 10²³.

In our exercise, we calculate the moles of NaOH by dividing its mass by the molar mass (the mass of one mole). Simple division yields the moles of NaOH, which, in this case, is 0.107 moles. This value is crucial for students to progress to the final step of calculating the molarity of the NaOH solution. Providing clear and concise steps helps ensure that students not only reach the correct answer but also understand the relationship between the mass of a solute, its molar mass, and the number of moles. This understanding is the cornerstone of mastering solution concentration measurements.