Question

For each of the following, the number of moles of solute is given, followed by the total volume of solution prepared. Calculate the molarity. a. 0.426 mol of \(\mathrm{NaOH} ; 0.500 \mathrm{L}\) b. 0.213 mol of \(\mathrm{NaOH} ; 0.250 \mathrm{L}\) c. 1.28 mol of \(\mathrm{NaOH} ; 1.50 \mathrm{L}\) d. 4.26 mol of \(\mathrm{NaOH} ; 5.00 \mathrm{L}\)

Short answer

The molarity for each case is as follows: a. \(M = 0.852 \, \text{M}\) b. \(M = 0.852 \, \text{M}\) c. \(M = 0.853 \, \text{M}\) d. \(M = 0.852 \, \text{M}\)

Step-by-step solution

a. Calculate the molarity for 0.426 mol of NaOH in 0.500 L of solution.

Using the formula, we have: \[ M = \frac{0.426 \, \text{mol}}{0.500 \, \text{L}} \] Now, solve for M: \[ M = 0.852 \, \text{M} \]

b. Calculate the molarity for 0.213 mol of NaOH in 0.250 L of solution.

Using the formula, we have: \[ M = \frac{0.213 \, \text{mol}}{0.250 \, \text{L}} \] Now, solve for M: \[ M = 0.852 \, \text{M} \]

c. Calculate the molarity for 1.28 mol of NaOH in 1.50 L of solution.

Using the formula, we have: \[ M = \frac{1.28 \, \text{mol}}{1.50 \, \text{L}} \] Now, solve for M: \[ M = 0.853 \, \text{M} \]

d. Calculate the molarity for 4.26 mol of NaOH in 5.00 L of solution.

Using the formula, we have: \[ M = \frac{4.26 \, \text{mol}}{5.00 \, \text{L}} \] Now, solve for M: \[ M = 0.852 \, \text{M} \]

Key concepts

Molarity Formula

Understanding the molarity formula is crucial for students in chemistry to calculate the concentration of a solution. Molarity, denoted by the symbol 'M,' is the term used to describe the concentration of a solute in a solution, and it represents the number of moles of solute per liter of solution. The formula to calculate molarity is straightforward:

\[ M = \frac{\text{moles of solute}}{\text{liters of solution}} \]
To use the molarity formula, you need to know two key pieces of information: the amount of solute in moles, and the total volume of the solution in liters. Let's apply this formula to a practical example:

If you have 0.426 moles of sodium hydroxide (NaOH) dissolved in 0.500 liters of water, the molarity of the NaOH solution is calculated as \[ M = \frac{0.426 \, \text{mol}}{0.500 \, \text{L}} = 0.852 \, \text{M} \]
This result indicates a concentration of 0.852 moles of NaOH per liter of solution, conveyed as 0.852 M NaOH.

Moles per Liter

When dealing with molarity, one of the recurring themes is the concept of 'moles per liter'. Moles represent the amount of substance and are a fundamental unit in chemistry.

One mole corresponds to Avogadro's number of particles, which is approximately \(6.022 \times 10^{23}\). Meanwhile, 'per liter' explains the volume of the entire solution in which the solute has been dissolved.

To grasp this concept, think about dispersing a certain number of particles uniformly throughout a container. When the container's size is one liter, the number of moles of particles you've distributed across it gives you the concentration in moles per liter. This is a direct measure of how concentrated or dilute the solution is.

NaOH Solution Concentration

Sodium hydroxide (NaOH), commonly known as lye or caustic soda, is a strong base used in various chemical processes. The concentration of an NaOH solution is a critical factor that affects its reactivity and handling.

In chemistry, the concentration of NaOH solutions is typically expressed in molarity, which reveals how many moles of this compound are present in one liter of solution. To calculate the molarity of NaOH, you'd use the same molarity formula. For example, if you have 4.26 moles of NaOH and the total volume of the solution is 5.00 liters, the molarity would be \[ M = \frac{4.26 \, \text{mol}}{5.00 \, \text{L}} = 0.852 \, \text{M} \]
This indicates a moderate concentration. NaOH solutions can range widely in concentration, and it's important to know the molarity for appropriate use in laboratory settings and industrial applications.