Molarity: Videos & Practice Problems

Molarity, often denoted by the capital letter M, is a key concept in chemistry that quantifies the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution, providing a precise measure of how much solute is present in a given volume of solvent. The formula for calculating molarity is expressed as:

M = \(\frac{\text{moles of solute}}{\text{liters of solution}}\)

In this context, the term "concentration" is sometimes used interchangeably with molarity, but it is important to note that concentration is a broader term that refers to the amount of solute in a specific volume of solution. Understanding molarity allows for more accurate calculations and comparisons in chemical reactions and solutions.

To calculate molarity, one must first determine the number of moles of the solute, which can be found using the formula:

moles = \(\frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\)

Once the moles of solute are known, dividing this value by the volume of the solution in liters will yield the molarity. This concept is fundamental in various applications, including preparing solutions, diluting concentrations, and conducting stoichiometric calculations in chemical reactions.

To calculate the molarity of a sodium hydroxide (NaOH) solution, we start with the formula for molarity, which is defined as the number of moles of solute divided by the volume of solution in liters. The formula can be expressed as:

Molarity (M) = \(\frac{\text{moles of solute}}{\text{liters of solution}}\)

In this case, we need to determine the moles of sodium hydroxide from the given mass. We know that 23.7 grams of NaOH is dissolved in enough water to make 2.50 liters of solution. First, we calculate the molar mass of sodium hydroxide:

NaOH is composed of one sodium (Na), one oxygen (O), and one hydrogen (H). The atomic masses from the periodic table are approximately:

• Na: 22.99 g/mol
• O: 16.00 g/mol
• H: 1.01 g/mol

Adding these together gives:

Molar mass of NaOH = 22.99 g/mol + 16.00 g/mol + 1.01 g/mol = 40.00 g/mol

Next, we convert grams of NaOH to moles using the molar mass:

moles of NaOH = \(\frac{23.7 \text{ g}}{40.00 \text{ g/mol}} = 0.5925 \text{ moles}\)

Now, we can substitute the number of moles and the volume of the solution into the molarity formula:

Molarity = \(\frac{0.5925 \text{ moles}}{2.50 \text{ L}} = 0.237 \text{ M}\)

Thus, the molarity of the sodium hydroxide solution is 0.237 M. This calculation illustrates the relationship between mass, moles, and volume in preparing solutions, which is fundamental in chemistry for understanding concentrations and reactions in solution.

Molarity is a crucial concept in chemistry that allows us to calculate unknown quantities in solutions. It is defined as the number of moles of solute per liter of solution, expressed as mol/L or M. When solving problems involving molarity, we can utilize a given amount of solute and conversion factors to isolate the desired quantity. Understanding dimensional analysis and conversion factors is essential, as molarity itself acts as a conversion factor due to its dual-unit nature.

For instance, when we refer to a solution as 5.8 M sodium chloride (NaCl), this indicates that there are 5.8 moles of NaCl in every 1 liter of solution. This relationship can be expressed as a conversion factor:

$$\frac{5.8 \text{ moles NaCl}}{1 \text{ liter solution}}$$

By recognizing molarity as a conversion factor, we can effectively incorporate it into our calculations to determine unknown values in various chemical scenarios. This understanding is foundational for performing accurate and meaningful calculations in chemistry.

To determine the grams of sodium phosphate in a solution, we start with the given information: a 0.550 molar sodium phosphate solution and a volume of 300 milliliters. The molecular mass of sodium phosphate is 163.94 grams per mole. The key to solving this problem lies in understanding the relationship between molarity, volume, and moles.

Molarity (M) is defined as the number of moles of solute per liter of solution, expressed as:

M = \frac{moles}{liters}

From this, we can rearrange the formula to find moles:

moles = liters × molarity

First, we need to convert the volume from milliliters to liters:

300 mL = 0.300 L (since 1 mL = 0.001 L)

Next, we can calculate the moles of sodium phosphate:

moles = 0.300 L × 0.550 mol/L = 0.165 moles

Now that we have the moles, we can convert this to grams using the molecular mass:

grams = moles × molecular mass

grams = 0.165 moles × 163.94 g/mol = 27.0501 grams

When reporting the final answer, we must consider significant figures. The values provided have the following significant figures: 300.0 mL has 4 significant figures, 0.550 M has 3 significant figures, and the molecular mass has 5 significant figures. Therefore, we round our final answer to the least number of significant figures, which is 3:

Final answer: 27.1 grams of sodium phosphate

In summary, when given a volume and molarity, you can find the moles of solute and then convert to grams using the molecular mass. This process highlights the importance of unit conversions and significant figures in chemical calculations.