Molarity: Videos & Practice Problems

Molarity, represented as M=moles of soluteliters of solution, quantifies the concentration of a solute in a solution. It is crucial for calculations involving solutions, where molarity serves as a conversion factor. For instance, a 5.8 M sodium chloride solution contains 5.8 moles of NaCl per liter. Understanding molarity enhances problem-solving skills in chemistry, particularly in stoichiometry and titration calculations, facilitating accurate quantitative analysis of chemical reactions.

Molarity

Molarity, often denoted as 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 measurement 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 can refer to various ways of expressing the amount of solute in a solution, while molarity specifically focuses on the ratio of moles to volume. Understanding molarity is essential for solving problems related to solution preparation and chemical reactions, where precise measurements of reactants are crucial.

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 are calculated, dividing this value by the volume of the solution in liters will yield the molarity. This foundational knowledge of molarity and its calculation is vital for further studies in chemistry, particularly in areas involving solution chemistry and stoichiometry.

Molarity Example 1

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 equation can be expressed as:

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

In this case, we have 23.7 grams of sodium hydroxide dissolved in 2.50 liters of solution. First, we need to convert grams of sodium hydroxide into moles. To do this, we calculate the molar mass of NaOH by adding the atomic masses of its constituent elements: sodium (Na), oxygen (O), and hydrogen (H).

The atomic masses are approximately:

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

Thus, the molar mass of sodium hydroxide is:

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

Next, we convert the mass of sodium hydroxide to moles using the formula:

Moles of NaOH = \(\frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\)

Substituting the values, we have:

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

Now that we have the number of moles, we can calculate the molarity of the solution:

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

Therefore, the molarity of the sodium hydroxide solution is 0.237 M, indicating the concentration of the solution in moles per liter.

Molarity

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 in units of moles per liter (mol/L). When solving problems involving molarity, we can utilize conversion factors to isolate the desired quantity. This approach builds on the principles of dimensional analysis, which is essential for accurate calculations.

For instance, consider a solution with a molarity of 5.8 M (molar). This means there are 5.8 moles of sodium chloride (NaCl) in every 1 liter of the solution. We can express this relationship as a conversion factor:

\[ \frac{5.8 \text{ moles NaCl}}{1 \text{ liter solution}} \]

By using this conversion factor, we can convert between moles of NaCl and liters of solution, facilitating the calculation of unknown amounts in various scenarios. Understanding how to manipulate these units effectively is key to solving molarity-related problems.

Molarity Example 2

To determine the grams of sodium phosphate in a solution, we start with the information provided: 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 equation, we can rearrange it to find moles:

moles = liters \times molarity

First, we need to convert the volume from milliliters to liters. Since 1 milliliter is equal to \(10^{-3}\) liters, we convert 300 milliliters as follows:

300 \, \text{mL} = 300 \times 10^{-3} \, \text{L} = 0.300 \, \text{L}

Next, we can calculate the number of moles of sodium phosphate in the solution:

moles = 0.300 \, \text{L} \times 0.550 \, \text{mol/L} = 0.165 \, \text{moles}

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

grams = moles \times molecular \, mass

grams = 0.165 \, \text{moles} \times 163.94 \, \text{g/mol} = 27.0501 \, \text{grams}

Finally, we need to consider significant figures. The volume (300.0 mL) has 4 significant figures, the molarity (0.550 M) has 3 significant figures, and the molecular mass (163.94 g/mol) has 5 significant figures. The least number of significant figures is 3, so we round our final answer to:

27.1 \, \text{grams}

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.

What volume in (µL) of 0.125 M HBr contains 0.170 moles HBr?

• A. 7.35x10³ μ L
• B. 7.35x10⁶ μ L
• C. 1.36x10³ μ L
• D. 1.36x10⁹ μ L
• E. 1.36x10⁶ μ L

Answer: (E)

Hypernatremia is a medical condition where a patient has high levels of sodium in their blood, and is the result of the body containing too little water. A patient has a measured sodium level of 165 mM. If 30.0 mL of their blood were drawn, what mass (in ng) of sodium would be present?

• A. 1.14x10⁷ ng
• B. 1.14x10⁶ ng
• C. 1.14x10⁸ ng
• D. 4.18x10⁸ ng
• E. 4.18x10⁶ ng

Answer: (C)

2.64 grams of an unknown compound was dissolved in water to yield 150 mL of solution. The concentration of the solution was 0.075 M. What was the molecular weight of the substance?

• A. 190 g/mol
• B. 30 g/mol
• C. 90 g/mol
• D. 230 g/mol
• E. 320 g/mol

Answer: (D)

A solution with a final volume of 750.0 mL was prepared by dissolving 30.00 mL of benzene (C₆H₆, density = 0.8787 g/mL) in dichloromethane. Calculate the molarity of benzene in the solution.

• A. 0.45 M
• B. 0.035 M
• C. 0.35 M
• D. 0.71 M
• E. 0.091 M

Answer: (A)

Here’s what students ask on this topic:

What is molarity and how is it calculated?

Molarity (M) is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The formula for molarity is:

$M=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute}}{\mathrm{liters} \mathrm{of} \mathrm{solution}}$

For example, if you dissolve 1 mole of sodium chloride (NaCl) in 1 liter of water, the molarity of the solution is 1 M. This concept is crucial for various calculations in chemistry, such as stoichiometry and titration.

How do you calculate the molarity of a solution given the moles of solute and volume of solution?

To calculate the molarity of a solution, you need to know the number of moles of solute and the volume of the solution in liters. The formula is:

$M=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute}}{\mathrm{liters} \mathrm{of} \mathrm{solution}}$

For example, if you have 2 moles of solute dissolved in 0.5 liters of solution, the molarity is:

$M=\frac{2 \mathrm{moles}}{0.5 \mathrm{liters}}=4 M$

What is the difference between molarity and concentration?

While molarity and concentration are often used interchangeably, they are not exactly the same. Concentration is a general term that describes the amount of solute in a given amount of solution. Molarity, on the other hand, is a specific type of concentration that measures the number of moles of solute per liter of solution. The formula for molarity is:

$M=\frac{\mathrm{moles} \mathrm{of} \mathrm{solute}}{\mathrm{liters} \mathrm{of} \mathrm{solution}}$

For example, a 1 M solution of NaCl means there is 1 mole of NaCl in 1 liter of solution.

How can molarity be used as a conversion factor in chemical calculations?

Molarity can be used as a conversion factor in chemical calculations because it relates moles of solute to liters of solution. For example, if you have a 5.8 M solution of NaCl, this means there are 5.8 moles of NaCl per liter of solution. You can use this relationship to convert between moles and liters. For instance, if you need to find out how many moles are in 2 liters of this solution, you can set up the following calculation:

$5.8 \mathrm{moles}/\mathrm{liter} \times 2 \mathrm{liters}=11.6 \mathrm{moles}$

This makes molarity a powerful tool for stoichiometry and other quantitative analyses in chemistry.

What are some common applications of molarity in chemistry?

Molarity is widely used in various applications in chemistry, including:

• Stoichiometry: Molarity helps in calculating the amounts of reactants and products in chemical reactions.
• Titration: Molarity is used to determine the concentration of an unknown solution by reacting it with a solution of known molarity.
• Solution Preparation: Molarity is essential for preparing solutions with precise concentrations for experiments.
• Concentration Calculations: Molarity aids in converting between moles and liters, facilitating various concentration-related calculations.

Understanding molarity is crucial for accurate quantitative analysis in these and other chemical processes.