Question

An aqueous solution contains \(3.75 \% \mathrm{NH}_{3}\) (ammonia) by mass. The density of the aqueous ammonia is 0.979 \(\mathrm{g} / \mathrm{mL}\). What is the molarity of \(\mathrm{NH}_{3}\) in the solution?

Short answer

The molarity of NH3 in the solution is approximately 2.156 M.

Step-by-step solution

Determine the mass of the solution

To find the mass of the solution, assume we have 100 g of the solution. In this case, the solution contains 3.75 g of \(\mathrm{NH}_{3}\) and 96.25 g of water (since 100 g - 3.75 g = 96.25 g).

Calculate the volume of the solution

Since we know the density of the solution is 0.979 \(\text{g/mL}\), we can calculate its volume using the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). Thus, \( \text{Volume} = \frac{100 \, \text{g}}{0.979 \, \text{g/mL}} \approx 102.14 \, \text{mL} \).

Convert the volume to liters

Before calculating the molarity, convert the volume from milliliters to liters because molarity is expressed in moles per liter. \(102.14 \, \text{mL} \) is \(0.10214 \, \text{L} \).

Calculate the number of moles of NH3

Determine the moles of \(\mathrm{NH}_{3}\) using its molar mass. The molar mass of \(\mathrm{NH}_{3}\) is approximately 17.03 \(\text{g/mol}\). So, the number of moles is \( \frac{3.75 \, \text{g}}{17.03 \, \text{g/mol}} \approx 0.2202 \, \text{moles} \).

Calculate the molarity

Molarity is defined as the number of moles of solute per liter of solution. Therefore, the molarity of \(\mathrm{NH}_{3}\) is \( \frac{0.2202 \, \text{moles}}{0.10214 \, \text{L}} \approx 2.156 \, \text{M} \).

Key concepts

Density Calculation

Understanding density is fundamental in chemistry, especially when dealing with solutions. When we say that the density of a substance is 0.979 g/mL, it means that every milliliter of this substance weighs 0.979 grams. Calculating the density involves a simple formula:

• Density = Mass/Volume

In our example, the mass of the solution is assumed to be 100 grams. Therefore, to find the volume, we rearrange the formula to Volume = Mass/Density. Plugging the values in, the volume of the solution becomes approximately 102.14 mL. This step is crucial because molarity calculations require knowing the volume of the solution in liters. Converting this volume to liters, we get 0.10214 L, setting us up for the next steps.

Molar Mass

The molar mass of a compound tells us the mass of a mole of its molecules. It is usually expressed in grams per mole (g/mol). For \(\mathrm{NH}_3\), the molar mass can be calculated by adding the atomic masses of nitrogen (N) and hydrogen (H) atoms.

• Nitrogen: roughly 14.01 g/mol
• Hydrogen: 1.008 g/mol × 3 = 3.024 g/mol

Together, they sum up to approximately 17.03 g/mol. Knowing the molar mass is key when calculating how many moles of a substance are present in a given mass. In the exercise, we have 3.75 g of \(\mathrm{NH}_3\). Dividing this by the molar mass (17.03 g/mol), we find that the solution contains about 0.2202 moles of \(\mathrm{NH}_3\). This is an important figure as it directly relates to chemical concentration.

Aqueous Solution

Aqueous solutions are mixtures where water is the solvent. In these solutions, various substances, known as solutes, are dissolved in water. Understanding this concept is key to grasping the nature of many chemical reactions, as water is a universal solvent due to its polarity and ability to dissolve a wide range of substances. In the given exercise, \(\mathrm{NH}_3\) is dissolved in water, making it an aqueous solution. This means that every part of the solution is uniformly composed of \(\mathrm{NH}_3\) and water. Knowing this helps us make accurate calculations of molarity because it tells us that the properties of the solution, like density, are tied directly to its composition.

Chemical Concentration

Chemical concentration refers to the amount of solute present in a given quantity of solution. One of the most common units for expressing concentration in chemistry is molarity, represented by \(M\). Molarity is defined as the number of moles of solute divided by the volume of the solution in liters. It can be visualized as:

• Molarity (M) = Moles of solute / Volume of solution in liters

In our example, the molarity of \(\mathrm{NH}_3\) was calculated by taking the number of moles of \(\mathrm{NH}_3\) (0.2202 moles) and dividing it by the volume of the solution in liters (0.10214 L). Doing this gives us around 2.156 M. Knowing the concentration like this is crucial, especially when preparing solutions for reactions, as it tells you how much of each component you'll have in your chemical processes.