Question

What is the molarity of a concentrated HBr solution if the solution is \(48.0 \% \mathrm{HBr}\) by mass and has a density of \(1.50 \mathrm{~g} / \mathrm{mL}\) ?

Short answer

The molarity of the HBr solution is approximately 8.86 M.

Step-by-step solution

Convert the Percent Mass to Grams

Given that the solution is 48.0% HBr by mass, this means there are 48.0 g of HBr in every 100 g of the solution.

Calculate the mass of the solution

The density of the solution is given as 1.50 g/mL. Since there are 48 g of HBr in 100g of solution, the volume of solution containing the 48 g of HBr can be calculated as \( \frac{100 g}{1.50 g/mL} \approx 66.7 mL \).

Calculate the molar mass of HBr

The molar mass of HBr (Hydrogen bromide) is 1.01 g/mol for H and 79.904 g/mol for Br, giving a total of 80.91 g/mol.

Calculate the Molarity

Molarity (M) is defined as the number of moles of solute per liter of solution. Thus, the molarity of the HBr solution can be calculated using the formula \( M = \frac{moles of solute}{liters of solution} \). Here, the moles of HBr = \( \frac{48 g}{80.91 g/mol} \approx 0.593 mol \) and the volume of solution = \( \frac{66.7 mL}{1000 mL/L} \approx 0.067 L \). Thus, \( M = \frac{0.593 mol}{0.067 L} \approx 8.86 M \)

Key concepts

Percent Mass

Percent mass is a way to express the concentration of a component in a solution. It indicates how much mass of a substance is present in a given mass of the entire solution. The formula for percent mass is given by:

• \( \text{Percent Mass} = \frac{\text{mass of solute}}{\text{mass of solution}} \times 100\% \)

In the exercise, a concentration of 48.0% by mass for HBr in the solution means there are 48 grams of hydrogen bromide (HBr) in every 100 grams of the solution.
This gives a clear picture of the solution composition without needing to delve into moles or molarity right away. When dealing with liquid solutions, this type of mass concentration provides a straightforward comparison of the solute to the total solution. This approach is particularly useful when the densities of the solute and solvent are fairly similar, as it gives a quick reference of each component's contribution to the total weight.

Molar Mass

The molar mass is the mass of one mole of a given substance and is usually expressed in grams per mole (g/mol).
To calculate the molar mass of a compound, you sum the average atomic masses of all the atoms represented in the compound's chemical formula.

• The atomic mass of hydrogen (H) is approximately 1.01 g/mol.
• The atomic mass of bromine (Br) is approximately 79.904 g/mol.

When added together, the molar mass of hydrogen bromide (HBr) becomes:

• \( 1.01 + 79.904 = 80.914 \mathrm{~g/mol} \)

Understanding molar mass is crucial because it allows conversion between grams and moles, which is a common step while calculating molarity. This can further help in relating the mass of substances used in reactions to the number of molecules involved, providing clarity in both lab settings and theoretical calculations.

Density

Density is a measure of how much mass is contained in a given volume, typically expressed as grams per milliliter (g/mL) or kilograms per liter (kg/L).
It's an important property that can help determine the mass or volume of a substance when the other quantity is known. It's calculated using the formula:

• \( \text{Density} = \frac{\text{mass}}{\text{volume}} \)

In this exercise, the density of the HBr solution is given as 1.50 g/mL. This means for every milliliter of solution, there is 1.50 grams of mass. From this information, one can calculate the volume of a specific mass of solution.
For instance, if you have 100 grams of the solution and know the density, you can find the volume. By using the formula:

• Volume = \( \frac{100 g}{1.50 g/mL} \)

This is how we determined the approximate 66.7 mL volume for 100 g of the solution, which is an essential step for subsequent molarity calculations.

Solution Concentration

Solution concentration refers to the amount of solute that is present in a given quantity of solvent or solution. There are several ways to express concentration. Molarity (M) is one of the most common methods, defined as moles of solute per liter of solution.To find molarity, you can use the formula:

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

In order to calculate the molarity of the HBr solution in the exercise, first find the moles of HBr using its mass and molar mass.
The mass given is 48 g, and the molar mass is 80.91 g/mol. This results in approximately:

• \( \text{Moles of HBr} = \frac{48 \, g}{80.91 \, g/mol} \approx 0.593 \, mol \)

Next, convert the volume of the solution from milliliters to liters (66.7 mL = 0.067 L). Finally, use these values to find molarity:

• \( M = \frac{0.593 \, mol}{0.067 \, L} \approx 8.86 \, M \)

Understanding solution concentration through molarity allows chemists to easily manipulate solutions for reactions, as they know exactly how many moles of solute are present per liter of solution.