Question

How many moles of \(\mathrm{H}^{+}\) ions are present in each of the following aqueous solutions? (a) \(1.4 \mathrm{~mL}\) of \(0.75 \mathrm{M}\) hydrobromic acid (b) \(2.47 \mathrm{~mL}\) of \(1.98 \mathrm{M}\) hydriodic acid (c) \(395 \mathrm{~mL}\) of \(0.270 \mathrm{M}\) nitric acid

Short answer

0.00105 moles, 0.0048906 moles, 0.10665 moles

Step-by-step solution

- Understand the relationship between molarity, volume, and moles

Molarity (M) is defined as moles of solute per liter of solution. To find the number of moles, use the formula: \[ \text{Moles} = \text{Molarity} \times \text{Volume (in liters)} \]

- Convert the given volume to liters

Volumes are given in milliliters (mL), and we need to convert them to liters (L) since molarity is in moles per liter. Use the conversion: \[ 1 \text{ mL} = 0.001 \text{ L} \]

- Calculate moles for each solution

(a) Hydrobromic acid: Volume = 1.4 mL = 0.0014 L, Molarity = 0.75 M\[ \text{Moles} = 0.75 \text{ M} \times 0.0014 \text{ L} = 0.00105 \text{ moles} \] (b) Hydriodic acid: Volume = 2.47 mL = 0.00247 L, Molarity = 1.98 M\[ \text{Moles} = 1.98 \text{ M} \times 0.00247 \text{ L} = 0.0048906 \text{ moles} \] (c) Nitric acid: Volume = 395 mL = 0.395 L, Molarity = 0.270 M\[ \text{Moles} = 0.270 \text{ M} \times 0.395 \text{ L} = 0.10665 \text{ moles} \]

Key concepts

molarity

Molarity is a fundamental concept in chemistry, especially when dealing with solutions. It measures the concentration of a solute in a given volume of solution, using the formula: \(M = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}} \). This means that molarity (M) tells you how many moles of a substance are present in one liter of a solution. For example, a solution with 1 mole of table salt in 1 liter of water has a molarity of 1 M (1 mol/L). Molarity is essential in stoichiometry calculations and helps in predicting how different solutions will react with each other. Knowing the molarity of a solution allows you to determine the amount of solute present, which is the key to solving many chemistry problems.

volume conversion

Volume conversion is critical when working with solutions, especially because molarity is based on liters. Given volumes often come in milliliters (mL), which must be converted to liters (L). Take note that 1 liter is equivalent to 1,000 milliliters. Therefore, to convert milliliters to liters, you simply multiply the number of milliliters by 0.001. For example:

• 1 mL = 0.001 L
• 50 mL = 50 × 0.001 = 0.05 L

By ensuring the volume is in liters, you can correctly use the molarity formula: \(\text{Moles} = \text{Molarity} \times \text{Volume in liters} \). Let's use the example from the exercise:

• 1.4 mL = 1.4 × 0.001 = 0.0014 L
• 2.47 mL = 2.47 × 0.001 = 0.00247 L
• 395 mL = 395 × 0.001 = 0.395 L

Once the conversion is complete, you can easily calculate the number of moles using the molarity formula.

aqueous solutions

An aqueous solution is simply a solution where water is the solvent. In other words, substances are dissolved in water to form these solutions. Water is a universal solvent, which means it can dissolve many compounds and is commonly used in chemistry. Aqueous solutions are particularly important in understanding how different substances react in water. Many reactions, such as acid-base reactions or ionic dissociations, happen in aqueous solutions. For example, acids like hydrobromic acid (HBr), hydriodic acid (HI), and nitric acid (HNO3) dissolve in water to release \(\mathrm{H}^{+}\) ions, contributing to the characteristics of stomach acid. To summarize, when dealing with problems involving aqueous solutions:

• Determine the substance's molarity.
• Convert the given volume to liters.
• Use the molarity formula to find the number of moles desired.

Follow these steps, and you'll be able to navigate calculations involving aqueous solutions effectively.