Question

How many moles are present in \(2.5\) litre of \(0.2 \mathrm{M}\) \(\mathrm{H}_{2} \mathrm{SO}_{4}{ }_{4} ?\) (a) \(0.25\) (b) \(0.5\) (c) \(0.75\) (d) \(0.2\)

Short answer

The number of moles present is 0.5; option (b).

Step-by-step solution

Understanding Molarity

Molarity (M) is a measure of the concentration of a solution, in terms of the amount of substance in a specific volume of solution. It is expressed as moles of solute per liter of solution. The formula for calculating molarity is: \[ M = \frac{n}{V} \] where \( n \) is the number of moles of solute and \( V \) is the volume of the solution in liters.

Identifying Given Values

We are given the molarity \( M = 0.2 \) M and the volume \( V = 2.5 \) liters of the \( \text{H}_2\text{SO}_4 \) solution. We need to find the number of moles \( n \).

Using the Molarity Formula

Rearrange the molarity formula to solve for the number of moles: \[ n = M \times V \]. Substitute the given values into the equation: \[ n = 0.2 \ \text{M} \times 2.5 \ \text{L} \].

Performing the Calculation

Calculate the number of moles: \[ n = 0.2 \times 2.5 = 0.5 \] moles. Thus, there are 0.5 moles present in 2.5 liters of 0.2 M \( \text{H}_2\text{SO}_4 \).

Key concepts

Calculating moles

Calculating the number of moles in a solution is an essential skill in chemistry. Moles represent a count of particles, whether atoms, molecules, or ions, in a sample. This concept makes chemistry calculations more manageable because substances react according to the number of moles.
To determine the moles, one needs a clear understanding of its relationship with molarity and volume. The number of moles in a solution can be calculated using the formula:

• Molarity (M): the concentration of a solution given as moles per liter (mol/L).
• Volume (V): the space the solution occupies, measured in liters.

The simple formula derived from the definition of molarity is: \[ n = M \times V \] where

• \( n \): the number of moles of the solute,
• \( M \): the molarity or concentration of the solution in moles per liter,
• \( V \): volume in liters.

By knowing the concentration and the amount of the solution prepared, the number of moles can easily be calculated. For example, using the provided formula, if you have a solution with a molarity of 0.2 M and a volume of 2.5 liters, the number of moles would be 0.5, as calculated by multiplying the given values (0.2 * 2.5). This allows us to practically use theoretical chemistry in real-world scenarios.

Concentration of solutions

Understanding the concentration of solutions is crucial for predicting how substances will behave in various chemical reactions. The concentration describes how much solute is dissolved in a solution, allowing chemists to determine how substances interact. One of the most common ways to express concentration is molarity.
Molarity (M) is defined as the number of moles of solute per liter of solution. It provides a straightforward means to express the amount of a dissolved substance in a solution and is commonly used because it directly relates to chemical equations and reactions.

• A high molarity means there is a large amount of solute in the solution, which often results in faster reaction rates and more product formation in chemical processes.
• Solutions with a low molarity have less solute per unit volume. This often results in slower reactions due to fewer collisions between particles.

For instance, if you have an acid solution with a molarity of 0.2 M, it informs that every liter of this solution contains 0.2 moles of acid. This degree of concentration is particularly important when mixing solutions to ensure desired chemical properties and reactions.

Acid solutions

Acid solutions play a pivotal role in chemistry due to their unique properties, which are primarily due to the hydrogen ions (\( H^+ \)) they release into a solution. Commonly encountered acids in both laboratory and real-world scenarios include sulfuric acid (\( \text{H}_2 ext{SO}_4 \)), which is a strong acid widely used in industrial and laboratory applications.
A solution's acidity, or acid strength, directly relates to the concentration of hydrogen ions present. Sulfuric acid, as a typical example, dissociates in water to release hydrogen ions, thus making the solution acidic. The extent of dissociation, and thus the solution's strength or acidity, is often expressed in terms of its molarity.

• Strong acids like \( \text{H}_2 ext{SO}_4 \) completely dissociate in water, providing a higher concentration of hydrogen ions.
• Weak acids dissociate partially, resulting in fewer hydrogen ions in solution.

Understanding acid molarity is vital when dealing with reactions in a laboratory setting, as it affects the pH, reaction rates, and solubility of other compounds. Handling acid solutions safely requires knowledge of their concentration, emphasizing how imperative it is to calculate molarity correctly.