Problem 46 - A Complete Resource Book in Chemistry for JEE Main

Question

\(3.65\) grams of \(\mathrm{HCl}\) is dissolved in \(16.2\) grams of water The mole fraction of \(\mathrm{HCl}\) in the resulting solution is (a) \(0.4\) (b) \(0.3\) (c) \(0.2\) (d) \(0.1\)

Step-by-Step Solution

Answer

The mole fraction of HCl in the solution is 0.1, so the answer is (d).

Step 1: Calculate the moles of HCl

First, find the moles of hydrogen chloride (HCl). Use the formula for moles: \(\text{moles} = \frac{\text{mass in grams}}{\text{molar mass}}\). The molar mass of HCl is approximately \(36.5\,\text{g/mol}\). Thus, the moles of HCl is \(\frac{3.65}{36.5} = 0.1\,\text{moles}\).

Step 2: Calculate the moles of water

Next, calculate the moles of water. The molar mass of water (H\(_2\)O) is approximately \(18\,\text{g/mol}\). Therefore, the moles of water is \(\frac{16.2}{18} \approx 0.9\,\text{moles}\).

Step 3: Calculate the total moles in the solution

Add the moles of HCl and the moles of water to find the total moles in the solution: \(0.1 + 0.9 = 1.0\,\text{moles}\).

Step 4: Calculate the mole fraction of HCl

The mole fraction of HCl is found by dividing the moles of HCl by the total moles in the solution: \(\frac{0.1}{1.0} = 0.1\).

Step 5: Determine the correct answer

The calculated mole fraction of HCl is \(0.1\), which corresponds to option (d) in the given choices.

Key Concepts

Moles Calculation

When dealing with chemical reactions and solutions, it's crucial to understand the concept of moles. Moles are a way to express the amount of a substance. One mole contains Avogadro's number of entities, which is approximately \(6.022 \times 10^{23}\). To calculate moles, you'll use the formula:

• \(\text{Moles} = \frac{\text{Mass in grams}}{\text{Molar mass in grams per mole}}\).

In the provided example, the moles of hydrochloric acid (HCl) were calculated using its mass (3.65 grams) and its molar mass (36.5 g/mol). Thus, the calculation \(\frac{3.65}{36.5} = 0.1\) moles of HCl, shows us how many moles of HCl are in the solution.

• This calculation helps in determining the amount of substance you have.
• Knowing the moles is vital for further calculations, such as calculating the mole fraction or concentrations.

Molar Mass

Molar mass plays a pivotal role in converting between mass and moles. It is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). Understanding molar mass is fundamental for any calculation involving substances.

• For instance, the molar mass of HCl is around 36.5 g/mol. This value is obtained from adding the atomic masses of hydrogen (1.008 g/mol) and chlorine (35.453 g/mol).
• Similarly, the molar mass of water (H\(_2\)O) is approximately 18 g/mol, as it is the sum of twice the atomic mass of hydrogen and the atomic mass of oxygen (16 g/mol).

By recognizing and using molar mass, you'll be able to calculate the number of moles from a given mass which is a key step in many chemical calculations.

• This helps us to convert between grams and moles, allowing chemists to measure substances efficiently.
• Having this knowledge makes it possible to engage in precise chemical equations and reactions.

Solution Chemistry

Solution chemistry involves understanding how different substances interact and dissolve in a solvent, forming a solution. The concept of mole fraction is integral to this.

• A solution is made when a solute (e.g., HCl) is dissolved in a solvent (e.g., water).
• The mole fraction is a way to express the concentration of a component in the solution. It is the ratio of the moles of one component to the total number of moles.

In this exercise, we calculated the mole fraction of HCl by taking its moles (0.1 moles) and dividing by the total moles in the solution (1.0 moles total). The resulting mole fraction is \(\frac{0.1}{1.0} = 0.1\).

• Mole fraction is a dimensionless number that helps understand mixture compositions.
• By knowing the mole fractions, we can predict how a solution will behave chemically and physically.

Understanding these calculations ensures effective chemistry practice, allowing you to mix and gauge capabilities of different solutions and substances.