Which of the following concentration factors can be calculated if the mole fraction and density of aqueous solution of `HCl` are known?

Options

A. Molality
B. Molarity
C. Percent by mass
D. Normality

Answer

To solve the problem of determining which concentration factors can be calculated from the mole fraction and density of an aqueous solution of HCl, we can follow these steps:

### Step 1: Understand the Definitions
1. **Mole Fraction (X)**: The mole fraction of a component in a solution is the ratio of the number of moles of that component to the total number of moles of all components in the solution.
\[ X_{HCl} = \frac{n_{HCl}}{n_{HCl} + n_{H2O}} \]

2. **Density (ρ)**: The density of the solution allows us to convert mass to volume, which is crucial for calculating molarity.

### Step 2: Calculate Moles of Water
Using the density of water (approximately 1 kg/L), we can find the number of moles of water (n2):
\[ n_{H2O} = \frac{W}{M} = \frac{1000 \text{ g}}{18 \text{ g/mol}} \approx 55.55 \text{ moles} \]

### Step 3: Calculate Moles of HCl
From the mole fraction of HCl, we can rearrange the mole fraction formula to find the number of moles of HCl (n1):
\[ X_{HCl} = \frac{n_{HCl}}{n_{HCl} + n_{H2O}} \implies n_{HCl} = X_{HCl} \times (n_{HCl} + n_{H2O}) \]
This can be solved to find \( n_{HCl} \).

### Step 4: Calculate Molality (m)
Molality is defined as the number of moles of solute per kilogram of solvent:
\[ m = \frac{n_{HCl}}{mass_{H2O} \text{ (in kg)}} \]
Since we know \( n_{H2O} \) and its mass, we can calculate molality.

### Step 5: Calculate Molarity (M)
Molarity is defined as the number of moles of solute per liter of solution:
\[ M = \frac{n_{HCl}}{V_{solution}} \]
To find \( V_{solution} \), we use:
\[ V_{solution} = \frac{mass_{solution}}{density_{solution}} \]
Where \( mass_{solution} = mass_{HCl} + mass_{H2O} \).

### Step 6: Calculate Normality (N)
Normality is related to molarity by the formula:
\[ N = M \times n_{factor} \]
For HCl, the n-factor is 1, so:
\[ N = M \]

### Step 7: Calculate Percentage by Mass
Percentage by mass is calculated as:
\[ \text{Percentage by mass} = \frac{mass_{HCl}}{mass_{solution}} \times 100 \]
Where \( mass_{solution} = mass_{HCl} + mass_{H2O} \).

### Conclusion
From the above calculations, we can conclude that knowing the mole fraction and density of the aqueous solution of HCl allows us to calculate:
- Molality
- Molarity
- Normality
- Percentage by mass

Thus, all options are correct.