What is molarity of a solution of HCl which contains 49% by weight of solute and specific gravity is 1.41

Options

A. `15.25`
B. `16.75`
C. `18.92`
D. `20.08`

Answer

To find the molarity of a solution of HCl that contains 49% by weight of solute and has a specific gravity of 1.41, we can follow these steps:

### Step 1: Understand the Given Information
- Percentage by weight of HCl = 49%
- Specific gravity of the solution = 1.41

### Step 2: Calculate the Density of the Solution
Since specific gravity is the ratio of the density of a substance to the density of water, we can calculate the density of the HCl solution:
- Density of water = 1 g/mL
- Density of HCl solution = Specific gravity × Density of water
- Density of HCl solution = 1.41 × 1 g/mL = 1.41 g/mL

### Step 3: Calculate the Mass of HCl in 1 mL of Solution
Using the percentage by weight, we can find the mass of HCl in 1 mL of the solution:
- Mass of HCl in 1 mL = Density × Volume × Percentage by weight
- Mass of HCl in 1 mL = 1.41 g/mL × 1 mL × (49/100)
- Mass of HCl in 1 mL = 1.41 g × 0.49 = 0.6909 g

### Step 4: Calculate the Mass of HCl in 1000 mL of Solution
To find the mass of HCl in 1 liter (1000 mL) of solution:
- Mass of HCl in 1000 mL = Mass of HCl in 1 mL × 1000
- Mass of HCl in 1000 mL = 0.6909 g × 1000 = 690.9 g

### Step 5: Calculate the Number of Moles of HCl
To find the number of moles of HCl, we use the molar mass of HCl:
- Molar mass of HCl = 1 (H) + 35.5 (Cl) = 36.5 g/mol
- Number of moles of HCl = Mass of HCl / Molar mass of HCl
- Number of moles of HCl = 690.9 g / 36.5 g/mol ≈ 18.9 mol

### Step 6: Calculate the Molarity of the Solution
Molarity (M) is defined as the number of moles of solute per liter of solution:
- Molarity = Number of moles of HCl / Volume of solution in liters
- Molarity = 18.9 mol / 1 L = 18.9 M

### Final Answer
The molarity of the HCl solution is approximately **18.9 M**.

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