An aqueous solution of concentrated hydrobromic acid contains `48%` HBr by mass. If the density of the solution is `1.50g//L`, what is its concentration :

Options

A. `11.4 "mol"//L`
B. `8.9 "mol"//L`
C. `5.9 "mol"//L`
D. `18.5 "mol"//L`

Explanation

To find the concentration of the hydrobromic acid (HBr) solution, we can follow these steps:

### Step 1: Understand the Given Information
We have:
- Mass percentage of HBr = 48%
- Density of the solution = 1.50 g/mL

### Step 2: Convert Density to g/L
Since the density is given in g/mL, we can convert it to g/L:
\[ 1.50 \, \text{g/mL} = 1.50 \times 1000 \, \text{g/L} = 1500 \, \text{g/L} \]

### Step 3: Calculate the Mass of HBr in 1 Liter of Solution
Using the mass percentage, we can find the mass of HBr in 1 liter of the solution:
\[ \text{Mass of HBr} = \text{Mass percentage} \times \text{Total mass of solution} \]
The total mass of the solution (1 L) is 1500 g (from the density).
\[ \text{Mass of HBr} = 0.48 \times 1500 \, \text{g} = 720 \, \text{g} \]

### Step 4: Calculate the Molar Mass of HBr
The molar mass of HBr can be calculated as follows:
- Molar mass of H = 1 g/mol
- Molar mass of Br = 80 g/mol
\[ \text{Molar mass of HBr} = 1 + 80 = 81 \, \text{g/mol} \]

### Step 5: Calculate the Number of Moles of HBr
Now, we can calculate the number of moles of HBr in the solution:
\[ \text{Number of moles of HBr} = \frac{\text{Mass of HBr}}{\text{Molar mass of HBr}} \]
\[ \text{Number of moles of HBr} = \frac{720 \, \text{g}}{81 \, \text{g/mol}} \approx 8.89 \, \text{mol} \]

### Step 6: Calculate the Concentration in mol/L
Since we have the number of moles in 1 liter of solution, the concentration (C) is:
\[ C = \text{Number of moles of HBr} = 8.89 \, \text{mol/L} \]

### Final Answer
The concentration of the hydrobromic acid solution is approximately **8.89 mol/L**.

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