Molarity of `HCI(aq)` if its density is 1.17 g/cc

Options

A. 36.5
B. 18.25
C. 32.05
D. 42.1

Explanation

To find the molarity of HCl (aq) with a given density of 1.17 g/cm³, we can follow these steps:

### Step 1: Understand the definition of molarity
Molarity (M) is defined as the number of moles of solute per liter of solution.

### Step 2: Use the density to find mass and volume
The density of the solution is given as 1.17 g/cm³. This means that 1 cm³ (or 1 mL) of the solution has a mass of 1.17 grams.

### Step 3: Convert the volume from cm³ to liters
Since molarity is expressed in moles per liter, we need to convert the volume from cm³ to liters:
\[ 1 \text{ cm}^3 = 1 \text{ mL} = 0.001 \text{ L} \]

### Step 4: Calculate the number of moles of HCl
To find the number of moles of HCl in 1.17 grams, we need to know the molar mass of HCl. The molar mass of HCl is calculated as follows:
- Atomic mass of Hydrogen (H) = 1 g/mol
- Atomic mass of Chlorine (Cl) = 35.5 g/mol
- Molar mass of HCl = 1 + 35.5 = 36.5 g/mol

Now, we can calculate the number of moles of HCl:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} = \frac{1.17 \text{ g}}{36.5 \text{ g/mol}} \]

### Step 5: Calculate the molarity
Now we can substitute the number of moles and the volume of the solution into the molarity formula:
\[ \text{Molarity (M)} = \frac{\text{Number of moles}}{\text{Volume (L)}} \]
Substituting the values we have:
\[ \text{Molarity} = \frac{\frac{1.17}{36.5}}{0.001} = \frac{1.17 \times 1000}{36.5} \]

### Step 6: Perform the calculation
Calculating the above expression:
\[ \text{Molarity} = \frac{1170}{36.5} \approx 32.05 \text{ mol/L} \]

### Final Answer:
The molarity of HCl (aq) is approximately **32.05 mol/L**.

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