Concentration hydrochloric acid has 38% of HCl by weight with a density of 1.1885 g per ml. Calculate the molarity of the acid. What volume of the acid on dilution to one litre gives finally decimolar solution?

Answer

To solve the problem step by step, we will first calculate the molarity of the hydrochloric acid solution and then determine the volume needed to dilute it to a decimolar solution.

### Step 1: Calculate the Molarity of the Hydrochloric Acid Solution

1. **Identify the Given Values:**
- Weight percentage of HCl (x) = 38%
- Density of the solution (d) = 1.1885 g/mL
- Molecular mass of HCl = 36.5 g/mol

2. **Use the Formula for Molarity:**
The formula for molarity (M) is given by:
\[ M = \frac{x \times d \times 10}{M_m} \]
where:
- \( x \) = weight percentage
- \( d \) = density of the solution in g/mL
- \( M_m \) = molecular mass of the solute in g/mol

3. **Substitute the Values:**
\[ M = \frac{38 \times 1.1885 \times 10}{36.5} \]

4. **Calculate the Molarity:**
- First, calculate the numerator:
\[ 38 \times 1.1885 \times 10 = 451.43 \]
- Now divide by the molecular mass:
\[ M = \frac{451.43}{36.5} \approx 12.37 \text{ M} \]

### Step 2: Calculate the Volume of Acid Needed for Dilution

1. **Identify the Desired Final Concentration:**
- Desired molarity (M2) = 0.1 M (decimolar)
- Final volume (V2) = 1 L = 1000 mL

2. **Use the Dilution Formula:**
The dilution formula is:
\[ M1 \times V1 = M2 \times V2 \]
where:
- \( M1 \) = initial molarity (12.37 M)
- \( V1 \) = volume of concentrated acid needed (unknown)
- \( M2 \) = final molarity (0.1 M)
- \( V2 \) = final volume (1000 mL)

3. **Rearrange the Formula to Solve for V1:**
\[ V1 = \frac{M2 \times V2}{M1} \]

4. **Substitute the Values:**
\[ V1 = \frac{0.1 \times 1000}{12.37} \]

5. **Calculate V1:**
- First, calculate the numerator:
\[ 0.1 \times 1000 = 100 \]
- Now divide by the initial molarity:
\[ V1 = \frac{100}{12.37} \approx 8.08 \text{ mL} \]

### Final Answers:
- The molarity of the hydrochloric acid solution is approximately **12.37 M**.
- The volume of concentrated acid needed to dilute to a decimolar solution is approximately **8.08 mL**.