How many millilitree of `6.0` M hydrochloric acid should be used to prepare 150 ml of 0.30 M HCl solution ?

Options

A. `3.0`
B. `7.5`
C. `9.3`
D. `30`

Answer

To solve the problem of how many milliliters of 6.0 M hydrochloric acid (HCl) are needed to prepare 150 mL of a 0.30 M HCl solution, we can use the dilution formula:

\[ M_1 V_1 = M_2 V_2 \]

Where:
- \( M_1 \) = initial molarity (6.0 M)
- \( V_1 \) = volume of the concentrated solution we need to find (in mL)
- \( M_2 \) = final molarity (0.30 M)
- \( V_2 \) = final volume (150 mL)

### Step-by-Step Solution:

1. **Identify the known values:**
- \( M_1 = 6.0 \, \text{M} \)
- \( M_2 = 0.30 \, \text{M} \)
- \( V_2 = 150 \, \text{mL} \)

2. **Set up the dilution equation:**
\[ M_1 V_1 = M_2 V_2 \]

3. **Substitute the known values into the equation:**
\[ 6.0 \, \text{M} \cdot V_1 = 0.30 \, \text{M} \cdot 150 \, \text{mL} \]

4. **Calculate the right-hand side:**
\[ 0.30 \, \text{M} \cdot 150 \, \text{mL} = 45 \, \text{M mL} \]

5. **Now, substitute this value back into the equation:**
\[ 6.0 \, \text{M} \cdot V_1 = 45 \, \text{M mL} \]

6. **Solve for \( V_1 \):**
\[ V_1 = \frac{45 \, \text{M mL}}{6.0 \, \text{M}} = 7.5 \, \text{mL} \]

### Final Answer:
Thus, you need **7.5 mL** of 6.0 M hydrochloric acid to prepare 150 mL of a 0.30 M HCl solution.