A 7.0 M solution of KOH in water contains 28% by mass of KOH.
What is density of solution in gm/ml ?

Answer

To find the density of a 7.0 M solution of KOH that contains 28% by mass of KOH, we can follow these steps:

### Step 1: Understand the given data
We have:
- Molarity (M) = 7.0 M
- Percentage by mass of KOH = 28%

### Step 2: Assume a mass of the solution
To simplify calculations, we can assume the mass of the solution to be 100 grams. This assumption helps us easily calculate the mass of the solute (KOH).

### Step 3: Calculate the mass of KOH
Since the solution is 28% KOH by mass:
\[ \text{Mass of KOH} = 28\% \text{ of } 100 \text{ g} = 28 \text{ g} \]

### Step 4: Calculate the mass of the solvent (water)
The mass of the solvent (water) can be calculated as:
\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of KOH} = 100 \text{ g} - 28 \text{ g} = 72 \text{ g} \]

### Step 5: Calculate the number of moles of KOH
To find the number of moles of KOH, we need its molar mass. The molar mass of KOH (Potassium Hydroxide) is approximately:
- K = 39 g/mol
- O = 16 g/mol
- H = 1 g/mol

Thus, the molar mass of KOH is:
\[ \text{Molar mass of KOH} = 39 + 16 + 1 = 56 \text{ g/mol} \]

Now, we can calculate the number of moles of KOH:
\[ \text{Number of moles of KOH} = \frac{\text{Mass of KOH}}{\text{Molar mass of KOH}} = \frac{28 \text{ g}}{56 \text{ g/mol}} = 0.5 \text{ moles} \]

### Step 6: Calculate the volume of the solution using molarity
Molarity (M) is defined as:
\[ M = \frac{\text{Number of moles of solute}}{\text{Volume of solution in liters}} \]
Rearranging gives us:
\[ \text{Volume of solution} = \frac{\text{Number of moles of KOH}}{M} = \frac{0.5 \text{ moles}}{7.0 \text{ M}} = 0.0714 \text{ L} \]

### Step 7: Convert volume from liters to milliliters
To convert liters to milliliters, we multiply by 1000:
\[ \text{Volume of solution in mL} = 0.0714 \text{ L} \times 1000 = 71.4 \text{ mL} \]

### Step 8: Calculate the density of the solution
Density is defined as mass per unit volume:
\[ \text{Density} = \frac{\text{Mass of solution}}{\text{Volume of solution}} = \frac{100 \text{ g}}{71.4 \text{ mL}} \approx 1.4 \text{ g/mL} \]

### Final Answer
The density of the KOH solution is approximately **1.4 g/mL**.

---