The concentration of a solution is 8% (w/w) and 10% (w/v) Calculate density (in gm/ml) of solution?

Answer

To solve the problem of calculating the density of a solution with given concentrations of 8% (w/w) and 10% (w/v), we can follow these steps:

### Step 1: Understand the Definitions
- **Weight/Weight (w/w)**: This means the mass of solute per mass of solution, expressed as a percentage.
- **Weight/Volume (w/v)**: This means the mass of solute per volume of solution, expressed as a percentage.

### Step 2: Calculate the Mass of Solute and Mass of Solution
Given that the solution is 8% (w/w):
- This means that in 100 grams of solution, there are 8 grams of solute.
- Therefore, the mass of the solute (m_solute) = 8 grams.
- The mass of the solution (m_solution) = 100 grams.

### Step 3: Calculate the Volume of the Solution
Given that the solution is 10% (w/v):
- This means that in 100 mL of solution, there are 10 grams of solute.
- We already know that the mass of the solute is 8 grams.
- Using the formula for w/v:
\[ \text{w/v} = \frac{\text{mass of solute}}{\text{volume of solution}} \times 100 \]
We can rearrange this to find the volume:
\[ 10 = \frac{8}{V} \times 100 \]
Solving for V:
\[ V = \frac{8 \times 100}{10} = 80 \text{ mL} \]

### Step 4: Calculate the Density of the Solution
Density (d) is defined as mass per unit volume:
\[ d = \frac{\text{mass of solution}}{\text{volume of solution}} \]
Substituting the values we have:
\[ d = \frac{100 \text{ grams}}{80 \text{ mL}} = 1.25 \text{ grams/mL} \]

### Final Answer
The density of the solution is **1.25 grams/mL**.

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