Molarity and molality of a solution of an liquid (mol.mass `=50`) in aqueous solution is `9` and 10 respectively. what is the density of solution ?

Options

A. ` 1g//"cc"`
B. ` 0.95 g// "cc"`
C. ` 1.05 g//"cc"`
D. ` 1.35 g//"cc"`

Answer

To find the density of the solution given the molarity and molality, we can follow these steps:

### Step 1: Write down the known values
- Molarity (M) = 9 mol/L
- Molality (m) = 10 mol/kg
- Molar mass (MM) = 50 g/mol

### Step 2: Use the relationship between molality and molarity
The relationship between molality (m) and molarity (M) is given by the formula:

\[ m = \frac{1000 \times M}{1000 \times d - M \times MM} \]

Where:
- \(d\) is the density of the solution in g/mL.

### Step 3: Substitute the known values into the formula
Substituting the known values into the equation:

\[ 10 = \frac{1000 \times 9}{1000 \times d - 9 \times 50} \]

### Step 4: Simplify the equation
First, simplify the right side:

\[ 10 = \frac{9000}{1000d - 450} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:

\[ 10(1000d - 450) = 9000 \]

### Step 6: Distribute and rearrange the equation
Distributing the left side:

\[ 10000d - 4500 = 9000 \]

Now, add 4500 to both sides:

\[ 10000d = 13500 \]

### Step 7: Solve for density (d)
Now, divide both sides by 10000:

\[ d = \frac{13500}{10000} = 1.35 \text{ g/mL} \]

### Final Answer
The density of the solution is **1.35 g/mL**.

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