Molarity and Molality of a solution of a liquid (molecular weight = 50)
in aqueous solution is 9 and 18 respectively. What is the density of solution?

Options

A. 1 g/cc
B. 0.95 g/cc
C. 1.05 g/cc
D. 0.662 g/cc

Answer

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

### Step 1: Write down the known values
- Molarity (M) = 9 mol/L
- Molality (m) = 18 mol/kg
- Molecular Weight (MW) = 50 g/mol

### Step 2: Use the relationship between molality, molarity, and density
The relationship between molality (m), molarity (M), and density (D) can be expressed as:
\[ m = \frac{M \times 1000}{1000 \times D - M \times MW} \]

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation:
\[ 18 = \frac{9 \times 1000}{1000 \times D - 9 \times 50} \]

### Step 4: Simplify the equation
This simplifies to:
\[ 18 = \frac{9000}{1000D - 450} \]

### Step 5: Cross-multiply to eliminate the fraction
Cross-multiplying gives:
\[ 18(1000D - 450) = 9000 \]

### Step 6: Distribute and rearrange the equation
Distributing the left side:
\[ 18000D - 8100 = 9000 \]

### Step 7: Solve for density (D)
Rearranging the equation:
\[ 18000D = 9000 + 8100 \]
\[ 18000D = 17100 \]
\[ D = \frac{17100}{18000} \]
\[ D = 0.95 \text{ g/cm}^3 \]

### Final Answer
The density of the solution is **0.95 g/cm³**.

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