A current of dry air was bubbled through in a bulb containing 26.66g of a n organic substance in 200gms of water, then through a bulb at the same temperature containing pure water and finally through a tube containing fused calcium chloride. The loss in weight of water bulb is `0.0870` gms and gain in weight of `CaCl_(2)` tube is 2.036 gm. Calculate the molecular weight of the organic substance in the solution.

Answer

To calculate the molecular weight of the organic substance in the solution, we will follow these steps:

### Step 1: Understand the problem and gather the data
We have the following data:
- Mass of organic substance (w) = 26.66 g
- Mass of water (W) = 200 g
- Loss in weight of water bulb (Δm_solvent) = 0.0870 g
- Gain in weight of CaCl2 tube (Δm_CaCl2) = 2.036 g

### Step 2: Relate the loss of weight of the water bulb to the gain in weight of the CaCl2 tube
Using the relationship from Raoult's law, we can write:
\[ \frac{\Delta m_{\text{solvent}}}{\Delta m_{\text{CaCl2}}} = \frac{w}{M} \div \frac{w}{M} + \frac{W}{M_w} \]
Where:
- \(M\) = molecular weight of the organic substance
- \(M_w\) = molecular weight of water = 18 g/mol

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ \frac{0.0870}{2.036} = \frac{26.66}{M} \div \left(\frac{26.66}{M} + \frac{200}{18}\right) \]

### Step 4: Simplify the equation
This can be rearranged to:
\[ \frac{0.0870}{2.036} = \frac{26.66}{M} \div \left(\frac{26.66 + \frac{200M}{18}}{M}\right) \]
This simplifies to:
\[ \frac{0.0870}{2.036} = \frac{26.66}{26.66 + \frac{200M}{18}} \]

### Step 5: Cross-multiply to solve for M
Cross-multiplying gives:
\[ 0.0870 \left(26.66 + \frac{200M}{18}\right) = 2.036 \cdot 26.66 \]
Expanding and simplifying:
\[ 0.0870 \cdot 26.66 + \frac{0.0870 \cdot 200M}{18} = 2.036 \cdot 26.66 \]
Calculating the constants:
\[ 2.036 \cdot 26.66 \approx 54.24 \]
Thus, we have:
\[ 2.32 + \frac{1.74M}{18} = 54.24 \]

### Step 6: Isolate M
Rearranging gives:
\[ \frac{1.74M}{18} = 54.24 - 2.32 \]
Calculating the right-hand side:
\[ \frac{1.74M}{18} = 51.92 \]
Multiplying through by 18:
\[ 1.74M = 51.92 \cdot 18 \]
Calculating:
\[ 1.74M = 934.56 \]
Thus:
\[ M = \frac{934.56}{1.74} \approx 537.75 \]

### Step 7: Final calculation
The molecular weight of the organic substance is approximately:
\[ M \approx 53.75 \text{ g/mol} \]