In a Victor Meyer's determination of molecular mass, 0.15 g of a volatile substance displaced 31.64 mL of air at 25°C and 755 mm pressure. Calculate the molecular mass of the substance.

Answer

To calculate the molecular mass of the volatile substance using Victor Meyer's method, we will follow these steps:

### Step 1: Convert the given temperature from Celsius to Kelvin
The temperature given is 25°C. To convert this to Kelvin, we use the formula:
\[ T(K) = T(°C) + 273.15 \]
So,
\[ T = 25 + 273.15 = 298.15 \, K \]

### Step 2: Use the ideal gas law to find the volume of air displaced at STP
We know that at STP (Standard Temperature and Pressure), the temperature is 273 K and the pressure is 760 mmHg. We can use the formula derived from the ideal gas law:
\[ \frac{P_1 V_1}{T_1} = \frac{P_2 V_2}{T_2} \]
Where:
- \( P_1 = 760 \, mmHg \) (STP pressure)
- \( V_1 = ? \) (volume at STP)
- \( T_1 = 273 \, K \) (STP temperature)
- \( P_2 = 755 \, mmHg \) (given pressure)
- \( V_2 = 31.64 \, mL \) (given volume)
- \( T_2 = 298.15 \, K \) (temperature at which the volume is measured)

Rearranging the equation to solve for \( V_1 \):
\[ V_1 = \frac{P_2 V_2 T_1}{P_1 T_2} \]
Substituting the values:
\[ V_1 = \frac{755 \, mmHg \times 31.64 \, mL \times 273 \, K}{760 \, mmHg \times 298.15 \, K} \]
Calculating this gives:
\[ V_1 \approx 28.79 \, mL \]

### Step 3: Calculate the molecular mass of the substance
According to Victor Meyer's method, the molecular mass can be calculated using the formula:
\[ M = \frac{m \times V_{STP}}{V_{displaced} \times 22400} \]
Where:
- \( m = 0.15 \, g \) (mass of the substance)
- \( V_{STP} = 22400 \, mL \) (molar volume at STP)
- \( V_{displaced} = 28.79 \, mL \) (volume of air displaced at STP)

Substituting the values:
\[ M = \frac{0.15 \, g \times 22400 \, mL}{28.79 \, mL} \]
Calculating this gives:
\[ M \approx 116.70 \, g/mol \]

### Final Answer
The molecular mass of the substance is approximately **116.70 g/mol**.

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