Ask a New Question
Menu

How to calculate molar mass of a volatile liquid given its mass, temperature and pressure values?

1 answer

To calculate the molar mass of a volatile liquid, you typically use the ideal gas law in conjunction with the mass of the liquid, as well as its measured temperature and pressure values. Here's how you can do it step by step:

Step-by-Step Calculation:

  1. Gather Required Information:

    • Mass of the volatile liquid (m) in grams.
    • Temperature (T) in Kelvin (K).
    • Pressure (P) in atmospheres (atm) or other suitable units.

  2. Convert Temperature to Kelvin (if not already given in K): \[ T(K) = T(°C) + 273.15 \]

  3. Use the Ideal Gas Law: The ideal gas law is given by: \[ PV = nRT \] where:

    • \( P \) = pressure in atm (use proper conversion if in different units)
    • \( V \) = volume of the gas in liters
    • \( n \) = number of moles of gas
    • \( R \) = universal gas constant (\( R = 0.0821 , \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol}) \))
    • \( T \) = temperature in Kelvin

  4. Rearrange the Ideal Gas Law to solve for the number of moles (\( n \)): \[ n = \frac{PV}{RT} \]

  5. Measure or Determine Volume: You need to know the volume (\( V \)) of the vapor produced at the given conditions. This might be an experimental measurement or calculation based on the setup. Ensure it is expressed in liters.

  6. Calculate the Number of Moles: Substitute your values of \( P \), \( V \), \( R \), and \( T \) into the equation for \( n \): \[ n = \frac{P \cdot V}{R \cdot T} \]

  7. Calculate Molar Mass (\( M \)): Molar mass is calculated by dividing the mass of the volatile liquid by the number of moles: \[ M = \frac{m}{n} \] where \( m \) is the mass of the volatile liquid in grams and \( n \) is the number of moles calculated in the previous step.

Example Calculation:

Assume you have:

  • Mass of the liquid (\( m \)) = 10 g
  • Temperature (\( T \)) = 25°C
  • Pressure (\( P \)) = 1 atm
  • Volume of gas (\( V \)) = 0.5 L

Convert Temperature: \[ T(K) = 25 + 273.15 = 298.15 , K \]

Calculate Moles: \[ n = \frac{PV}{RT} = \frac{(1 , \text{atm}) \cdot (0.5 , \text{L})}{(0.0821 , \text{L} \cdot \text{atm} / (\text{K} \cdot \text{mol})) \cdot (298.15 , K)} \approx 0.0202 , \text{mol} \]

Calculate Molar Mass: \[ M = \frac{m}{n} = \frac{10 , \text{g}}{0.0202 , \text{mol}} \approx 495.5 , \text{g/mol} \]

This final value gives you the molar mass of the volatile liquid. Adjust your experiments and considerations based on actual conditions and accuracy requirements for your calculations.