Question

A cylindrical tank of diameter 20 cm and height 40 cm is half filled with methanol at 27°C. The methanol is lost to air surrounding the tank by evaporation. Determine the rate of loss of methanol in gm/sec for the following data

P= pressure = 760 mm Hg
Diffusion coefficient of methanol in air= 0.15 cm2/sec and
Vapor pressure of methanol at 27°C = 160 mm Hg

You may assume that negligible methanol is present in the air outside the tank and that methanol behaves like an ideal gas. Finally, determine approximately the time taken for the liquid level in the tank to fall by 1 cm.

Answer 1

The question involves finding the rate of evaporation of methanol and the time for the liquid level to fall by 1 cm using principles of gaseous diffusion. Calculations are based on the given vapor pressure of methanol, diffusion coefficient, and tank dimensions, but missing the density of methanol, which is necessary to provide a numerical answer.

Step-by-step explanation:

The question is asking how to calculate the rate of evaporation (loss) of methanol in a cylindrical tank and to find out how much time it would take for the methanol level to fall by 1 cm. To solve this, we need to apply the principles of gaseous diffusion and use Graham's law of effusion.

The rate of evaporation can be estimated using the formula:

Rate = (P1 - P2) * D / d

where:

• P1 is the vapor pressure of methanol inside the tank.
• P2 is the partial pressure of methanol is negligible in the air, assumed to be 0 mm Hg.
• D is the diffusion coefficient of methanol in air.
• d is the distance over which diffusion occurs, which is the diameter of the tank in this case.

However, it is essential to note that additional information is required to perform this calculation, such as the density of methanol at the given temperature to convert the rate from cm³/sec to gm/sec and to further calculate the time taken for the liquid level to fall by 1 cm.

Without the density value, we cannot provide an exact numerical answer to the question. It is suggested that the student reviews the course material or experiments to obtain the missing value to complete the problem.