Surface Tension

Step 1: Determine the pressure inside a soap bubble in vacuum.
For a soap bubble, there are two liquid-air interfaces. The excess pressure inside a soap bubble compared to the outside pressure is given by: where is the surface tension of the soap solution and is the radius of the bubble.
Since the bubbles are kept in vacuum, the outside pressure . Therefore, the pressure inside the bubble is: Step 2: Apply the ideal gas law to the air inside the bubble.
Assume the air inside the soap bubble behaves as an ideal gas. The ideal gas law is: where is the pressure, is the volume, is the number of moles, is the ideal gas constant, and is the absolute temperature.
The number of moles can be expressed as , where is the mass of the gas and is the molar mass of the gas. So, the ideal gas law becomes: We want to find the ratio of masses, so rearrange this equation to solve for : Step 3: Substitute the pressure and volume of the bubble into the mass equation.
The volume of a spherical bubble is .
Substitute and into the equation for : (Note: Using for temperature to avoid confusion with surface tension ).
Simplify the expression: Since the bubbles are at a constant temperature, and (surface tension), (molar mass of air), and (gas constant) are constants, the term in the parenthesis is a constant. Let's call it . This shows that the mass of air inside the bubble is directly proportional to the square of its radius.
Step 4: Determine the ratio of masses for bubbles A and B.
For bubble A with radius and mass : For bubble B with radius and mass : The ratio of their masses is: Thus, the ratio of masses is . The final answer is .