Final answer:
Using the proportion of pressure and volume from the tank and balloons, and assuming constant temperature, the tank can fill 20 balloons with helium, which is the correct answer, option c) 20.
Step-by-step explanation:
To determine how many balloons can be filled with helium from the tank, we must first understand the concept of gas laws that relate the volume, pressure, and number of moles of a gas. The number of moles of helium in the tank can be calculated using the ideal gas law, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the universal gas constant, and T is the temperature. Since temperature and the gas constant are not provided, we will assume they are constant and therefore, can be canceled out when we set up the proportion between conditions in the tank and in the balloons.
Using the provided pressures and volumes for the tank and balloons we can set up a proportion:
(Pressure of Helium in Tank x Volume of Helium in Tank) = Number of Balloons x (Pressure Required for one Balloon x Volume of one Balloon)
So, we calculate the number of balloons as follows:
Number of Balloons = (15,200 kPa x 0.150 m³) / (101 kPa x 0.113 m³) = 20.2124
Since we can't fill a partial balloon, the number of balloons that can be filled is 20.
The correct answer is option c) 20.