JCE Classroom Activities are edited by Erica K. Jacobsen
Instructor Information
JCE Classroom Activity: #100
How Heavy Is a Balloon? Using the Ideal Gas Law
Bettie Obi Johnson* and Henry Van Milligan University of South Carolina Lancaster, 476 Hubbard Dr., Lancaster, SC 29720; *
[email protected] In this Activity, students explore buoyancy with helium-filled Mylar balloons. They use the ideal gas law to predict the mass of the balloon if it were empty, compare it to the actual mass of the empty balloon, and discuss experimental sources of error. The buoyant force on a helium-filled balloon is an upward force equal in magnitude to the weight of the air displaced by the balloon (1, 2). Students attach weights to a helium-filled Mylar balloon until it has neutral buoyancy. The upward force is then equal to the mass of the empty balloon, the helium inside, and the attached weights (eq 1). Students then use this relationship along with the ideal gas law (eq 2) and an ellipsoid function (eq 3) to solve for the mass of the empty balloon. mass of empty balloon = mass of displaced air - mass of helium - mass of weights (1) m = (P V M) / (R T)
(2)
Vellipsoid= 4/3(πa2b)
(3)
In eq 2, m = mass of displaced air (g), P = current barometric pressure (atm), V = volume of the balloon (L), M = weighted average molar mass of air (28.97 g/mol), R = ideal gas constant [0.0821 (L atm) / (mol K)], and T = temperature (K). Balloon volume can be measured by various methods (3, 4). An ellipsoid function (eq 3) provides relatively accurate results in a simple manner without deflating the balloon. In eq 3, a and b are equal to half of the diameter and half of the width of the balloon respectively, as illustrated on the Student Activity. The mass of helium inside the balloon is determined in a similar manner, using the molar mass of helium (4.00 g/mol) in place of the average molar mass of air.
Integrating the Activity into Your Curriculum This Activity demonstrates the ideal gas law and introduces students to the concept of buoyancy. It can be done in the classroom, laboratory, or as a take-home activity with the students weighing their balloons and weights in lab the next day.
perforated
About the Activity
A typical balloon with weights attached to provide neutral buoyancy. Note the assorted weights on its tail.
18-in. circular Mylar balloons freshly filled with helium can be purchased at local discount stores or supermarkets. Students can attach large and small paperclips, and adhesive Post-It notes and message flags to the balloons as weights. An 18-inch balloon with its string removed requires ~4 g of weights. Data sheets, a sample data set, and a challenge problem are available as supplemental material online. The calculated empty balloon’s mass was typically 5–15% lower than the actual empty mass. One source of error is the estimation of the balloon’s volume. A balloon is not a perfect ellipsoid due to crimping along the seam and protruded opening at the bottom. Diameter and width measurements varied by ±0.2 cm for a given balloon. These errors in volume could cause the calculated mass to be erroneously high or low. The pressure of the helium inside the balloon may have been greater than atmospheric pressure, especially if it was tightly filled. This would lead to a lower calculated mass of displaced air and a lower value for the empty balloon’s mass. The helium could be impure and could contain a small amount of air due to leakage between the balloon and surrounding air. This would result in a higher empty balloon mass.
Answers to Questions 1. A percent error of
