A clown at a birthday party has brought along a helium cylinder, with which he intends to fill balloons. When full, each balloon contains 0.036 m3 of helium at an absolute pressure of 1.2 x 10^5 Pa. The cylinder contains helium at an absolute pressure of 1.6 x 10^7 Pa and has a volume of 0.0031 m3. The temperature of the helium in the tank and in the balloons is the same and remains constant. What is the maximum number of people who will get a (fully inflated) balloon?
Figure the moles in the cylinder
n=PV/RT
figure the moles in each balloon
nb=.036*1.2E5/RT
number of people=molesincyl/moleinballon
To find the maximum number of people who will get a fully inflated balloon, we need to calculate the number of moles of helium in both the cylinder and each balloon.
First, let's calculate the number of moles in the cylinder. We can use the ideal gas law equation: PV = nRT, where P is the absolute pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Given:
Absolute pressure in the cylinder (Pc) = 1.6 x 10^7 Pa
Volume of the cylinder (Vc) = 0.0031 m^3
To find the number of moles (nc) in the cylinder, we rearrange the ideal gas law equation:
nc = Pc * Vc / RT
Next, let's calculate the number of moles in each balloon. We can use the same ideal gas law equation, but with the volume and pressure values specific to the balloon.
Given:
Absolute pressure in the balloon (Pb) = 1.2 x 10^5 Pa
Volume of each balloon (Vb) = 0.036 m^3
To find the number of moles (nb) in each balloon, we rearrange the ideal gas law equation:
nb = Pb * Vb / RT
Finally, to find the maximum number of people who will get a fully inflated balloon, we divide the number of moles in the cylinder by the number of moles in each balloon:
Maximum number of people = nc / nb
Plug in the values for the given parameters (R is the ideal gas constant, which is 8.314 J/(mol·K) for helium), and you will get the final answer.