A tank with a volume of 0.150 m³ contains 27.0 $\degree$C helium gas at a pressure of 100 atm.How many balloons can be blown up if each filled balloon is a sphere 30.0 cm in diameter at 27.0 $\degree$C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons. A)963 balloons B)884 balloons C)776 balloons D)598 balloons

Question

Quizplus · Accepted Answer

First, we need to convert the initial volume of the tank to liters, as the diameter of the balloon is given in centimeters:

0.150 m³ = 150 L

Next, we can use the ideal gas law to calculate the number of moles of helium in the tank:

PV = nRT

n = PV/RT

where P = 100 atm, V = 150 L, R = 0.0821 L·atm/(mol·K), and T = 300 K (27°C + 273).

n = (100 atm)(150 L)/(0.0821 L·atm/(mol·K)·300 K) = 730.7 mol

Now we can use the ideal gas law again to find the volume of each balloon:

PV = nRT

V = nRT/P

where n and T are the same as before, and P is now 1.2 atm (the absolute pressure, which includes atmospheric pressure).

V = (730.7 mol)(0.0821 L·atm/(mol·K)·300 K)/(1.2 atm) = 15,984 L

Note that we could simplify this calculation by using the fact that P and T are constant, so V ∝ n, and the ratio of balloon volume to tank volume is:

(4/3)π(0.15 m)³ / (150 L) = 0.141

Therefore, the volume of each balloon is:

V = 0.141 × 150 L = 21.2 L

Finally, we can divide the total volume of helium by the volume of each balloon to find the number of balloons that can be filled:

730.7 mol × 22.4 L/mol / 21.2 L = 884 balloons

Therefore, the answer is B, 884 balloons.

A Tank with a Volume of 0 °\degree° C Helium Gas at a Pressure of 100 Atm

A Tank with a Volume of 0 $\degree$ C Helium Gas at a Pressure of 100 Atm