A tank with a volume of 0.15 m³ contains 25.0°C helium gas at a pressure of 100 atm.How many balloons can be blown up if each filled balloon is a sphere 31.0 cm in diameter at 25.0°C and absolute pressure of 1.20 atm? Assume all the helium is transferred to the balloons. A)401 balloons B)802 balloons C)178 balloons D)1 002 balloons E)126 balloons

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Quizplus · Accepted Answer

To solve this problem, we use the ideal gas law, PV = nRT, and the fact that the amount of gas (in moles, n) and the temperature (in Kelvin) remain constant. The volume of a single balloon can be calculated using the formula for the volume of a sphere, $V = \frac{4}{3}\pi r^3$, where r is the radius in meters. Given the diameter is 31.0 cm, the radius is 15.5 cm or 0.155 m. Thus, the volume of one balloon is $V = \frac{4}{3}\pi (0.155)^3 \approx 0.0156 \, m^3$.Since the initial conditions are 100 atm and 0.15 $m^3$ and the final conditions for each balloon are 1.20 atm and 0.0156 $m^3$, we can use the principle that $P_1V_1 = P_2V_2$ (since the number of moles and temperature are constant, and thus cancel out in the comparison between initial and final states).Rearranging for $V_2$, we get $V_2 = \frac{P_1V_1}{P_2}$.Plugging in the values, we get $V_2 = \frac{100 \, atm \times 0.15 \, m^3}{1.20 \, atm} = 12.5 \, m^3$.To find out how many balloons can be filled, we divide the total volume of helium in the final condition by the volume of one balloon: $\frac{12.5 \, m^3}{0.0156 \, m^3/balloon} \approx 802$ balloons.

A Tank with a Volume of 0