A helium balloon, assumed to be a perfect sphere, has a a radius of 22.0 cm . At room temperatur

step 1 We have a helium balloon perfectly spherical with the radius of 22 centimeters. We want to find

A helium balloon, assumed to be a perfect sphere, has a a...

A helium balloon, assumed to be a perfect sphere, has a a radius of 22.0 $\mathrm{cm} .$ At room temperature $\left(20^{\circ} \mathrm{C}\right),$ its internal pressure is 1.06 atm. Determine the number of moles of helium in the balloon, and the mass of helium needed to inflate the balloon to these values.

A helium balloon, assumed to be a perfect sphere, has a a radius of 22.0 $\mathrm{cm} .$ At room temperature $\left(20^{\circ} \mathrm{C}\right),$ its internal
pressure is 1.06 atm. Determine the number of moles of helium in the balloon, and the mass of helium needed to inflate the balloon to these values.

Key Concepts

Molar Mass

Molar mass is the mass of one mole of a substance, and it links the number of moles to mass. When the moles of a gas are determined using the ideal gas law, the molar mass is used to convert this quantity into the actual mass of the gas, which is essential in practical applications, such as inflating a balloon.

Unit Conversion

Unit conversion is a key concept in physics and chemistry to ensure that all measurements are in consistent units before applying formulas. This includes converting the radius from centimeters to meters, converting temperature from degrees Celsius to Kelvin, and making sure pressure and volume units are consistent with the gas constant used in the ideal gas law.

Volume Calculation for Spheres

Calculating the volume of a sphere is essential when dealing with spherical containers or objects. The volume is given by the formula V = (4/3)?r³, where r is the radius. This concept allows one to determine the space available for the gas in a spherical balloon or any other spherical structure.

Ideal Gas Law

The ideal gas law (PV = nRT) is a fundamental equation in thermodynamics that relates the pressure, volume, and temperature of a gas to the number of moles present. This concept is crucial for determining the amount of gas in a container when the other properties are known, and it assumes that the gas behaves ideally, meaning that the interactions between gas molecules are negligible and the volume occupied by the molecules themselves is very small compared to the container's volume.

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