I used the Ideal Gas Law `PV = nRT`

where

P is the pressure of the gas

P = 1.033 kgf/cm squared

V is the unknown volume of the gas

n is the amount of substance of gas (also known as number of moles)

n = 40.7 mole

R is the ideal, or universal, gas constant, equal to the product of the Boltzmann constant and the Avogadro constant.

R = 8.3145

T is the temperature of the gas

T = 298.15 K

**incorrect work snipped**

**UPDATE**

figured it out.

I used some of the work found here: http://www.newton.dep.anl.gov/askasci/phy99/phy99471.htm

and then used ideal gas law against his answer to derive a volume of 266 gallons

I then used density = mass / volume against his answer and achieved similar results so as to feel confident that 266 gallons is correct at SATP

**UPDATE 2:**

Here's a calculator specifically for this problem http://keyvanfatehi.com/balloon

You can find the source code here: https://github.com/keyvanfatehi/balloon

It uses https://www.npmjs.org/package/gas-density-calculator and https://www.npmjs.org/package/archimedes-principle

## Best Answer

The simplest way to approach this is to note that the molar volume of an ideal gas (helium and air are close to ideal at STP) is $22.4$ litres. This means that $22.4$ litres of helium weighs $4$g and similarly $22.4$ litres of air (average $M_W = 28.8$) weighs $28.8$g.

Archimedes' principle tells us that the upthrust is equal to the weight of fluid displaced, so when $22.4$ litres of helium displaces $22.4$ litres of air the net upthrust (weight of air - weight of helium) is $28.8 - 4 = 24.8$g.

From this you should be able to work out what volume of helium is required to produce an upthrust of $1$kg.