Ideal Gas Law question

Question

Imagine we have a balloon filled with argon gas and the room conditions are 1.00 atm
and 25°C. Above what temperature would we have to heat the balloon so that it
would float? Assume the partial pressure of nitrogen in the air is 0.79 atm, with the
rest being oxygen

Answer 1

This is a density problem. the main step of this problem is to determine the density of the air, and then if the density of the argon balloon is less , the balloon will float. Density of the air = Density of the argon.

We can alter the density of the argon by adding heat.

The Ideal gas Law can be used to determine density of a gas at non-STP.

At STP the density of a gas is calculated by the mass of 1 mole of the gas divided by 22.4 liters

At STP d = M/22.4 L

BUT we are not at STP, 273K and 1 atm

Therefore we need to calculate the density of the air, and since the air is a mixture, we need to use mole fractions of the oxygen gas and the nitrogen gas

We can use PV=nRT to get density by rearranging the equation and then multipling both sides by M (molar mass)

n/V=P/RT

(M) n/V = P/RT (M)

density= m/V= PM/RT

or you can memorize this equation by using the mnemonic "Dreams Push Me over Rough Times

(from Pearson Chemistry textbook

So lets get started

molar mass of air = mole fraction of O2 x M + mole fraction N2 x M

.21 x 32g/mole + .79 x 28g/mole = 28.9g/mole

density of air= d=PM/RT= 1atm x 28.9 / .082 x 298K= 1.182 g/liter air

density of balloon = 1,182= 1atm x 40g/mole of argon /.082 x T

solve for T T= 412 K