I'm teaching a home-schooled 13 year old some physics and chemistry, and last night's experiment was an attempt to measure the density of air.
Using an electronic balance that has proved pretty reliable, and weighs things up to several tens of grams to a precision of +/- 0.01 g, we weighed an empty balloon in a little cardboard platform (total about 7g).
Then we inflated it by blowing into it and weighed it again.
The weight difference was 0.3g.
We then captured the air as follows, using:
- a large bowl of water
- a 1l plastic kitchen measuring jug, calibrated in 50ml increments
The jug was filled with water by dipping under the surface in the bowl, and held inverted with the rim about 1cm below the surface of the water.
The air was released from the balloon under water, capturing it in the inverted jug, stopping the flow and refilling the jug with water when 800ml had been collected each time.
Total volume of air collected: 4000 ml, +/- 200 ml.
This gives a density of:
(1,000,000 / 4000) x 0.3 = 75g per cubic meter.
Whereas the accepted density of dry air is more like 1.3 kg per cubic meter.
So my result is a factor of 17 too small!!
My method was fairly crude, but there is clearly a colossal error here.
Certainly exhaled air is wet, and warmer than ambient, with more carbon dioxide and less oxygen, and hence of a different density – but not by a factor of 17!
Collecting the air under water could also have introduced errors – however, with each jugful of water I was careful to ensure that once I'd collected each lot of 800ml of air, the water level inside the jug was the same as the water level in the bowl, so that the air inside the jug would be pretty close to ambient atmospheric pressure. Again, errors here would be a few percent, not a huge factor!
I think the pressure in the balloon is irrelevant – the contained air weighs whatever it weighs – it's the collected volume that's important, not the volume in the balloon.
So, what am I doing wrong?
Edit to describe updated method:
Having recovered from my embarrassment at failing to do this properly the first time, some may be interested in a repeat of the experiment which has yielded a much better result:
I cut the valve out of a bicycle inner tube and glued it into the lid of a 2 litre pop bottle, having first drilled a suitable hole in the lid through which to poke the valve.
This enabled me to pump the bottle up to about 25 psi with a bicycle pump.
This time, unlike the balloon, the bottle stretches only very slightly under pressure, so the extra weight really is the extra weight of the air.
We collected the weighed extra air over water as before to measure its volume. 2.65 g air had a volume of 2.4 l.
The density came out as 1100 g/m3, which isn't too far from the accepted value of 1225.
Best Answer
Your method is the problem,
Imagine for an instant trying to measure the density of helium by the same method, your balance would measure a negative weight (the balloon rise), and hence a negative density. Which isn't the case.
Archimede's fault really
As @akhmeteli pointed out, pressure look like a far better explanation, if the pressure inside is 10% more ($1.1$ atm which seems realistic), the mass would also increase by 10%, and lead to the kind of mass difference you are expecting. My first explanation involved CO2, but this gas does not represent a sufficiently large portion of breathed air to explain anything.