# Is it physically possible to have and how dense is styrofoam with helium or hydrogen replacing the air or whatever gas fills the spaces in it?

Is it physically possible to have styrofoam with helium or hydrogen replacing the air or whatever gas fills the spaces in it? How dense would it be? Would it float on air? How much less dense than ordinary styro would it be?

• I will formulate a more quantitative answer tomorrow.
– Gert
Apr 18, 2021 at 2:06
• What's the down vote for? Apr 18, 2021 at 2:54
• I upvoted and posted an answer.
– Gert
Apr 18, 2021 at 9:28

'tom10s' answer is informative but says precious little about the effect of substituting air with lighter gas. I will do that here.

The density of styrofoam is approx.: $$\rho\approx 50\mathrm{kg/m^3}$$ Using the resp. suffixes $$s$$ and $$a$$ for polystyrene and air we have: $$\rho=\frac{m}{V}=\frac{m_s+m_a}{V_s+V_a}=50$$ And for $$1\mathrm{m^3}$$ of the foam: $$m_s+m_a=50\text{ and }V=V_s+V_a$$ Let $$\chi$$ be a mass fraction (multiply by $$100$$ to get a percentage): $$\chi_s=\frac{m_s}{m_s+m_a}\Rightarrow m_s=50\times \chi_s$$ $$\chi_a=\frac{m_a}{m_s+m_a}\Rightarrow m_a=50\times (1-\chi_s)$$ $$V_s=\frac{m_s}{\rho_s}\text{ and }V_a=\frac{m_a}{\rho_a}$$ $$V_s+V_a=\frac{m_s}{\rho_s}+\frac{m_a}{\rho_a}=\frac{m_s\rho_a+m_a\rho_s}{\rho_s\rho_a}$$ $$\rho=\frac{50\rho_s\rho_a}{m_s\rho_a+m_a\rho_s}$$ $$\rho=\frac{\rho_s\rho_a}{\rho_a\chi_s+\rho_s(1-\chi_s)}$$ $$\rho\left[\rho_a\chi_s+\rho_s\left(1-\chi_s\right)\right]=\rho_s\rho_a$$ $$\rho\rho_a\chi_s+\rho\rho_s-\rho\rho_s\chi_s=\rho_s\rho_a$$ Finally: $$\boxed{\chi_s=\frac{\rho_s\rho_a-\rho\rho_s}{\rho\rho_a-\rho\rho_s}}$$ $$\rho_a=1.225\mathrm{kg/m^3}\text{ and }\rho_s=1000\mathrm{kg/m^3}$$ $$\chi_s=\frac{1000\times 1.225-50\times 1000}{50\times 1.225-50\times 1000}=0.98$$ So approx. $$98\text{%}$$ of the mass of the styrofoam is polystyrene.

This of course means that the effect of substituting air with lighter gas on foam density will be minimal.

The idea here is that for something to float in air, it must weigh less than the air it displaces. This applies to the volume as a whole, so if it is a hollow item or foam, the weight of the entire volume (item added to the weight of whatever fills it: air, or helium, or whatever) must be less than the air it displaces.

Styrofoam is a name brand of foamed polystyrene, and polystyrene has a density of about $$1\,{\mathrm {g/cm^3}}$$ and the foamed version at foamiest is 98% air, so about $$0.02\,{\mathrm {g/cm^3}}$$. Air is about $$0.0012\,{\mathrm {g/cm^3}}$$.

Therefore styrofoam is about $$17 \times$$ heavier than air, and will never float in air. Replacing the air with helium would make it a bit lighter but far from floating.

Styrofoam is fairly permeable to air (and helium) so it would be easy to replace the air, but not obvious how to keep the air displaced.

Even the lightest aerogel is about as dense as air, so (barely) wouldn't float if it were filled with helium either.

There is, though, aerographene which has a density at $$0.00016\,{\mathrm {g/cm^3}}$$, or about 15% the density of air, and this would float if you replaced the air with helium.

• I like your answer, but it could do with editing to make it clearer. Density in physics is measured in kilograms per cubic meter, isn't it? It's not clear why helium styro would not float in air. That's just to name two problems. Some citations would be nice, too. Apr 18, 2021 at 1:28