What is the volume of 1 tons CO2 in supercritical condition?

I got #"2648.12 L CO"_2(sc)#, but you have only provided 1 significant figure. Also, apparently the van der Waals equation of state is not great for #"CO"_2# at this temperature and pressure.

If you repeat the calculation with the actual critical volume value of #barV_c = 0.0919color(white)(.)(pm 0.0010)# #"L/mol"# provided on NIST, you would instead get:

#V_c = 20613.16 cancel("mols CO"_2(sc)) xx "0.0919 L"/cancel("mol CO"_2(sc))#

#= "1894.35 L CO"_2(sc)#

and the critical molar volume based on van der Waals constants is #39.8%# off from the true value.

Well, one would have to know the critical parameters of #"CO"_2#.

You have not specified which equation of state to use. I have to assume that you are referring to the van der Waals equation of state...

I have done a derivation here:
https://socratic.org/scratchpad/f64889e085f35da07e9a

I had shown that:

#barV_c = 3b#, the critical volume

#T_c = (8a)/(27bR)#, the critical temperature

#P_c = a/(27b^2)#, the critical pressure

Typically, we know #T_c# and #P_c# for #"CO"_2# first. From NIST, the most precise and accurate values for those are:

#T_c = "304.2 K"#
#P_c = "73.83 bar"#

From these, we can calculate the van der Waals constants #a# (for intermolecular interactions) and #b# (for excluded volume).

#T_c/P_c = (8cancel(a))/(cancel(27b)R) cdot (cancel(27)b^cancel(2))/cancel(a)#

#= (8b)/R#

As a result,

#b = (RT_c)/(8P_c)#

#= ("0.083145 L"cdotcancel"bar""/mol"cdotcancel"K" cdot 304.2 cancel"K")/(8 cdot 73.83 cancel"bar")#

#=# #"0.04282 L/mol"#

This reference gives the true value as actually #"0.04286 L/mol"#, so this was done correctly.

Therefore, the critical molar volume of #"CO"_2# is:

#barV_c = V_c/n#

#= 3 cdot "0.04282 L/mol"#

#=# #"0.1285 L/mol"#

Now that we have that, #"1 US ton"# of #"CO"_2# is #"907.185 kg"#, so:

#907.185 cancel("kg CO"_2) xx (1000 cancel"g")/cancel"1 kg" xx ("1 mol CO"_2)/(44.01 cancel("g CO"_2))#

#= "20613.16 mols CO"_2#

This gives a volume of supercritical #bb("CO"_2)# of:

#color(blue)(V_c) = 20613.16 cancel("mols CO"_2(sc)) xx "0.1285 L"/cancel("mol CO"_2(sc))#

#= color(blue)("2648.12 L CO"_2(sc))#