How do you solve this problem?

Question

OK, its about the combined gas law and stuff like that... here it is:

"We can estimate the temperature of the centre of the sun by assuming it consists of gases with a average molar mass of 2.00 g/mol. If the density is 1.40 g/cm^3 at a pressure of 1.30 x 10^9 atm, calculate the temperature in degrees Celsius.

OK, now heres the tricky part. My teacher wont allow us to use the modified gas law that incorporates density and molar mass in PV=nRT. He wants us to use stoichiometry and other methods to somehow solve this problem. Im stumped on how to get the Volume and the number of moles from the info given.

Some help would be appreciated.

Answer 1

pV = nRT

so T= pV/nR

we calculate all in MKS

p =1.3 *10^9 *101325 =1.317*10^14 Pa

we calculate the number of moles by m^3

1.4g/cm^3 = 1.4*10^6g/m3

you divide by 2 you obtain n =710^5 moles/m^3

so T =1.317*10^14/(710^5*8.31)=2.26410^7°K
to have celsius you must substract 273