Using the ideal gas law, calculate the density of CO2 at 4.00 atm pressure and -20.0 oC.

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Using the Ideal gas law we can solve for the density of gas. First, let us write down the Ideal gas equation and the formula for density.

`PV = nRT`

`rho = (mass)/(volume) = M/V`

We know that moles = mass (M)/ molar mass, so we can substitute it to the Ideal gas equation thus having:

`PV = (M)/(molar mass) * RT`

Further arrangement in the expression we can have:

`(P)/(RT) =(M)/(molar mass * V)`

Finally,

`(P* molar mass)/(RT) =(M)/(V)= rho`

`rho =(P* molar mass)/(RT)`

  • P = 4.00 atm
  • T = -20.0 + 273.15 = 253.15K
  • R = 0.08206 atm-L/mol-K
  • Molar mass of CO_2 = 44.01 grams/mol

`rho =(4.00* 44.01)/(0.08206* 253.15)`

`rho` = 8.47 g/L = 0.00847 g/ml

 

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