Question

What is the density of carbon dioxide gas at -25.2°C and 98.0 kPa? A. 0.232 g/L OB. 0.279 g/L OC. 0.994 g/L OD. 1.74 g/L O E. 2.09 g/L

Answer 1

E.
`2.09(g)/(L)`

Step-by-step explanation:

From the ideal gasses equation we have:

PV=nRT

where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.

The number of moles is also expressed as:
`n=(mass)/(Molar mass)`

If replacing this in the ideal gasses equation we have:

`PV=(mass)/(Molarmass).RT`

If we pass V to divide, we have:

`P=(mass)/(V).(RT)/(Molarmass)`

And the density d =
`(mass)/(V)`, so replacing, we have:

`P=(dRT)/(M)`

Solving for d, we have:

`d=(P.M)/(R.T)`

Now we have to be sure that we have the correct units, so we need to convert the units for pressure and temperature:

-Convert P=98kPa to atm

`98.0kPa*(0.00986923atm)/(1kPa)=0.97atm`

-Convert T=-25.2°C to K

`-25.2^(o)C+273.15=247.95K`

Finally we can replace the values in the equation:

`d=((0.97atm)*(44.01(g)/(mol)))/((0.082(atm.L)/(mol.K))*(247.15K))`

`d=2.09(g)/(L)`