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

Answer:

E. $2.09\frac{g}{L}$

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: $n=\frac{mass}{Molar mass}$

If replacing this in the ideal gasses equation we have:

$PV=\frac{mass}{Molarmass}.RT$

If we pass V to divide, we have:

$P=\frac{mass}{V}.\frac{RT}{Molarmass}$

And the density d = $\frac{mass}{V}$, so replacing, we have:

$P=\frac{dRT}{M}$

Solving for d, we have:

$d=\frac{P.M}{R.T}$

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

$98.0kPa*\frac{0.00986923atm}{1kPa}=0.97atm$

-Convert T=-25.2°C to K

$-25.2^{o}C+273.15=247.95K$

Finally we can replace the values in the equation:

$d=\frac{(0.97atm)*(44.01\frac{g}{mol})}{(0.082\frac{atm.L}{mol.K})*(247.15K)}$

$d=2.09\frac{g}{L}$