PV = nRT    (from the ideal gas equation)

P = 0.9900atm
V = ?
n = ?
R = molar gas constant, 0.082atm.dm³.mol⁻¹.K⁻¹
T = (55 + 273)K = 328K

Here we have two unknowns, n and V.
We arrange them both on one side.

\frac{V}{n} = \frac{RT}{P}

Remember, n (mol) = \frac{mass}{molar mass}

The equation now becomes,
\frac{V}{mass / molar mass} = \frac{RT}{P}

\frac{(V)(molar mass)}{mass} = \frac{RT}{P}

Multiply both sides by \frac{1}{molar mass}

\frac{V}{mass} = \frac{RT}{(P)(molar mass)}

Now again, we have V and mass on one side, and we're solving for density.

But density is equal to mass/volume

If \frac{V}{mass} = \frac{RT}{(P)(molar mass)} ,

then \frac{mass}{V} = \frac{(P)(molar mass)}{RT}

Therefore, our m/v, which is density, is equal to;

\frac{(P)(molar mass)}{RT}

We have extracted all values, except the molar mass.

Molar mass of CO₂ = 12 + (16 × 2) = 44gmol⁻¹

Substituting all values in our equation, we have;

d= \frac{43.56}{26.896}

d = 1.62g/L

Ah! But density is g/dm³ abi? Yes, 1dm³ = 1L, so our units are still correct.

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