Question

Estimate the density of liquid ethanol at 453.15 k and 200 bar

Answer 1

Density of the liquid ethanol is 191.43 Kg/m³

Given,

Temperature of ethanol (T) = 453.15 K.

Pressure of ethanol (p) = 200 bar.

Ethanol chemical formula = C₂H₅OH

Molar mass of ethanol (M) = 2(mass of carbon) + 5(mass of hydrogen) + mass of oxygen + mass of hydrogen

M = 2(12) + 5(1) + 16 + 1

M = 24 + 5 + 6 + 1

M = 36 g

From formula PV = nRT

where n (no. of moles) = Weight of the molecule (w) / molecular weight(M)

PV = W/M × RT  

P = d$\frac{W}{MV} \times {RT}\\\\\\P = \frac{d}{M} \times{RT}$

Where Weight(W) /Volume(V) = Density (d)

R = universal gas constant = 0.083 bar mol⁻¹ K⁻¹

d = $\frac{PM}{RT}$

d =  $\frac{(200) (36)}{(0.083) (453.15)}$

d =  $\frac{7200}{37.61}$

d = 191.43 Kg/m³

density of ethanol is 191.43 Kg/m³