Calculate the density of a mixture of methanol and water at 20ºC, composition 40 per cent w/w methanol.

Density of water at $20^{\circ} C$ 998.2 $kg / m ^{3}$

Density of methanol at $20^{\circ} C$ 791.2 $kg / m ^{3}$

Question

Calculate the density of a mixture of methanol and water at 20ºC, composition 40 per cent w/w methanol.

Density of water at [latex]20^{\circ} C[/latex] 998.2 [latex]kg / m ^{3}[/latex]

Density of methanol at [latex]20^{\circ} C[/latex] 791.2 [latex]kg / m ^{3}[/latex]

Accepted Answer

Basis: 1000 kg

[latex] ext { Volume of water }=\frac{0.6 imes 1000}{998.2}=0.601 m ^{3}[/latex]

[latex] ext { Volume of methanol }=\frac{0.4 imes 1000}{7912}=0.506 m ^{3}[/latex]

[latex] ext { Total } 1.107 m ^{3}[/latex]

[latex] ext { Density of mixture }=\frac{1000}{1.107}=903.3 kg / m ^{3}[/latex]

Experimental value = 934.5 [latex]kg / m ^{3}[/latex]

[latex] ext { Error }=\frac{934.5-903.3}{903.3}=\begin{array}{c}3 ext { per cent, which would be acceptable for most } \ ext { engineering purposes }\end{array}[/latex]

If data on the variation of density with temperature cannot be found, they can be approximated for non-polar liquids from Smith’s equation for thermal expansion (Smith et al., 1954).

[latex]\beta=\frac{0.04314}{\left(T_{c}-T ight)^{0.641}}[/latex] (8.2)

where β = coefficient of thermal expansion, [latex]K ^{-1}[/latex],

[latex]T_{c}[/latex] = critical temperature, K,

T = temperature, K.

Question 8.1: Calculate the density of a mixture of methanol and water at ...

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