A small amount of liquid ethanol (0.23 g, C_2H_5OH) is placed in a 4.7-L bottle
ID: 474004 • Letter: A
Question
A small amount of liquid ethanol (0.23 g, C_2H_5OH) is placed in a 4.7-L bottle and tightly sealed. The bottle is placed in a refrigerator/freezer where the liquid reaches equilibrium with its vapor at -11 degree C. What mass of ethanol is present in the vapor? (The vapor pressure of ethanol is 10.0 torr at -2.3 degree C and 40.0 torr at 19 degree C.) Enter your answer in scientific notation. When the container is removed and warmed to room temperature, 20 degree C, will all the ethanol vaporize? No, all the ethanol will not vaporize. Yes, all the ethanol will vaporize.Explanation / Answer
To solve this question , you have to assume that ethanol is ideal and that ethanol vapor acts as an ideal gas. You need to find out the vapor pressure at -11oC from the given data.
if we use the clausius clapeyron equation
ln(P1/P2) = (dHvap/R) x (1/T2 - 1/T1)
(dHvap/R) = ln(P1/P2) / (1/T2 - 1/T1)
use this value of dHvap/R to find (P3, T3).. pick either point.. say (P1,T1)
ln(P3/P1) = (dHvap/R) x (1/T1 - 1/T3)
substituting in that (dHvap/R) from above...
ln(P3/P1) = [ln(P1/P2) / (1/T2 - 1/T1)] x (1/T1 - 1/T3)
rearranging..
ln(P3/P1) = ln(P1/P2) x [(1/T1 - 1/T3) / (1/T2 - 1/T1)]
taking exp of both sides... and noting exp(AxB) = exp(a) + exp(b).. and exp(ln(A)) = A
P3 / P1 = (P1/P2) + exp[(1/T1 - 1/T3) / (1/T2 - 1/T1)]
P3 = P1 x (P1/P2) + exp[(1/T1 - 1/T3) / (1/T2 - 1/T1)]
solving..
P3 = 10torr x (10torr / 40torr) + exp[ (1/270.85K - 1/262.15K) / (1/292.15K - 1/270.85K)]
P3 = 4.08 torr =0.0054 atm
Use this value of P in ideal gas equation.
PV = nRT
or, PV = (m/M.wt)RT
or, 0.0054 atm *4.7L = (m/46.07g/mol) * 0.082 Latm/moleK * 262.15 K
or, m = 0.054 gm = 5.4*10^-2 gm
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At room temperature vapour pressure of ethanol is = 40 torr =0.052 atm
Now use this value to find out the mass of the vapour.
PV = (m/m.wt) * RT
0.053 atm * 4.7 L = (m/46.07) * 0.082 L atm/K/mol * 293K
or, m =0.48 gm
This means that all the ethanol will vaporize.
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