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ollegr [7]
2 years ago
8

In the "Méthode Champenoise," grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is the following

. C6H12O6(aq) → 2 C2H5OH(aq) + 2 CO2(g) Fermentation of 754 mL of grape juice (density = 1.0 g/cm3) is allowed to take place in a bottle with a total volume of 840. mL until 13% by volume is ethanol (C2H5OH). Assuming that the CO2 is insoluble in H2O (actually a wrong assumption), what would be the pressure of CO2 inside the wine bottle at 21°C? (The density of ethanol is 0.79 g/cm3.) WebAssign will check your answer for the correct number of significant figures. atm
Chemistry
1 answer:
prohojiy [21]2 years ago
5 0

Answer:

The pressure inside the wine bottle at 21 °C is 4.8 · 10² atm

Explanation:

Hi there!

We know that 1 mol of CO₂ is produced per mol of produced ethanol.

If the final concentration of ethanol is 13%, let´s calculate how many moles of ethanol are present at that concentration.

A concentration of 13% means that in 100 ml of solution, 13 ml is dissolved ethanol. We have 754 ml of solution, then, the volume of ethanol will be:

754 ml solution · (13 ml ethanol/100 ml solution) = 98 ml ethanol

With the density, we can calculate the mass of ethanol present:

density = mass/ volume

0.79 g/ml = mass / 98 ml

mass = 0.79 g/ml · 98 ml

mass = 77 g

The molar mass of ethanol is 46.07 g/mol, then 77 g of ethanol is equal to:

77 g · (1 mol/46.07 g) = 1.7 mol

Then, the number of moles of CO₂ produced will be 1.7 mol.

Using the equation of the ideal gas law, we can calculate the pressure of CO₂:

P = nRT/V

Where:

P = pressure

n = number of moles

R = ideal gas constant

T = temperature

V = volume

The volume will be the headspace of the bottle (840 ml - 754 ml) 86 ml = 0.086 l.

The temperature in kelvin will be: 21 + 273 = 294 K

The gas constant is 0.082 l atm / K mol

Then:

P = (1.7 mol · 0.082 l atm/K mol · 294 K)/ 0.086 l

P = 4.8 · 10² atm

The pressure inside the wine bottle at 21 °C is 4.8 · 10² atm

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A mixture containing 20 mole % butane, 35 mole % pentane and rest
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Answer:

2.5 % butane, 42.2 % pentane and 55.3 % hexane

Explanation:

Hello,

In this case, the mass balance for each substance is given by:

Butane:z_bF=y_bD+x_bB\\\\Pentane: z_pF=y_pD+x_pB\\\\Hexane: z_hF=y_hD+x_hB

Whereas y accounts for the fractions at the outlet distillate and x for the fractions at the outlet bottoms. Moreover, with the 90 % recovery of butane, we can write:

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So we can compute the product of the molar fraction of butane at the distillate by total distillate flow by assuming a 100-mol feed:

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And the total bottoms flow:

F=D+B\\\\B=F-D=100mol-18.95mol=81.05mol

Next, by using the mass balance of butane, we compute the molar fraction of butane at the bottoms:

x_b=\frac{z_bF-y_bD}{B} =\frac{0.2*100mol-18mol}{81.05} =0.025

Then, the molar fraction of pentane and hexane:

x_p=\frac{z_pF-y_pD}{B} =\frac{0.35*100mol-0.04*18.95mol}{81.05} =0.422

x_h=\frac{z_hF-y_hD}{B} =\frac{(1-0.2-0.35)*100mol-(1-0.95-0.04)*18.95mol}{81.05} =0.553

Therefore, the molar composition of the bottom product is 2.5 % butane, 42.2 % pentane and 55.3 % hexane.

NOTE: notice the result is independent of the value of the assumed feed, it means that no matter the basis, the compositions will be the same for the same recovery of butane at the feed, only the flows will change.

Regards.

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