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Paraphin [41]
2 years ago
5

Mixtures of benzene and cyclohexane exhibit ideal behavior. A solution was created containing 1.5 moles of liquid benzene and 2.

5 moles of liquid cyclohexane, and at 50°C the total vapor pressure of the solution was measured to be 340 torr. Another solution was created containing 1.5 moles of liquid benzene and 3.5 moles of liquid cyclohexane, and at 50°C the measured total vapor pressure was 370 torr.
(A) Calculate the vapor pressures of pure benzene and pure cyclohexane at 50°C.
Chemistry
1 answer:
goblinko [34]2 years ago
3 0

Answer:

Vapour pressure of cyclohexane at 50°C is 490torr

Vapour pressure of benzene at 50°C is 90torr

Explanation:

Using Raoult's law, pressure of a solution is defined by the sum of the product sbetween mole fraction of both solvents and pressure of pure solvents.

P_{solution} = X_{A}P^0_{A}+X_{B}P^0_{B}

In the first solution:

X_{cyclohexane}=\frac{2.5mol}{2.5mol+1.5mol} =0.625

X_{benzene}=\frac{1.5mol}{2.5mol+1.5mol} =0.375

340torr = 0.625P^0_{A}+0.375P^0_{B} <em>(1)</em>

For the second equation:

X_{cyclohexane}=\frac{3.5mol}{3.5mol+1.5mol} =0.700

X_{benzene}=\frac{1.5mol}{3.5mol+1.5mol} =0.300

370torr = 0.700P^0_{A}+0.300P^0_{B}<em>(2)</em>

Replacing (2) in (1):

340torr = 0.625P^0_{A}+0.375(1233.3-2.333P^0_{A})

340torr = 0.625P^0_{A}+462.5-0.875P^0_{A}

-122.5torr = -0.250P°A

P^0_{A} = 490 torr

<em>Vapour pressure of cyclohexane at 50°C is 490torr</em>

And for benzene:

370torr = 0.700*490torr+0.300P^0_{B}

P^0_{B}=90torr

<em>Vapour pressure of benzene at 50°C is 90torr</em>

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A sample of carbon dioxide occupies a 5.13 dm3 container at STP. What is the volume of the gas at a pressure of 286.5 kPa and a
suter [353]

Considering the ideal gas law and STP conditions, the volume of the gas at a pressure of 286.5 kPa and a temperature of 12.9°C is 1.8987 L.

<h3>Definition of STP condition</h3>

The STP conditions refer to the standard temperature and pressure. Pressure values at 1 atmosphere and temperature at 0 ° C are used and are reference values for gases. And in these conditions 1 mole of any gas occupies an approximate volume of 22.4 liters.

<h3>Ideal gas law</h3>

Ideal gases are a simplification of real gases that is done to study them more easily. It is considered to be formed by point particles, do not interact with each other and move randomly. It is also considered that the molecules of an ideal gas, in themselves, do not occupy any volume.

The pressure, P, the temperature, T, and the volume, V, of an ideal gas, are related by a simple formula called the ideal gas law:

P×V = n×R×T

where:

  • P is the gas pressure.
  • V is the volume that occupies.
  • T is its temperature.
  • R is the ideal gas constant. The universal constant of ideal gases R has the same value for all gaseous substances.
  • n is the number of moles of the gas.  

<h3>Volume of gas</h3>

In first place, you can apply the following rule of three: if by definition of STP conditions 22.4 L are occupied by 1 mole of carbon dioxide, 5.13 L (5.13 dm³= 5.13 L, being 1 dm³= 1 L) are occupied by how many moles of carbon dioxide?

amount of moles of carbon dioxide=\frac{5.13 Lx1 mole of carbon dioxide}{22.4 L}

<u><em>amount of moles of carbon dioxide= 0.229 moles</em></u>

Then, you know:

  • P= 286.5 kPa= 2.8275352 atm (being 1 kPa= 0.00986923 atm)
  • V= ?
  • T= 12.9 C= 285.9 K (being 0°C= 273 K)
  • R= 0.082 \frac{atmL}{mol K}
  • n= 0.229 moles

Replacing in the ideal gas law:

2.8275352 atm× V = 0.229 moles×0.082 \frac{atmL}{mol K} × 285.9 K

Solving:

V= (0.229 moles×0.082 \frac{atmL}{mol K} × 285.9 K)÷ 2.8275352 atm

<u><em>V= 1.8987 L</em></u>

Finally, the volume of the gas at a pressure of 286.5 kPa and a temperature of 12.9°C is 1.8987 L.

Learn more about

STP conditions:

brainly.com/question/26364483

brainly.com/question/8846039

brainly.com/question/1186356

the ideal gas law:

brainly.com/question/4147359

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