Be careful of units! All the conversions you need are in the information section

Question

Be careful of units! All the conversions you need are in the information section of the lab.

Suppose the volume of the syringe is 46 cc. You measure the pressure as 1.91 atm, and the temperature as 17.5o C. Assume: the diameter of the plunger on the syringe is 2.02 cm.

a)Find

- the number of moles of gas in the syringe
n =  moles

- the number of molecules of gas in the syringe.
N =  molecules

- the mass of air in the syringe. (Use the molar mass of air given in the information section of the lab.)
mair =  kg

b)Supose you push down the syringe so the volume is now 40.3 cc, with the temperature remaining unchanged. Find:

- the new pressure inside the syringe.
P =  atm

- the magnitude of the force exerted by the gas on the plunger of the syringe.
F =  N

c) Suppose you suddenly press down on the syringe so the volume is now 27.2 cc, and plunge it into cold water. When the temperature is 8.99o C, find the pressure inside the syringe.
P =  atm

Assume the absolute zero apparatus is initially open to the air.
The volume of a sphere is: V = 4?r3/3

a) Assume that air pressure is Po = 1.00 atm and the air temperature is To = 27.6o C. How many moles of air will the sphere hold?
nair =  moles

b) Suppose now that the apparatus, initially open, is now sealed with the air inside. If the apparatus is now heated to to 551o C, find the pressure inside the apparatus now.
P =  atm

c) Assume now that, while maintaining a temperature of 551o, the sphere is injected with another 0.0426 moles of air. What is the new pressure inside the ball?
P =  atm

Explanation / Answer

R = 0.0821
n = ??
T = 17.5 + 273 = 290.5 oK
P = 1.91 atm
V = 46 cc = 46mL = 46 mL * 1 L / 1000 mL = 0.046 L

Use PV = nRT in the form of n = PV/(RT)

1.88 * 0.046/(0.0821 *290.5) = 0.00362 moles

molecules
- - - - - - - -
1 mole = 6.02 * 10^23 molecules
0.00362 moles = x

x = 0.00362 * 6.02*10^23
x = 2.18 * 10^21 molecules.

Mass
- - - -
A mole of air is about 28 grams.

1 mole = 28 grams
0.00362 mole = x

x = 0.10136 grams
x = 1.0136 * 10^-5 kg


Part B
======
P = ??
V = 0.030
n = 0.00362
T = 290.5 oK
R = 0.0821

P = n*R*T/(V)
P = 0.00362 * 0.0821 * 290.5 / 0.03
P = 2.87 atmospheres.

Force
- - - - -
P = F/A
F = ???
A = pi * r^2 = pi * (0.0202/2) ^2 = 1.28*10^-3

1 atmosphere = 101325 pascals.

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