Oxygen and mercury in a tube problem

In summary, the problem involves a tube with an open top and closed bottom, filled with oxygen and a 10 cm column of mercury on top. The initial temperature is 20oC and when the tube is flipped and heated to 40oC, the column of mercury shifts by 8cm. The question asks for the initial height of the gas column given an atmospheric pressure of 105 Pa. Using the ideal gas law and considering atmospheric pressure and mercury pressure, we can calculate the initial height of the gas column.
  • #1
Rugile
79
1

Homework Statement


We have a tube with the top end open and the bottom end closed. There is some oxygen gas in the tube and on top of the oxygen there is 10 cm high column of mercury. The initial temperature is 20oC. Then the tube is flipped over and heated to 40oC. The column of mercury shifts by h = 8cm. What was the initial height of column of the gas if the atmospheric pressure is 105 Pa?

Homework Equations


Ideal gas law

The Attempt at a Solution


We can assume that the gas is ideal, from which we know that ##\frac{pV}{T} = const## thus ##\frac{p_0 V_0}{T_0} = \frac{p_1 V_1}{T_1}##. When we flip the tube over we also know that ##p_{ox} + p_{merc} = p_a##, where pox is oxygen pressure, pmerc is mercury pressure, and pa is atmospheric pressure. Also, we can state that ##V_1 = V_0 + Sh##, ##Sh_1 = Sh_0 + Sh##, thus we can rewrite the equation: ##\frac{p_0 S h_0}{T_0} = \frac{(p_a - p_{merc}) S (h_0 + h)}{T_1} => \frac{p_0 h_0}{T_0} = \frac{(p_a - p_{merc}) (h_0 + h)}{T_1}##. The only additional unknown here is p0, which I don't know how to calculate. I was thinking of using the equation ##p_0 V_0 = \frac{m}{M}RT_0##, but I don't have enough information to solve that equation for p0. Any ideas?
 
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  • #2
Initial condition: capillary containing oxygen confined by 10 cm Hg column,
Rugile said:
10 cm high column of mercury.
open to atmosphere.
 
  • #3
So do you mean that ##p_a = p_{merc} + p_0##? But what about the fact that the bottom end is sealed?
 
  • #4
Bottom end.
 
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Likes Rugile
  • #5
Sooo, the pressure of the gas is caused by the atmospheric pressure and mercury, thus ##p_0 = p_{merc} + p_a## instead? I'm confused
 
  • #6
Rugile said:
pressure of the gas is caused by the atmospheric pressure and mercury
Very good.
 
  • #7
Thank you for the help!
 

1. What is the purpose of the oxygen in a tube in the mercury problem?

The oxygen in the tube serves as an oxidizing agent to prevent the mercury from evaporating. It creates a barrier that limits the contact between the mercury and air, preventing the mercury from oxidizing and turning into a gas.

2. Why is it important to maintain a specific amount of oxygen in the tube?

The specific amount of oxygen in the tube is crucial for the stability of the mercury. Too much oxygen can cause the mercury to oxidize and evaporate, while too little oxygen can lead to the formation of a mercury oxide layer on the surface, hindering its properties.

3. How does the presence of oxygen affect the properties of mercury in a tube?

The presence of oxygen in the tube helps to maintain the liquid state of the mercury and prevents it from evaporating. It also helps to prevent the mercury from forming a layer of oxide on its surface, which can affect its physical and chemical properties.

4. Can the amount of oxygen in the tube be adjusted to alter the properties of mercury?

Yes, the amount of oxygen in the tube can be adjusted to alter the properties of mercury. For example, increasing the amount of oxygen can lead to the formation of a mercury oxide layer, which can change the surface tension and viscosity of the mercury. However, this should be done carefully and with caution as excessive oxygen can cause the mercury to evaporate.

5. What happens if there is no oxygen in the tube in the mercury problem?

If there is no oxygen in the tube, the mercury will be exposed to air and can easily evaporate. This can also lead to the formation of a mercury oxide layer, which can affect its properties. Without the presence of oxygen, the stability of the mercury will be compromised and it may not be suitable for certain experiments or applications.

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