# What is the Relationship Between Gas Pressure and Fluid Column Height?

• krbs
In summary, the Homework Equations state that: p = ghd, where p is the pressure of the gas, ghd is the height of the gas column due to water displacement, and C is the volume of gas displaced. The pressure of the gas is equal to the liquid pressure exerted by the water column on top of it.
krbs

## Homework Statement

I need to find the amount of H2 being lost to water by being stored underneath a column of water. About 16 mL of H2 is made and it displaces the column by 16 cm. However the total amount of water is 30 ml/30 cm. I'm not sure which relationship to use to find the pressure of the gas. I hypothesize that that pressure of the H2 is equal to the liquid pressure exerted by the water column on top of it.

## Homework Equations

p = ghd

C = P/k
k= 7.8 x 10^-4 mol/L*atm

3. The Attempt at a Solution

p = ghd = (9.8m/s^2 x 0.30 m x 1000 kg/m^3)
= 2940 Pa
= 0.0290 atm

C = P/k = (0.0290 atm)/(7.8 x 10^-4 mol/l*atm) = 2.263 x 10^-5 mol/L

2.263 x 10^-5 mol/L x 0.016 L = 3.62 x 10^-7 moles H2 lost

What do you mean by "lost"?

In typical situation "stored under water" doesn't mean there is "water on top of the gas". It rather means water seals the gas so that it can't escape nor mix with the air.

Is really the 30 mL of water kept as a perfect column with an exact height of 30 cm?

What about the ambient (atmospheric pressure)?

Impossible to comment without knowing answers to these questions (most of them are related to your experimental setup).

What is preventing the H2 from rising in the column?

If you are using Henry's law, you need to use the absolute pressure, not just the hydrostatic part of the pressure. Is there a lid on the water column, or can the H2 diffuse to the top of the water and escape into the atmosphere?

Borek said:
What do you mean by "lost"?

In typical situation "stored under water" doesn't mean there is "water on top of the gas". It rather means water seals the gas so that it can't escape nor mix with the air.

Is really the 30 mL of water kept as a perfect column with an exact height of 30 cm?

What about the ambient (atmospheric pressure)?

Impossible to comment without knowing answers to these questions (most of them are related to your experimental setup).

Hey there,

I assumed by "lost" they meant how much gas dissolved in the water. But yes, water seals the gas. The gas also displaces the water by 16 ml as it is generated via electrolysis of water.

The water appears to remain at 30 ml (which when measured with a ruler corresponds to 30 cm on the vessel I am required to use).

The atmospheric pressure is 1 atm.

Chestermiller said:
What is preventing the H2 from rising in the column?

If you are using Henry's law, you need to use the absolute pressure, not just the hydrostatic part of the pressure. Is there a lid on the water column, or can the H2 diffuse to the top of the water and escape into the atmosphere?

Hello!

H2 does rise in the column. If we continue generating H2, it escapes as bubbles. However, we stop hydrolysis when the gas starts to bubble. It also raises the height of the water by 16 cm (corresponding to 16 mL H2 generated).

Yes, I am attempting to use Henry's law. There is no lid on the column. Would absolute pressure be hydrostatic + atm pressure?

krbs said:
I assumed by "lost" they meant how much gas dissolved in the water.

Then I would simply assume the atmospheric pressure of 1 atm.

Borek said:
Then I would simply assume the atmospheric pressure of 1 atm.
Can you tell me why? Would it hurt to add the fluid pressure too?

Without knowing the exact setup it is hard to tell what is the additional pressure. A lot depends on the geometry.

Besides, 30 cm means at most 3% error.

Also, if there's not a lid on top, all the gas will eventually diffuse through the water and be released into the air.

https://ibb.co/jSf6Ka
There is a drawing of the setup at the link. I don't have access to the equipment right now. The H2 gets up used up quickly to run a motor. Not much time for the gas to escape.

Borek said:
Without knowing the exact setup it is hard to tell what is the additional pressure. A lot depends on the geometry.

Besides, 30 cm means at most 3% error.
I added a picture below. Thank you.

Chestermiller said:
Also, if there's not a lid on top, all the gas will eventually diffuse through the water and be released into the air.

krbs said:
I don't see any picture.

Chestermiller said:
I don't see any picture.
He uploaded to an image site and provided a link in post #10. https://ibb.co/jSf6Ka

scottdave said:
He uploaded to an image site and provided a link in post #10. https://ibb.co/jSf6Ka
Sorry. The figure just doesn't make sense to me.

## 1. What is gas pressure?

Gas pressure is the force exerted by gas molecules on the walls of a container. It is caused by the constant random motion of gas molecules colliding with each other and the walls of the container.

## 2. How is gas pressure measured?

Gas pressure can be measured using a device called a manometer, which uses a column of liquid to measure the pressure exerted by the gas. It can also be measured using a barometer, which measures the pressure of the gas in the atmosphere.

## 3. What is the relationship between gas pressure and temperature?

According to the ideal gas law, there is a direct relationship between gas pressure and temperature. As temperature increases, the average kinetic energy of gas molecules increases, causing them to collide with more force and therefore increasing the gas pressure.

## 4. How does a change in the height of a fluid column affect gas pressure?

The pressure of a gas is directly proportional to the height of the fluid column above it. This means that as the height of the fluid column increases, the gas pressure also increases. This relationship is known as Pascal's law.

## 5. How does gas pressure affect the boiling point of a liquid?

As the gas pressure above a liquid increases, the boiling point of the liquid also increases. This is because the higher gas pressure prevents the liquid molecules from escaping into the gas phase, requiring them to reach a higher energy level before boiling can occur.

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