# Ideal gas law in terms of density

• goonking
In summary, the conversation is about solving a problem using the ideal gas law equation PV=nRT, where "n" represents the number of moles. The participants discuss integrating both sides of the equation to find pressure and using the formula for integration of 1/x. They also consider the concept of differentiation and definite integration. The conversation concludes with a mention of finding the pressure at a specific height and the solution of the problem being continued at a later time.
goonking

PV=nRT

## The Attempt at a Solution

not sure if this is the right approach

plugging into -ρg gives us -PMg/RT = dP/dy

now we have to integrate both sides to find P?

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How you can write n as?

Raghav Gupta said:
How you can write n as?
n? number of moles?

goonking said:
n? number of moles?
Yes

n = mass/molecular mass

goonking said:

## Homework Statement

View attachment 83508

PV=nRT

## The Attempt at a Solution

not sure if this is the right approach

View attachment 83509

plugging into -ρg gives us -PMg/RT = dP/dy

now we have to integrate both sides to find P?
The approach is right. What do you get if you integrate?

Raghav Gupta said:
The approach is right. What do you get if you integrate?
well, i have no idea how to integrate that! :(

i only know how to integrate stuff like x2 + 3

goonking said:
well, i have no idea how to integrate that! :(

i only know how to integrate stuff like x2 + 3
No, problem.
Do you know differentiation?

Raghav Gupta said:
No, problem.
Do you know differentiation?
no, I'm suppose to take that next year :(

goonking said:
no, I'm suppose to take that next year :(
Oh, okay
Then for the moment remember
$$\int dx/x = lnx + C$$
Now use this in your problem.
And tell what you are getting.

Raghav Gupta said:
Oh, okay
Then for the moment remember
$$\int dx/x = lnx + C$$
Now use this in your problem.
And tell what you are getting.
i'm staring at this and still have no idea what to do, ok, so I know i can take the constants out and put it behind the integral

(-Mg/RT) ∫ P = dP/dy

correct? all the constants are out except P

Ah, you may also not know the definite integration. I may have to do lot of work here.
$$\frac{-Mg}{RT}\int_0^{8812} dy = \int_{10^5}^P \frac{dp}{P}$$
At ground height is zero and pressure 105 pascals.
At height 8812 m we have to find pressure. The limits are taken accordingly.
Now I guess you know how to solve further ?

goonking
Raghav Gupta said:
Ah, you may also not know the definite integration. I may have to do lot of work here.
$$\frac{-Mg}{RT}\int_0^{8812} dy = \int_{10^5}^P \frac{dp}{P}$$
At ground height is zero and pressure 105 pascals.
At height 8812 m we have to find pressure. The limits are taken accordingly.
Now I guess you know how to solve further ?
the left side of the equation should equal -1.095, correct?

goonking said:
the left side of the equation should equal -1.095, correct?
I must go to school now, i will finish this problem next time.

goonking said:
the left side of the equation should equal -1.095, correct?
Yes, and what right side evaluates to?

## 1. What is the ideal gas law in terms of density?

The ideal gas law is a mathematical equation that describes the relationship between the pressure, volume, temperature, and number of moles of an ideal gas. In terms of density, the ideal gas law can be written as ρ = (MP)/(RT), where ρ is the density, M is the molar mass, P is the pressure, R is the gas constant, and T is the temperature.

## 2. How is density related to pressure, volume, temperature, and number of moles in the ideal gas law?

In the ideal gas law, density is directly proportional to pressure and molar mass, and inversely proportional to temperature and volume. This means that as pressure or molar mass increases, density increases, while as temperature or volume increases, density decreases.

## 3. What is the significance of the ideal gas law in terms of density?

The ideal gas law is important because it allows us to predict the behavior of gases under different conditions. In terms of density, it helps us understand how the density of a gas changes with variations in pressure, volume, temperature, and number of moles.

## 4. How is the ideal gas law used in real-world applications?

The ideal gas law is used in many practical applications, such as in the design of gas storage tanks, internal combustion engines, and refrigeration systems. It is also used in industries like chemical engineering, where the behavior of gases is critical in the production of various products.

## 5. What are the limitations of the ideal gas law in terms of density?

The ideal gas law assumes that gases behave ideally, which means they have no intermolecular forces and occupy no volume. In reality, gases do have intermolecular forces and occupy some volume, especially at high pressures and low temperatures. Therefore, the ideal gas law is not accurate for all gases under all conditions, and other equations, such as the van der Waals equation, must be used to account for these deviations from ideality.

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