# The ideal gas equation

• janiexo
In summary, at the start the pressure and temperature are both p_0, then the pressure changes to p_1*V_1/(T_1-T_0) and the temperature changes to T_1. There's still a volume of ethane (R) in the flask, but it has lost a certain amount of gas due to the pressure change. At the end, the pressure and temperature are both T_0, and the volume is still R.

#### janiexo

I'm really struggling with this concept and can't seem to get my head around it. I don't know why because it seems simple enough but I can't seem to get the answer :

Question:
A flask with a volume 'V', provided with a stopcock, contains ethane gas (C2H6) at a temperature of T_0 and atmospheric pressure p_0. The molar mass of ethane is M. The system is warmed to a temperature of T, with the stopcock open to the atmosphere. The stopcock is then closed and the flask cooled to its original temperature.

a) What is the final pressure of ethane in the flask?
b) How many grams of ethane remain in the flask (use 'R' for ideal gas constant)?

Okay, first what is the "ideal gas equation"? What are the starting pressure, temperature and what are the pressure and temperature just before the stopcock is closed? What must stay constant once the stopcock is closed? So what must change? What are teh temperature and pressure at the end?

Ok, well the equation is pV = nRT
So at the start it's pressure is p_0 and temperature T_0
Before it's closed the temperature is T and the pressure is ... I don't know what the pressure is, would it stay at p_0?
So once it's closed the volume stays constant so the pressure must change. The temperature at the end is T_0 once again but i have no idea about the pressure.

HallsofIvy gave you good pointers. During each process step, there is one property that remains constant. Try to understand what Charles and Boyle's laws say(in the same order).

janiexo said:
Ok, well the equation is pV = nRT
So at the start it's pressure is p_0 and temperature T_0
Before it's closed the temperature is T and the pressure is ... I don't know what the pressure is, would it stay at p_0?
So once it's closed the volume stays constant so the pressure must change. The temperature at the end is T_0 once again but i have no idea about the pressure.

Use (p_1*V_1)/T_1 = (p_2*V_2)/T_2

You know volume remains constant, you know the temperature, then you can work out the final pressure.

Then to find the mass, just use pV = nRT.

Thanks for your help everyone, I understand it now. Things seem a lot clearer in the light of day I guess :)

## 1. What is the ideal gas equation?

The ideal gas equation, also known as the universal gas law, is a mathematical equation that describes the behavior of ideal gases under various conditions. It is written as PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature.

## 2. What are the assumptions made in the ideal gas equation?

The ideal gas equation assumes that the gas particles have no volume, there are no intermolecular forces between gas particles, and the collisions between gas particles and with the container walls are perfectly elastic. It also assumes that the gas is at a low pressure and high temperature.

## 3. What is the significance of the gas constant (R) in the ideal gas equation?

The gas constant (R) is a proportionality constant that relates the properties of a gas, such as temperature and pressure, to the amount of gas present. It has a value of 8.314 J/mol·K and is the same for all gases in the ideal gas equation.

## 4. Can the ideal gas equation be applied to real gases?

The ideal gas equation is a theoretical equation that assumes ideal conditions. While it can provide a good approximation for real gases at low pressures and high temperatures, it does not account for the intermolecular forces and volume of gas particles. Therefore, it is not always accurate for real gases, but it can serve as a useful starting point for calculations.

## 5. How is the ideal gas equation used in practical applications?

The ideal gas equation is used in various practical applications, such as in the design of gas storage tanks, compressors, and engines. It is also used in the study of atmospheric conditions, such as in weather forecasting and in the production of industrial gases. Additionally, the ideal gas equation is used in the gas laws, which describe the relationship between pressure, volume, and temperature of a gas.