# Ideal Gas Laws with Temperature, Pressure and Volume

What is the temperature of 0.52mol of gas at a pressure of 1.3atm and a volume of 11.7L ?

This figure (Figure 1) shows a container that is sealed at the top by a movable piston. Inside the container is an ideal gas at 1.00 atm , 20.0 ∘ C , and 1.00 L . This information will apply to all parts of this problem A, B, and C.What will the pressure inside the container become if the piston is moved to the 2.00 L mark while the temperature of the gas is kept constant?

A weather balloon is inflated to a volume of 29.0L at a pressure of 744mmHg and a temperature of 31.3 ∘ C . The balloon rises in the atmosphere to an altitude, where the pressure is 360mmHg and the temperature is -14.1 ∘ C.Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude

Calculate the density of oxygen, O 2 , under each of the following conditions:•STP

•1.00 atm and 25.0 ∘ C

To identify a diatomic gas (X 2 ), a researcher carried out the following experiment: She weighed an empty 1.0-L bulb, then filled it with the gas at 1.30atm and 26.0 ∘ C and weighed it again. The difference in mass was 1.5g . Identify the gas.

A 1-L flask is filled with 1.25g of argon at 25 ∘ C . A sample of ethane vapor is added to the same flask until the total pressure is 1.05atm .What is the partial pressure of argon, P Ar , in the flask?What is the partial pressure of ethane, P ethane , in the flask?

Imagine that you have a 7.00L gas tank and a 3.00L gas tank. You need to fill one tank with oxygen and the other with acetylene to use in conjunction with your welding torch. If you fill the larger tank with oxygen to a pressure of 125atm , to what pressure should you fill the acetylene tank to ensure that you run out of each gas at the same time? Assume ideal behavior for all gases.

13.0 moles of gas are in a 3.00L tank at 20.9 ∘ C . Calculate the difference in pressure between methane and an ideal gas under these conditions. The van der Waals constants for methane are a=2.300L 2 ⋅atm/mol 2 and b=0.0430 L/mol .

To prevent tank rupture during deep-space travel, an engineering team is studying the effect of temperature on gases confined to small volumes. What is the pressure of 4.00mol of gas D measured at 251 ∘ C in a 1.75-L container assuming ideal behavior?

To prevent tank rupture during deep-space travel, an engineering team is studying the effect of temperature on gases confined to small volumes. What is the pressure of 4.00mol of gas D measured at 251 ∘ C in a 1.75-L container assuming real behavior?

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#### Solution Preview

Gases

What is the temperature of 0.52mol of gas at a pressure of 1.3atm and a volume of 11.7L ?

Use the Ideal Gas Law :

PV = nRT

P = Pressure of confined gas in atmospheres

V= Volume of the confined gas, in liters

N= Number of moles of gas

R= Gas Constant, 0.0821 L atm/ mol K

T = Temperature in Kelvin

So to find the temperature =

T = PV/nR

= 1.3 atm * 11.7 L/ 0.52 mol * 0.0821 L *atm/mol*K

= 357.04 K

This figure (Figure 1) shows a container that is sealed at the top by a movable piston. Inside the container is an ideal gas at 1.00 atm , 20.0 ∘ C , and 1.00 L . This information will apply to all parts of this problem A, B, and C.What will the pressure inside the container become if the piston is moved to the 2.00 L mark while the temperature of the gas is kept constant?

Use Ideal Gas Law

P1 = 1.00 atm P2= ?

V1 = 1.00L V2 = 2.00 L

T K = Tc + 273.15

= 20° C + 273.15

= 293.15 K

PV = nRT

Set the P1V1 = P2V2, so

P2 = P1V1/V2

= 1 atm * 1L/ 2 L

= 0.5 atm

A weather balloon is inflated to a volume of 29.0L at a pressure of 744mmHg and a temperature of 31.3 ∘ C . The balloon rises in the atmosphere to an altitude, where the pressure is 360mmHg and the temperature is -14.1 ∘ C.Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude

Use Ideal gas law

V1 = 29.0 L

P1 = 744 mmHg

T = 31.3 C

Tk1 = Tc1 + 273.15

= 31.3 C + 273.15

= 304.45 K

P2 = 360 mmHg

Tk2 = Tc2 + 273.15

= -14.1 C + 273.15

= 259.05 K

V2= ?

P1V1 = nRT1

P2V2 = nRT2

P1V1/T1 = nR

P2V2/T2 = nR

P1V1/T1 = P2V2/T2

V2 = P1V1T2/ T1P2

V2 = 744 mmHg 29.0L 259.05K/304.45 K 360 mmHg

= 50.99 L

Calculate the density of ...

#### Solution Summary

The ideal gas law relates the four variables of pressure, volume, temperature, and number of moles of gas within a closed system. The ideal gas law takes the form of PV= nRT. The ideal gas law is the combination of all the simple gas laws such as Boyle's Law, Charles' Law, and Avogadro's Law. These simple gas law can be derived from the ideal gas law equation. The ideal gas law have to assume that no forces acting among the particles of gases and that the particles do not take up any space. The ideal gas law equation can be use to solve a gas problem when amount of gas is given and the mass of the gas is constant. Below are examples of how the ideal gas equation is used to solve gas problems.