Ideal Gas Law: A Comprehensive Guide with Practice Problems, Exams of Law

Download Ideal Gas Law: A Comprehensive Guide with Practice Problems and more Exams Law in PDF only on Docsity!

1

Gas Laws

Gas Pressure in General Dalton’s Law Charles’s Law Boyle’s Law Gay-Lussac’s Law Combined Gas Laws Graham’s Law Ideal Gas Law

Ideal Gas Law

PV = nRT

2

4

R - The Gas Constant

PV = nRT

The factor “R” in the ideal gas law equation is known as the “gas constant”. R = PV nT The pressure times the volume of a gas divided by the number of moles and temperature of the gas is always equal to a constant number.

5

The Value of R

PV = nRT

R = PV

nT The numerical value of the constant depends on which units the pressure volume and temperature are in. There are numerous values for R that correspond to different groups of units of measurement.

7

The Value of R

■ When using the ideal gas equation you must choose the value of R that fits the other units you are using. ■ Note that the only difference in these three R values is the unit for pressure. ■ There are many other values of R for other combinations of measurement units. R = 8.314 L·kPa mol·K R = 0.0821 L·atm mol·K R = 62.4 L·mmHg mol·K For English engineering units the value of R is: 10.73 psi·ft 3 lbmol·˚R

8

Using the Ideal Gas Law

■ A cylinder of helium has a volume of 10 liters.

The pressure in the cylinder is 8 atm and the

temperature is 20°C. What is the quantity

(moles) of helium in the cylinder?

PV = nRT

n = PV RT P = 8 atm V = 10 L T = 20 + 273 = 293 K Pressure is in atm, volume is in liters, temp is in K For R we need to use R = 0.0821 L·atm mol·K

10

Using the Ideal Gas Law

■ The volume of this room is about 600,

liters. If the room was full of nitrogen at 1atm

and 20°C, how many grams of nitrogen are in

the room?

PV = nRT

n = PV RT P = 1 atm V = 600000 L T = 20 + 273 = 293 K Pressure is in atm, volume is in liters, temp is in K For R we need to use R = 0.0821 L·atm mol·K (^) handout

11

Using the Ideal Gas Law

PV = nRT n =^ PV

RT

P = 1 atm V = 600000 L T = 293 K R = 0.0821 L·atm mol·K n = PV RT = (1 atm)(600000 L) 0.0821 L·atm mol·K

(293 K)

= 24943 moles 24943 moles N 2 1 mole N 2 28.00 g N 2 = 698404 g nitrogen 1538 lbs. handout

13

Ideal Gas Law Practice

■ A balloon contains 1 gram of Helium. What is

the volume of the balloon if the pressure is

103 kPa and the temperature is 30°C?

PV = nRT V = nRT

P

n = 1 gram He 4.0 g/mol = 0.25 mol He T = 30 + 273 = 303 K V = (0.25 mol) (^) 8.314 L·kPa mol·K

(303 K)

103 kPa = 6.11 liters

14 Where Did 22.4 L/mol Come From?

■ What is the volume of 1 mole of a gas at STP?

PV = nRT V = nRT

P

P = 1 atm n = 1 mol T = 273 K R = 0.0821 L·atm mol·K V = nRT P

= 22.4 L

0.0821 L·atm mol·K

(273 K)

(1 mol) 1 atm (1 mol)