Ideal Gas LawPV = nRT

Application of PV=nRT Density

Molecular Mass

· By combining the gas laws we can write a general equation

where P is the pressure , V is the volume, n is the amount of

gas in mole, and T(K) is the temperatureThe constant is shown by R, gas Law

constant . The value of R, depends on the units of P & VR =0.08206[(atm.L)/(mol.K)], when P is

in atm and V is in L

Ideal Gas Law

Example: How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25°C?

V = 3.24 L, P = 24.3 psi, t = 25 °C and n=? Mol T(K) = 273.15+ t(0C) 1atm= 14.7 psi

R= 0.08206 (atm.L)/(mol.K)

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Knowing PV= nRT , Rearrange the equation to :

Standard ConditionsThe Standard Temperature & pressure, STP is when• Standard pressure = 1 atm• Standard temperature = 273 K, 0 °C

1 mole of any gas at STP condition has a volume equal to 22.4 L

Molar Volume = Volume of 1 mole of a gas• Solving the ideal gas equation for the volume of 1 mole

of any gas at STP gives a volume of 22.4 L– 1 mole of a gas has 6.022x1023 molecules of gas– 6.022x1023 molecules of gas occupies a volume of

22.4L at STP

• Molar volume of a gas at STP is 22.4 L

• One mole of different gases have the same volume at same temperature and pressure, but have different masses

Molar Volume and Molar mass

4.0 g 131.23 g 16.05 g6.022x1023atomsHe 6.022x1023atomsXe 6.022x1023 moleculesCH4

Different molar mass, same molar volume at same T &P

Example 2: A gas occupies 10.0 L at 44.1 psi and 27 °C. Calculate the volume this gas occupies at standard conditions using Ideal Gas law

• V1 =10.0L, P1= 44.1psi, t1= 27°C, P2 =1.00atm, t2=0°C and V2=?L

• T(K) = 273.15+ t(0C) 1atm= 14.7 psi

• PV= nRT and R= 0.08206 (atm.L)/(mol.K)

Example 2: Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 x 104 mmHg and –23 °C

• mSO2 = 637 g, P = 6.08 x 104 mmHg, t = −23 °C, &V=?L

• 1 atm= 760 mmHg 1 mole of SO2 = 64.07 g SO2 T(K) = 273.15+ t(0C)

• PV= nRT & R= 0.08206 (atm.L)/(mol.K)

Density at Standard Conditions• Density is the ratio of mass to volume• Density of a gas is generally given in g/L• The mass of 1 mole = molar mass• The volume of 1 mole at STP = 22.4 L

Example: Calculate the density of N2(g) at STP

Gas Density

• Density is directly proportional to molar mass• As Molar mass of a gas increases, its density is also

increase when T, n, P, & V are constant

Example : Calculate the density of N2 at 125°C and 755 mmHg

• P = 755 mmHg, t = 125 °C, dN2 = ? g/L

• 1 atm =760 mmHg, 1mole N2=28.0g N2, T(k) = 273.15 + t(0C)

Example2: Calculate the density of a gas at 775 torr and 27 °C if 0.250 moles weighs 9.988 g

• m = 9.988g, n = 0.250 mol, P = 1.0197 atm, T = 300.K Density= ?g/L•1atm =760 mmHg, T(K)=273.15+t(0C), PV=nRT, & d=(m/v)

Molar Mass of a Gas• One of the methods chemists use to determine the

molar mass of an unknown substance is to heat a weighed sample until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law to calculate the number of moles, then

Example: Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55°C and 886 mmHg

• m=0.311g, V=0.225L, P=1.1658 atm, T=328 K, molar mass= ? g/mol• 1atm =760 mmHg, T(K)=273.15+t(0C), PV=nRT, & Molar Mass =(mass/n)

g/mole

T(K) = 55°C + 273.15T = 328 K

What is the molar mass of a gas if 12.0 g occupies 197 L at 3.80 x 102 torr and 127 °C?• m = 12.0g, V = 197 L, P = 0.50 atm, T =400 K,

molar mass= ?g/mol• 1atm =760 mmHg, T(K)=273.15+t(0C), PV=nRT, & Molar Mass

=(mass/n) g/mole