Question

A sample of air contains 78.08% nitrogen, 20.94% oxygen, 0.0500% carbon dioxide, and 0.930% argon by volume. How many molecules of each gas are present in 5.12 L of the sample at 87°C and 7.52 atm? Enter your answers in scientific notation.

? = molecules N₂

? = molecules O₂

? = molecules CO₂

? = molecules Ar

Answer 1

Given that volume of air = 5.12 L

N2 : Air contains 78.08% nitrogen by volume

volume of N2 V = 78.08 % x 5.12 L = 4 L

temperature T = 87^oC = 87 + 273 K = 360 K

pressure P = 7.52 atm

moles n = ?

Ideal gas equation is

PV = nRT where R = universal gas constant = 0.0821 L atm mol^-1 K^-1

   n = PV/RT

= (7.52 atm x 4 L)/(0.0821 L atm mol^-1 K^-1 x 360 K)

= 1.02 moles

No of moles = 1.02 moles

No of molecules of N2 = moles x avogadro number

= 1.02 x 6.023 x 10²³

   = 6.14 x 10²³ molecules

No of molecules of N2 = 6.14 x 10²³ molecules

O2 :

Air contains 20.94 % oxygen by volume

volume of O2 V = 20.94 % x 5.12 L = 1.07 L

temperature T = 87^oC = 87 + 273 K = 360 K

pressure P = 7.52 atm

moles n = ?

Ideal gas equation is

PV = nRT where R = universal gas constant = 0.0821 L atm mol^-1 K^-1

   n = PV/RT

= (7.52 atm x 1.07 L)/(0.0821 L atm mol^-1 K^-1 x 360 K)

= 0.27 moles

No of moles = 0.27 moles

No of molecules of O2 = moles x avogadro number

= 0.27 x 6.023 x 10²³

   = 1.63 x 10²³ molecules

No of molecules of O2 = 1.63 x 10²³ molecules

CO2 :

Air contains 0.05 % CO2 by volume

volume of CO2 V = 0.05 % x 5.12 L = 0.00256 L

temperature T = 87^oC = 87 + 273 K = 360 K

pressure P = 7.52 atm

moles n = ?

Ideal gas equation is

PV = nRT where R = universal gas constant = 0.0821 L atm mol^-1 K^-1

   n = PV/RT

= (7.52 atm x 0.00256 L)/(0.0821 L atm mol^-1 K^-1 x 360 K)

= 0.00065 moles

No of moles = 0.00065 moles

No of molecules of CO2 = moles x avogadro number

= 0.00065 x 6.023 x 10²³

   = 0.0039 x 10²³ molecules

No of molecules of CO2 = 0.0039 x 10²³ molecules

Ar :

Air contains 0.93 % argon by volume

volume of Ar V = 0.93 % x 5.12 L = 0.048 L

temperature T = 87^oC = 87 + 273 K = 360 K

pressure P = 7.52 atm

moles n = ?

Ideal gas equation is

PV = nRT where R = universal gas constant = 0.0821 L atm mol^-1 K^-1

   n = PV/RT

= (7.52 atm x 0.048 L)/(0.0821 L atm mol^-1 K^-1 x 360 K)

= 0.012 moles

No of moles = 0.012 moles

No of molecules of Ar = moles x avogadro number

= 0.012 x 6.023 x 10²³

   = 0.072 x 10²³ molecules

No of molecules of Ar = 0.072 x 10²³ molecules