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Section summary

  • The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
  • The ideal gas law can be written in terms of the number of molecules of gas:
    PV = NkT , size 12{ ital "PV"= ital "NkT"} {}
    where P size 12{P} {} is pressure, V size 12{V} {} is volume, T size 12{T} {} is temperature, N size 12{N} {} is number of molecules, and k size 12{k} {} is the Boltzmann constant
    k = 1 . 38 × 10 23 J/K . size 12{k=1 "." "38" times "10" rSup { size 8{–"38"} } " J/K"} {}
  • A mole is the number of atoms in a 12-g sample of carbon-12.
  • The number of molecules in a mole is called Avogadro’s number N A size 12{N rSub { size 8{A} } } {} ,
    N A = 6 . 02 × 10 23 mol 1 . size 12{N rSub { size 8{A} } =6 "." "02" times "10" rSup { size 8{"23"} } `"mol" rSup { size 8{ - 1} } } {}
  • A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
  • The ideal gas law can also be written and solved in terms of the number of moles of gas:
    PV = nRT , size 12{ ital "PV"= ital "nRT"} {}
    where n size 12{n} {} is number of moles and R size 12{R} {} is the universal gas constant,
    R = 8 . 31 J/mol K . size 12{R=8 "." "31"`"J/mol" cdot K} {}
  • The ideal gas law is generally valid at temperatures well above the boiling temperature.

Conceptual questions

Find out the human population of Earth. Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth?

Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

Problems&Exercises

The gauge pressure in your car tires is 2 . 50 × 10 5 N/m 2 size 12{2 "." "50"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} at a temperature of 35 . 0 º C size 12{"35" "." 0°C} {} when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to 40 . 0 º C size 12{ +- "40" "." 0°C} {} ?

1.62 atm

Convert an absolute pressure of 7 . 00 × 10 5 N/m 2 size 12{7 "." "00" times "10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} to gauge pressure in lb/in 2 . size 12{"lb/in" rSup { size 8{2} } "." } {} (This value was stated to be just less than 90 . 0 lb/in 2 size 12{"90" "." "0 lb/in" rSup { size 8{2} } } {} in [link] . Is it?)

Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20 . 0 º C size 12{"20" "." 0°C} {} . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60 . 0 º C size 12{"60" "." 0°C} {} (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?

(a) 0.136 atm

(b) 0.135 atm. The difference between this value and the value from part (a) is negligible.

Large helium-filled balloons are used to lift scientific equipment to high altitudes. (a) What is the pressure inside such a balloon if it starts out at sea level with a temperature of 10 . 0 º C size 12{"10" "." 0°C} {} and rises to an altitude where its volume is twenty times the original volume and its temperature is 50 . 0 º C size 12{ +- "50" "." 0°C} {} ? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)

Confirm that the units of nRT size 12{ ital "nRT"} {} are those of energy for each value of R size 12{R} {} : (a) 8 . 31 J/mol K size 12{8 "." "31"" J/mol" cdot K} {} , (b) 1 . 99 cal/mol K size 12{1 "." "99 cal/mol" cdot K} {} , and (c) 0 . 0821 L atm/mol K size 12{0 "." "0821 L" cdot "atm/mol" cdot K} {} .

(a) nRT = ( mol ) ( J/mol K ) ( K ) = J size 12{ ital "nRT" = \( "mol" \) \( "J/mol" cdot K \) \( K \) =" J"} {}

(b) nRT = ( mol ) ( cal/mol K ) ( K ) = cal size 12{ ital "nRT" = \( "mol" \) \( "cal/mol" cdot K \) \( K \) =" cal"} {}

(c) nRT = ( mol ) ( L atm/mol K ) ( K ) = L atm = ( m 3 ) ( N/m 2 ) = N m = J

Questions & Answers

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or infinite solutions?
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Differences Between Laspeyres and Paasche Indices
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J, combine like terms 7x-4y
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f(n)= 2n + 1
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. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
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At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
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the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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Source:  OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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