Sunday, September 11, 2022

9702_w18_qp_42 Question 2

 

Answer:

  • An ideal gas is a gas that obeys the equation pV/T = constant where p is pressure, V is volume, and T is temperature of the gas.




Answer:

  • An equation linking the macroscopic properties p and V of an ideal gas to its microscopic properties is pV = ⅓ Nm<c2>, where

    • p and V are pressure and volume, respectively

    • Nm is the number of atoms times the mass of each atom, thus, the mass of the gas

    • <c2> is the mean-square speed

  • Substituting the given values, the <c2> is

    • <c2> = 3pV/Nm

    • <c2> = 3 (2.12 x 107) (1.84 x 10-2) / (3.20)

  • The root-mean-square speed is the square root of <c2>, so the answer is 605 m s-1.




Answer:

  • The amount n is calculated from the rearranged Ideal Gas equation.


n = pV/RT


  • The equation gives the n when all quantities are expressed in SI units. This means that the temperature T must be converted to kelvin before plugging in values.


n = (2.12 x 107) (1.84 x 10-2) / (8.31 x 295)


  • Therefore, n = 159 mol.



Answer:

  • The 2 versions of Ideal Gas Law i.e. pV = nRT and pV = NkT, when combined gives


nR = Nk


  • The mass M of a gas is equal to the number of atoms N in the gas multiplied by mass m.


M = Nm


so, N = M / m


  • Combining the 2 equations above, we should get


nR = M k/ m


m = Mk / nR


  • We also know that the Boltzmann constant k is the ratio of the gas constant R and Avogagadro’s number NA.


k = R / NA


k / R = 1 / NA


So our working equation becomes


mass of one atom m = M / (nNA)


where M is the mass of the gas and NA is the Avogadro’s constant.


  • The mass m, therefore is, 


m = 3.20 / (159 x 6.02 x 1023


m = 3.34 x 10-26 kg



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