Please help solve question 3. Now convert to the \"semi-\" SI units, /k mole. No

Question

Please help solve question 3.

Now convert to the "semi-" SI units, /k mole. Note that L and dm are the same so the result of your conversion should give you the same value for the units, dm^3 Pa/K mole. Carry least 5 significant digits. Finally, the Boltzmann constant, k, is a rather important quantity. Look up a valid value for k to at least 5 significant digits. Now take your result from part (a) and divide it by your value for k. Comment on your result (carrying 5 significant digits) and complete the following equation: R/k = Starting from the following view of the ideal gas law and ... P = nRT/V Derive (show the algebraic steps!!) a formula for the mass density: rho = m/v. You will need to use the following relationship: n = m/M where m is the mass, and M is the molar mass of the gas. Rearrange your formula in (a) solving for the molar mass, M. For a 0.897 g sample of gas that occupies 0.250 L at 1.000 atm and 298 K. An important quantity describing a gas is called the "Number Density." Simply put, this is a very large number telling you how many molecules are in your sample per m^3, (N/V). Using the ideal gas equation from exercise 1, derive a formula for the number density. Show the algebraic steps. You will need the formula: n = N/N_a, where N is the actual number of molecules and N_a is Avogadro's number. Calculate the number density in m^-3 for a sample of gas at 1.000 atm and 298 K. Calculate the number density in m^-3 for the region of space at 62 miles above Earth's surface, P = 0.032 Pa, T = -85 degree C. The International Space Station is 170 miles higher!

Explanation / Answer

3)
a)
from ideal gas law:
P*V = n*R*T
Here:n = N/Na
so,
P*V = (N/Na)*R*T
so,
N/V = P*Na/(R*T)
number density = P*Na/(R*T)

b)
1st lets find the number density in L-1
N/V = P*Na/(R*T)
= 1*(6.022*10^23)/(0.0821*298)
= 2.461*10^22 L-1
1L = 10^-3 m^3
so,
N/V = 2.461*10^22 * 10^3 = 2.461*10^25 m-3
Answer: 2.461*10^25 m-3

c)
P = 0.032 pa
T = -85 oC = (-85+273) K = 188 K
N/V = P*Na/(R*T)
= 0.032*(6.022*10^23)/(8.314*188)
= 1.233*10^19 m-3
Answer: 1.233*10^19 m-3

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