Question

Please help explain how to get these answers! I have a big test tomorrow and need help. Please write clear. Thanks!!

Problem 4: Gases & Solids (26 pts) Around 100 km above the surface of the Earth, the pressure is a low 3.2 x 104 mbar, while the temperature is an unexpectedly comfortable 300 K A balloon containing this sample is 40,582 L under these conditions. What is this balloon's volume (in ml) at Earth's surface-around 298 K and 1 atm? (6 pts) 12.7 ml How many gas particles are contained in 1 ml of air at 100 km, given the pressure and temperature there? (5 pts) 7.73x107 Oddly, in this region, there's about 400,000 atoms of sodium in every cubic centimeter of air. What is the mole fraction of sodium? (6 pts) 5.17X 10* Why would it be odd to observe sodium in the atmosphere? (3 pts) The sodium generally comes from meteors that vaporize in that portion of the atmosphere. Sodium metal adopts a body-centered cubic structure, which houses 2 full sodium atoms for every unit cell and is shown below. If the radius of a sodium atom is 227 pm, what is the edge length of a unit cell (also in pm)? (6 pts) 524 pm

Answer 1

PV = nRT - ideal gas law

P₁V₁ /T₁ = P₂V₂ /T₂

at 100 km height

P₁ = 3.2E-4 mbar = 3.2E-5 kPa ( 1 bar = 1 atm)

V₁ = 40582 L

T₁ = T₂ = 300 K - approx.

P₂ = 101 kPa ( 1 atm)

volume at earth surface

V₂ = V₁ * P₁/P₂ = 40582L * 3.4E-5 kPa/101kPa

= 1.286E-3 L

= 12.86 mL

b) Volume V = 1 mL = 1.0E-6 cu.m

P = 3.2E-2 Pa T = 300 K ; R = 8.3

n = PV/RT = 3.2E-2 *1.0E-6 /(8.3*300)

= 1.285E-11 moles

1 mol contains 6.02E+23 molecules ,Avogadro number

number of particles = 1.285E-11 * 6.02E+23 = 7,737E+12

c) 400000 atoms of Na per cc

= 4.0E+5/6.02E+23 = 6.64E-19 moles

molar fraction of sodium = 6.64E-19/1.285E-11 = 5.17E-8