Question

Express the concentrations/pressure of the following atmospheric constituents in each of the units atm, molL^-1, molecules cm^-3, and ppmv (assume 300 K)

a.) Oxygen (p=0.21 atm)

n/v = p/RT = 0.21 atm/ (o.0821 L atm mol^-1 K^-1 x 300K) = 8.5 x 10^-3 mol L ^-1

8.5 x 20 ^-3 mol L^-1 x Na(avagadros number) molecules / mol x 1 L / 1000 cm^3 = 5.1 x 10^18 molecules cm^-3

p (O2) = 0.21 x (1 ppmv / 10^-6 atm) = 2.1 x 10^5 ppmv

b) Carbon dioxide (p = 3.5 x 10^-4 atm)

c) Methane (p = 1700 ppbv)

d) Hydroxyl radical (c+ 5 x 10^5 molecules cm^-3)

Answer 1

b) The partial pressure of CO in the atmosphere is P_CO = 3.5*10^-4 atm.

Use the ideal gas law

P*V = n*R*T where n = number of moles of the gas

===> n/V = P/RT

Plug in values and get

n/V = (3.5*10^-4 atm)/(0.082 L-atm/mol.K).(300 K) = 1.42276*10^-5 mol/L ≈ 1.42*10^-5 mol/L (ans).

Use Avogadro’s law to find out the number of molecules corresponding to 1.42*10^-5 mol/L CO.

Convert mole to molecules by multiplying by Avogadro’s number.

Concentration of CO in molecules/cm³ = (1.42276*10^-5 mol/L)*(6.022*10²³ molecules/mol)*(1 L/1000 cm³) = 8.5678*10¹⁵ molecules/cm³ ≈ 8.57*10¹⁵ molecules/cm³ (ans).

Assume the total pressure to be 1 atm; henc, the concentration in ppm_v can be expressed as

P_CO = (ppm_v)*10^-6*P_tot

===> ppm_v = (P_CO/P_tot)*10⁶ = (3.5*10^-4 atm/1 atm)*10⁶ = 350 (ans).

c) Given ppm_v (CH₄) = 170, find the partial pressure of CH₄ in the atmosphere by using the relation

P_CH4 = (ppm_v)*10^-6*P_tot

Assume P_tot = 1 atm; hence, P_CH4 = (170)*10^-6*(1 atm) = 1.7*10^-4 atm (ans)

Use the ideal gas law to find the concentration in mol/L.

n/V = P/RT = (1.7*10^-4 atm)/(0.082 L-atm/mol.K).(300 K) = 6.9106*10^-6 mol/L ≈ 6.91*10^-6 mol/L (ans).

Convert the concentration in mol/L to molecules/cm³ = (6.9106*10^-6 mol/L)*(6.022*10²³ molecules/mol)*(1 L/1000 cm³) = 4.1616*10¹⁵ molecules/cm³ ≈ 4.16*10¹⁵ molecules/cm³ (ans).

d) Given the concentration of hydroxyl radicals is 5*10⁵ molecules/cm³, find the concentration in mole/L as (5*10⁵ molecules/cm³)*(1 mole/6.022*10²³ molecules)*(1000 cm³/1 L) = 8.3029*10^-16 mole/L ≈ 8.30*10^-16 mole/L (ans).

Next, find the pressure by using the relation

P = (n/V)*R*T where n/V is the concentration of hydroxyl radicals.

P = (8.3029*10^-16 mole/L)*(0.082 L-atm/mol.K)*(300 K) = 2.0425*10^-14 atm ≈ 2.04*10^-14 atm (ans).

Next find out ppm_v as ppm_v = (P_hydroxyl/P_tot)*10⁶ = (2.0425*10^-14 atm/1 atm)*10⁶ = 2.0425*10^-8 ≈ 2.04*10^-8 (ans).