The Henry\'s law constant for laughing gas (nitrous oxide. N_2O) is 0.025 M/atm.

Question

The Henry's law constant for laughing gas (nitrous oxide. N_2O) is 0.025 M/atm. A can of whipped cream uses nitrous oxide as a propellant and is pressurized to 3 atm. What is the molar solubility of nitrous oxide in the can? If it is 1 atm outside today, what is the molar solubility when it leaves the can? If all of the gas that escapes from the solution stays in a cream foam, how many ml of cream would you have to dispense to get 2 fluid ounces of whipped cream on your slice of pie at 22 degree C? Assume that the liquid cream itself is negligible contributor to the final foam volume.

Explanation / Answer

H = 0.025 M/ atm

Mi = H*P-i

P = 3 atm

a)

find molar solubility in can

assume total pressure is due to N2O

so

Mi = Hi*Pi

M-N2O = 0.025 M/ atm* 3 atm = 0.075 M = 0.075 mol / L

b)

if P = 1 atm outside, then

assume:

M-N2O = 0.025 M/ atm* 1 atm = 0.025 M = 0.025 mol / L

c)

mL of cream for 2 fluid oz = 59.1471 mL

M = mol/V = 0.075 mol /L

PV = nRT

n = PV/(RT)

n = (1)(59.14*10^-3)/(0.082*298) = 0.00242019 moles required

so

V = mol/M = (0.00242019)/(0.075) = 0.0322692 Liters = 0.0322692*10^3 = 32 mL of gas

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