I need help figuring out #3 parts A & B. Assuming ideal gas behavior, estimate t

Question

I need help figuring out #3 parts A & B.

Assuming ideal gas behavior, estimate the number of nitrogen molecules in a typical human breath of 0.5 L at 1.0 bar and 37 degree C. Air consists of about 78% N_2 molecules. Estimate the mass of N_2 in one human breath. Find expressions for alpha and kappa for a gas that follows the van der Waals equation of state. You do not need to reduce the expressions to simplest mathematical form. For ethylene gas the van der Waals constants are: a = 4.552 dm^6 atm mol^-2 and b = 5.82 Times 10^-2 dm^3 mol^-1 Use the results from part (a) to estimate alpha and kappa for ethylene gas at 40 degree C and 20.0 atm.

Explanation / Answer

2)

a)

volume of air = 0.5 L

pressure = 1.0 bar = 0.987 atm

T = 37 +273 = 310 K

P V = n R T

0.987 x 0.5 = n x 0.0821 x 310

n = 0.0194

moles of air = 0.0194

in these moles of only 78 % of N2

so moles of N2 = 0.0194 x 78 / 100 = 0.01513

1 mole N2----------------------> 6.023 x 10^23 molecules

0.01513 moles N2 --------------> 6.023 x 10^23 x 0.01513 = 9.11 x 10^21

number of nitrogen molecules = 9.11 x 10^21

b)

molar mass of N2 = 28 g/ mol

mass of nitrogen = moles x molar mass

                         = 0.01513 x 28

                        = 0.424 g

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