On a hot summer day, the density of air at atmospheric pressure at 36.5°C is 1.2

Question

On a hot summer day, the density of air at atmospheric pressure at 36.5°C is 1.2698 kg/m3. (a) What is the number of moles contained in 1.00 m3 of an ideal gas at this temperature and pressure? mol (b) Avogadro's number of air molecules has a mass of 2.82 102 kg. What is the mass of 1.00 m3 of air? (Assume air is an ideal gas.) kg (c) Does the value calculated in part (b) agree with the stated density of air at this temperature? (Consider that it does if the values are within 10% of each other.) Yes No

Explanation / Answer

a)

P = 1 atm = 1*.013*10^5 pa

T = 36.5 + 273 = 309.5 K

a) use ideal gas equation,

P*V = n*R*T

n/V = P/(R*T)

= 1.013*10^5/(8.314*309.5)

= 39.37 mol/m^3

so no of moles in 1 m^3 volume = 39.37 mol <<<<<<<<------------------Answer

b) no of moles in 1m^3 gas, n = 39.37

mass of this gas = 39.37*2.82*10^-2

= 1.11 kg <<<<<<<<------------------Answer

c) No

beacsue, density of air = mass/volume

= 1.11 kg/m^3

when we take the ration, 1.2698/1.11 = 1.1439

= 114.39%

so, there is a diffrence of 14.39%.

so, the answer is no.

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