Question

An "empty" container is not really empty if it contains air. How may moles of oxygen are in an "empty" two-liter cola bottle at atmospheric pressure (1 atm) and room temperature (25∘C)? Assume ideal behavior.

Answer 1

Answer:

The number of moles present in the container N = 81.56

Explanation:

Pressure = 1 atm = 101325 K pa

Temperature = 298 K

Volume = 0.002 $m^{3}$

Gas constant for oxygen = $\frac{8.314}{32}$ = 0.26 $\frac{KJ}{Kg K}$

From ideal gas equation

P V = m R T -------- (1)

Put all the values in above formula,

101325 × 0.002 = m × 0.26 × 298

⇒ m = 2.61 kg=  2610 gm

This is the mass of the gas.

Now no. of moles of the gas is calculated by

$Number of moles = \frac{Mass of substance}{Mass of one mole}$

$N = \frac{m}{M}$

Mass of one mole of oxygen = 32 gm

N = $\frac{2610}{32}$

N = 81.56

These are the number of moles present in the container.

Answer 2

The number of moles of the air is  0.08 moles.

Using the ideal gas law;

PV = nRT

P = pressure

V = volume

n = Number of moles

R = gas constant

T = temperature in Kelvin

The values are as follows;

P = 1 atm

T = 25∘C + 273 = 298 K

n = ?

R = 0.082 atmLK-1mol-1

V = 2 L

n = PV/RT

n =  1 atm ×  2 L/0.082 atmLK-1mol-1  × 298 K

n = 0.08 moles

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