Question

How many atoms are in 13.97 liters of water vapor at STP

Answer 1

Let's assume that water vapor has ideal gas behavior. 
Then we can use ideal gas formula,
PV = nRT

Where, P is the pressure of the gas (Pa), V is the volume of the gas (m³), n is the number of moles of gas (mol), R is the universal gas constant ( 8.314 J mol⁻¹ K⁻¹) and T is temperature in Kelvin.

P = 1 atm = 101325 Pa (standard pressure)
V = 13.97 L = 13.97 x 10⁻³ m³
n = ?
R = 8.314 J mol⁻¹ K⁻¹
T = 0 °C = 273 K (standard temperature)

By substitution,
101325 Pa x 13.97x 10⁻³ m³ = n x 8.314 J mol⁻¹ K⁻¹ x 273 K
                                          n = 0.624 mol

Hence, the moles of water vapor at STP is 0.624 mol.

According to the Avogadro's constant, 1 mole of substance has 6.022 × 10²³ particles.

Hence, number of atoms in water vapor = 0.624 mol x 6.022 × 10²³ mol⁻¹
                                                                = 3.758 x 10²³