# Question bb06f

Apr 19, 2015

NTP, or Normal Temperature and Pressure, conditions imply a temperature of ${20}^{\circ} \text{C}$, or 293.15 K, and a pressure of 1 atm.

$T = \text{293.15 K}$
$P = \text{1 atm}$

Since you also know the volume the gas occupies under these conditions, you can easily solve for the number of moles present by using the ideal gas law equation, $P V = n R T$.

Once you know how many moles of oxygen gas you have, you can calculate the number of oxygen molecules by using the fact that 1 mole of any substance contains exactly $6.022 \cdot {10}^{23}$ molecules of that substance - this is known as Avogadro's number.

So, start by figuring out he number of moles you have

$P V = n R T \implies n = \frac{P V}{R T}$

n = (1cancel("atm") * 11.2cancel("L"))/(0.082(cancel("L") * cancel("atm")/("mol" * cancel("K")) * 293.15cancel("K"))) = "0.4659 moles "# ${O}_{2}$

This is equivalent to having

$0.4659 \cancel{\text{moles") * (6.022 * 10^(23)"molecules")/(1cancel("mole")) = color(green)(2.81 * 10^(23)"molecules}}$

Since oxygen is a diatomic molecule, i. e. it takes two oxygen atoms to make up an oxygen molecule, the number of oxygen atoms will be twice as big

$2.81 \cdot {10}^{23} \cancel{\text{molecules") * "2 atoms"/(1cancel("molecule")) = color(green)(5.62 * 10^(23)"atoms}}$