# Question 1cd39

Mar 15, 2015

You have approximately $1.02 \cdot {10}^{27}$ molecules of air in that volume under thos specific conditions.

In order to determine how many molecule of air you have, you must determine how many moles you have in the room. Before calculating the number of moles you have, convert the volume from cubic feet to liters

V_("room") = 12.0 * 12.0 * 10.0 = "1440 ft"^(3)

$\text{1440 ft"^(3) * "28.2 L"/"1 ft"^(3) = "40,608 L}$

Now just use the ideal gas law equation to solve for the number of moles

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

n = ("1.00 atm" * "40608 L")/(0.082("atm" * "L")/("mol" * "K") * (273.15 + 20)"K") = "1689.2 moles of air"#

Since 1 mole of a substance is defined as containing $6.022 \cdot {10}^{\setminus} \left(23\right)$ molecules of that substance - this is known as Avogadro's number - the total number of molecules of air in the room will be

$\text{1689.2 moles" * (6.022 * 10^(23)"molecules")/"1 mole" = 1.02 * 10^(27)"molecules}$

The answer is rounded to three sig figs.