# A sample of NH_3 gas occupies 75.0 L at STP. How many molecules is this?

Nov 25, 2015

$1.99 \cdot {10}^{24}$

#### Explanation:

Your strategy for this problem will be to determine how many moles of gas you have in that volume at STP, then use Avogadro's number to find the number of molecules of ammonia would be found in that many moles.

STP, Standard Temperature and Pressure, conditions are defined as a temperature of ${0}^{\circ} \text{C}$ and a pressure of $\text{100 kPa}$.

Under these conditions for pressure and temperature, One mole of any ideal gas occupies exactly $\text{22.7 L}$ - this is known as the molar volume of a gas at STP.

This means that you can use the molar volume of a gas to determine how many moles you have in $\text{75.0 L}$ of ammonia.

75.0color(red)(cancel(color(black)("L"))) * "1 mole"/(22.7color(red)(cancel(color(black)("L")))) = "3.304 moles"

Now, you know that one mole of any substance contains exactly $6.022 \cdot {10}^{23}$ molecules of that substance. IN you case, $3.304$ moles of ammonia will contain

3.304color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules NH"_3)/(1color(red)(cancel(color(black)("mole")))) = color(green)(1.99 * 10^(24)"molecules NH"_3