# Question 19ce3

Mar 24, 2016

$\text{37.8 L}$

#### Explanation:

Your strategey here will be to

• use the molar mass of the gas to convert the sample to moles

• use the molar volume of a gas a STP as a conversion factor

The molar volume of a gas at STP can be used as a conversion factor that helps you go from moles to liters, or vice versa.

As its name suggest, the molar volume of a gas at STP will tell you what volume would one mole of a gas occupy under STP conditions.

Now, STP conditions are currently defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$. Under these conditions for pressure and temperature, one mole of any ideal gas occupies $\text{22.7 L}$.

In other words, a gas kept under STP conditions will have a molar volume of ${\text{22.7 L mol}}^{- 1}$.

In your case, the problem provides you with the mass of neon, which means that you're going to have to use its molar mass to convert it to moles.

33.6 color(red)(cancel(color(black)("g"))) * overbrace("1 mole Ne"/(20.18color(red)(cancel(color(black)("g")))))^(color(brown)("molar mass of Ne")) = "1.665 moles Ne"#

So, if one mole occupies $\text{22.7 L}$ at STP, it follows that this many moles will occupy

$1.665 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles Ne"))) * overbrace("22.7 L"/(1color(red)(cancel(color(black)("mole Ne")))))^(color(purple)("molar volume of a gas at STP")) = color(green)(|bar(ul(color(white)(a/a)"37.8 L} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

The answer is rounded to three sig figs.

SIDE NOTE Many sources still use the old definition of STP, which implies a pressure of $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

Under these conditions, one mole of any ideal gas occupies $\text{22.4 L}$.

If this is the value given to you for the molar volume of a as at STP, simply redo the calculations using $\text{22.4 L}$ instead of $\text{22.7 L}$.