# Question 51c75

Apr 12, 2017

$\text{6.14 moles}$

#### Explanation:

All you have to do here is to use the ideal gas law equation, which looks like this

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{P V = n R T}}}$

Here

• $P$ is the pressure of the gas
• $V$ is the volume it occupies
• $n$ is the number of moles of gas present in the sample
• $R$ is the universal gas constant, equal to $0.0821 \left(\text{atm L")/("mol K}\right)$
• $T$ is the absolute temperature of the gas

Rearrange the equal to solve for $n$

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

Now, before plugging in the values, make sure that he units you have for volume, pressure, and temperature match the units used in the expression of the universal gas constant.

$\underline{\textcolor{w h i t e}{a a a a \textcolor{b l a c k}{\text{What you have")aaaaaaaaaacolor(black)("What you need}} a a a a a}}$

color(white)(aaaaaacolor(black)("liters " ["L"])aaaaaaaaaaaaaaacolor(black)("liters " ["L"])aaaa)color(darkgreen)(sqrt())

color(white)(aaacolor(black)("atmospheres " ["atm"])aaaaaacolor(black)("atmospheres " ["atm"])aaa)color(darkgreen)(sqrt())

color(white)(aacolor(black)("degrees Celsius " [""^@"C"])aaaaaaaaacolor(black)("Kelvin " ["K"])aaaa)color(red)(xx)#

Notice that you must convert the temperature from degrees Celsius to Kelvin. To do that, use the following conversion factor

$\textcolor{b l u e}{\underline{\textcolor{b l a c k}{T \left[\text{K"] = t[""^@"C}\right] + 273.15}}}$

You will have

$T = {44.0}^{\circ} \text{C" - 273.15 = "317.15 K}$

Now you're ready to solve for $n$

$n = \left(4.70 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{atm"))) * 34.0 color(red)(cancel(color(black)("L"))))/(0.0821 (color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * 317.15color(red)(cancel(color(black)("K}}}}\right)$

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{n = \text{6.14 moles}}}}$

The answer is rounded to three sig figs.