What pressure will be exerted by 2.01 mol hydrogen gas in a 6.5 L cylinder at 20°C?

Feb 17, 2017

$\text{7.4 atm}$

Explanation:

In order to be able to solve this problem, you must be familiar with 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

In your case, you must find the pressure exerted by the gas, so rearrange the ideal gas law equation to isolate $P$

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

Now, before plugging in your values, make sure that the units given to you by the problem match those used in the expression of the universal gas constant.

In this case, you have

In this case, you have

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

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

color(white)(aaaaacolor(black)("moles " ["mol"])aaaaaaaaaaaaacolor(black)("moles " ["mol"])aaa)color(darkgreen)(sqrt())

color(white)(acolor(black)("degrees Celsius " [""^@"C"])aaaaaaaaaacolor(black)("Kelvin " ["K"])aaaa)color(red)(xx)

To convert the temperature from degrees Celsius to Kelvin, use the conversion factor

color(blue)(ul(color(black)(T["K"] = t[""^@"C"] + "273.15")))

Plug in your values into the above equation and solve for $P$

$P = \left(2.01 \textcolor{red}{\cancel{\textcolor{b l a c k}{\text{moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * (20 + 273.15) color(red)(cancel(color(black)("K"))))/(6.5 color(red)(cancel(color(black)("L}}}}\right)$

$\textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{P = \text{7.4 atm}}}}$

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one significant figure for the temperature of the gas.