# Question 077bf

May 16, 2017

The volume will be $10500$ L, rounded to three significant figures.

#### Explanation:

This question involves the ideal gas law.

$P V = n R T$,

where $P$ is pressure, $V$ is volume, $n$ is moles, $R$ is a gas constant, and $T$ is the temperature in Kelvins.

Before you can use the equation, the mass of hydrogen needs to be converted into moles of hydrogen, and the temperature must be converted to Kelvins by adding $273.15$ to the Celsius temperature.

color(blue)("Convert mass of hydrogen to moles hydrogen".

Multiply the mass of hydrogen by the inverse of its molar mass. Its molar mass is its atomic weight on the periodic table in grams/mole, or g/mol.

$454 \text{g H"xx(1"mol H")/(1.008"g H")="450. mol H"=4.50xx10^2"mol H}$

color(blue)("Organize your data".

Given/Known
$P = \text{1.05 atm}$
$n = 4.05 \times {10}^{2} \text{mol}$
$R = \text{0.082056 L atm K"^(-1) "mol"^(-1)}$
$T = \text{25"^@"C"+273.15="298 K}$
https://en.wikipedia.org/wiki/Gas_constant

Unknown: $V$

color(blue)("Solve"
Rearrange the equation to isolate $V$. Insert the given/known data into the equation and solve.

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

V=(4.05xx^2color(red)cancel(color(black)("mol"))xx0.082056color(white)(.)"L" color(red)cancel(color(black)("atm")) color(red)cancel(color(black)("K"))^(-1) color(red)cancel(color(black)("mol"))^(-1)xx298color(red)cancel(color(black)("K")))/(1.05color(red)cancel(color(black)("atm")))="10500 L"#
(rounded to three significant figures)