# What mass of sulfur gas would be found in a 2.45 liter container at SATP?

Jun 29, 2017

$3.21$ $\text{g S}$

#### Explanation:

We're asked to to find the mass of gaseous sulfur that occupies a volume of $2.45$ $\text{L}$ at standard ambient temperature and pressure.

I'll assume for these purposes that the sulfur is present as individual, gaseous atoms, rather than ${\text{S}}_{8}$ (which is reasonable considering ${\text{S}}_{8}$ is a solid at these conditions).

Standard ambient temperature and pressure (SATP) is defined as

• $298.15$ $\text{K}$ (temperature; equal to ${25.0}^{\text{o""C}}$)

• $1$ $\text{atm}$ (pressure)

We can use the ideal-gas equation to solve for the number of moles of sulfur, $n$, knowing that the gas constant, $R$ is equal to $0.082057 \left(\text{L"•"atm")/("mol"•"K}\right)$:

$P V = n R T$

$n = \frac{P V}{R T} = \left(\left(1 \cancel{\text{atm"))(2.45cancel("L")))/((0.082057(cancel("L")•cancel("atm"))/("mol"•cancel("K")))(298.15cancel("K}}\right)\right)$

= color(red)(0.100 color(red)("mol S"

Now, let's use the molar mass of sulfur, $32.07$ $\text{g/mol}$, to calculate the number of grams:

0.100cancel("mol S")((32.07color(white)(l)"g S")/(1cancel("mol S"))) = color(blue)(3.21 color(blue)("g S"

Thus, if a $2.45$-$\text{L}$ tank is filled with pure gaseous sulfur at SATP, we can expect the sulfur sample to have a mass of color(blue)(3.21 sfcolor(blue)("grams".