Certainly! To find the moles of hydrogen gas in [tex]\( 570 \text{ g} \)[/tex] given the density of hydrogen gas is [tex]\( 0.090 \text{ g/L} \)[/tex] and one mole of hydrogen gas takes up [tex]\( 22.4 \text{ L} \)[/tex], you can use the following steps.
1. Determine the total volume of hydrogen gas:
Since density [tex]\( \rho \)[/tex] is given by [tex]\( \rho = \frac{\text{mass}}{\text{volume}} \)[/tex], we can rearrange to find the volume [tex]\( V \)[/tex]:
[tex]\[
V = \frac{\text{mass}}{\rho}
\][/tex]
Substituting the given values:
[tex]\[
V = \frac{570 \text{ g}}{0.090 \text{ g/L}}
\][/tex]
2. Determine the total moles of hydrogen gas:
Given that one mole of hydrogen gas occupies [tex]\( 22.4 \text{ L} \)[/tex], we can find the moles [tex]\( n \)[/tex] by dividing the total volume [tex]\( V \)[/tex] by the volume per mole:
[tex]\[
n = \frac{V}{22.4 \text{ L}} = \frac{\frac{570 \text{ g}}{0.090 \text{ g/L}}}{22.4 \text{ L}}
\][/tex]
So, leaving our answer as a math expression:
[tex]\[
\text{moles} = \frac{\frac{570 \text{ g}}{0.090 \text{ g/L}}}{22.4 \text{ L}}
\][/tex]
This setup gives you the expression to calculate the moles of hydrogen gas without performing the calculation steps.
