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Hydrogen gas has a density of [tex]$0.090 \, g/L$[/tex], and at normal pressure and [tex]$2.12^{\circ} C$[/tex] one mole of it takes up 22.4 L. How would you calculate the moles in [tex]$570 \, g$[/tex] of hydrogen gas?

Set the math up. Do not solve. Leave your answer as a math expression.

moles [tex]$= \frac{570 \, g}{0.090 \, g/L} \times \frac{1 \, mol}{22.4 \, L}$[/tex]



Answer :

GinnyAnswer
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.

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