# Question #c6b11

##### 1 Answer

#### Explanation:

The idea here is that you can use the **ideal gas law** equation to determine how many **moles** of hydrogen gas you have in the balloon.

Once you know that, use hydrogen's **molar mass** to determine how many *grams* would contain that many moles, then finally convert the grams to kilograms by using the conversion factor

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 kg" = 10^3"g")color(white)(a/a)|)))#

An interesting thing to notice here is that the problem mentions **STP** - you don't actually need to worry about that, since the number of moles of gas is assumed to be **constant**.

In other words, the number of moles of gas you used to fill up the balloon at STP **is equal** to the number of moles of gas present at

So, the ideal gas law equation looks like this

#color(blue)(|bar(ul(color(white)(a/a)PV = nRTcolor(white)(a/a)|)))" "# , where

*universal gas constant*, usually given as

**absolute temperature** of the gas

Notice that you must convert the pressure of the gas from *mmHg* to *atm*, so use the conversion factor

#color(purple)(|bar(ul(color(white)(a/a)color(black)("1 atm " = " 760 mmHg")color(white)(a/a)|)))#

Likewise, **do not** forget that you must *absolute temperature*, i.e. the temperature in Kelvin.

Rearrange the ideal gas law equation to solve for

#PV = nRT implies n = (PV)/(RT)#

Plug in your values to get

#n = (658/760color(red)(cancel(color(black)("atm"))) * 31000color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * [273.15 + (-8)]color(red)(cancel(color(black)("K"))))#

#n = "1232.9 moles H"_2#

Use hydrogen gas' **molar mass** to find the mass of hydrogen that would contain this many moles

#1232.9color(red)(cancel(color(black)("moles H"_2))) * "2.01588 g"/(1color(red)(cancel(color(black)("mole H"_2)))) = "2485.4 g"#

Expressed in *kilograms*, the answer will be

#"mass of hydrogen gas" = color(green)(|bar(ul(color(white)(a/a)"2.5 kg"color(white)(a/a)|)))#

I will leave the answer rounded to two **sig figs**.