okay let's try some calculations regarding the density of a gas. a gas was
found to have a density of 0.169 grams per liter at 17 degrees Celsius and a
pressure of 760 torr what is the gas? so we are going to need to do some
calculations regarding ideal gases. so if you need to review that concept go ahead
and check out my tutorial on ideal gases first and when you're ready give this a try.
okay so here's our given data 0.169 grams per liter 17 degrees Celsius and
760 torr so as we said we're going to need to use the ideal gas law
that's PV equals nRT and if we're going to identify this gas we're probably
going to want to find the molar mass of the gas and molar mass is grams per mole
we have some information that is associated with mass we have a density
so that helps and then we don't have moles so we are gonna want to get moles
so let's solve for moles here and it's going to be equal to PV over RT and so
now let's plug in what we know we have moles being equal to one point zero zero
atmospheres because we're gonna have to convert from tor two atmospheres and 760
torr is equal to one atmosphere and now for volume we have a density
right we have 0.169 grams per liter so what if we just go ahead and assume one
liter because we've got a ratio so if we plug in one liter and then we make sure
to remember that that means that we're looking at 0.169 grams then the math
should work out fine so let's assume one liter then we're gonna divide by our the
gas constant in this case it's going to be the version that is zero
point zero eight to one liters atmospheres per mole Kelvin and then
after that we have temperature and that is 17 degrees Celsius but we always want
to express temperatures in Kelvin when we do calculations so that will be 273
plus 17 which is 290 Kelvin so if we do the arithmetic we get zero point zero
for two moles of gas and now we actually can go further with this because if we
assumed one liter we also assumed 0.169 grams so we can go ahead and calculate
the molar mass because for the one liter sample that we are assuming we've got
0.169 grams over 0.042 moles and that gives us 4.0 grams per mole so we know
the molar mass of this unknown gas is 4.0 grams per mole. now luckily this
number is so small that it can only be one thing this gas has to be helium
because helium is mono atomic and helium weighs four atomic mass units so there's
only one guest that's lighter than that that's hydrogen and that's H2 that's two
atomic mass units or two grams per mole so helium is the only thing that works
here and that is the identity of this gas.