Question

Question #8dabc

Answer 1

The answer is : V = 2.80x10^-4L.

Gas' properties:
Volume (V)
Pressure (P)
Temperature (T- in Kelvins)
Amount (n - moles)
.
And a Constant R (0.0821 L x atm / mol x K)

The easiest way to solve this problem is to make a set up as follow: !!! STP !!!
V= ? L
P= 1 atm
T= 273 K
n= ?

1) We can get the amount of moles from `5.5 * 10^(-4) g` of `CO_2` gas.

`Molarmass_(CO_2) = 12.01+2 * 16 = 44.01g` of `CO_2`

Now take :

`5.5 * 10^(-4) g CO_2 * (1 mol e CO_2)/(44.01 g CO_2) = 1.25 * 10^(-5)` mol of `CO_2`

2) `PV=nRT`

`1 * V= 1.25 * 10^(-5) * 0.0821 * 273`
`V = 2.80 * 10^(-4) L`

And that's it !

I strongly hope I was helpful !

David Tran
trananhdavid@gmail.com

Answer 2

You would use the ideal gas law in order to solve this problem. The equation for the ideal gas law is `"PV"` = `"nRT"`. STP for the gas laws is `"0"^"o""C"` and `"1 atm"`. The temperature must be converted to Kelvins, and the mass of `"CO"_2` must be converted to moles.

Given/Known:
`"P"` = `"1 atm"`
`"molar mass of CO"_2` = `"44.01 g/mol"`
`"n"` = `"5.5 x 10"^(-4) "g"` x `"1 mol CO2"/"44.01 g CO2"` = `"1.2 x 10"^(-5) "mol CO"_2`
`"R"` = `"0.08205746 L atm K"^(-1) "mol"^(-1)"`
`"T"` = `"0"^"o""C" + 273.15 = 273.15 "K"`

Unknown:
`"V"`

Equation:
`"PV"` = `"nRT"`

Solution: Divide both sides of the equation by `"P"`, to isolate `"V"`. Solve for `"V"`.

`"V"` = `"nRT"/"P"` = `"1.2 x 10"^(-5)`x `"0.08205746"` x `"273.15"` `/` `"1"` = `"2.7 x 10"^(-4) "L"` (Units removed in order to make the equation more compact.)

Answer:
The volume of `"5.5 x 10"^(-4) "g CO"_2` at STP is `"2.7 x 10"^(-4) "L"`.

Answer 3

An alternative approach to this problem is by using molar volume at STP.
We know that, at STP, one mole of any ideal gas occupies `22.4L`.

The number of moles of `CO_2`, knowing that its molar mass is `44.01 g/(mol)`, is

`n_(CO_2) = m_(CO_2)/(molarmass) = (5.5 * 10^(-4)g)/(44.01 g/(mol)) = 1.2 * 10^(-5)` moles

Therefore, since `n = V/(V_(molar)`, we get

`V = n_(CO_2) * V_(molar) = 1.2 * 10^(-5) mol es * (22.4L)/(1 mol e) = 2.7 * 10^(-4) L`

One can use this method as a primary tool or as a way to double-check the result determined using the ideal gas law.