Question

Question #e7283

Answer 1

`"0.32 g"` methane.

Explanation:

Take the ideal gas law

`PV = nRT`

and the equation for molar mass,

`MM = m/"mol"`

When you rearrange that equation, you get

`n = m/(MM)`

When you plug in the rearranged molar mass equation into ideal gas law, you get

`PV = (mRT)/(MM)`

I wasn't sure what you use for room temp and pressure, so I went with `"298 K"` and `"1 atm"`. Typically this would be calculated at STP (standard temperature and pressure, `"273 K"` and `"1 atm"`) because room temperature is subjective.

The molar mass of methane is `"16.04 g/mol"`; the ideal gas constant in atmospheres `(R)`, is `0.08206 ("atm" * "L")/("mol" * "K")`

Plug in all of these values into the rearranged ideal gas law:

`("1 atm")("0.48 L") = (m(0.08206 ("atm" * "L")/("mol" * "K"))("298 K")) / ("16.04 g/mol")`

Plug this into a calculator and for `m` (mass), you get `"0.32 g"`.