Question

Question #24fe2

Answer 1

`"16.6 g/mol"`

Explanation:

The idea here is that you need to use the ideal gas law to determine how many moles of gas you have in that sample.

Once you know how many moles you get in `"0.742 g"` of gas, you can find its molar mass.

So, the ideal gas law equation looks like this

`PV = nRT" "`, where

`P` - the pressure of the gas;
`V` - the volume it occupies;
`n` - the number of moles of gas;
`R` - the ideal gas constant, equal to `0.082"atm L"/"mol K"`
`T` - the temperature of the gas, expressed in Kelvin.

Rearrange this equation to find the number of moles of gas you have in that sample under those specific conditions for pressure and temperature

`n = (PV)/(RT)`

`n = (1.30color(red)(cancel(color(black)("atm"))) * 825 * 10^-3color(red)(cancel(color(black)("L"))))/(0.082(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 19)color(red)(cancel(color(black)("K")))) = "0.04477 moles"`

The molar mass of a substance tells you what the mass of one mole of that substance is. In yur case, you have

`M_"M" = m/n`

`M_"M" = "0.742 g"/"0.04477 moles" = "16.57 g/mol"`

I'll leave the answer rounded to three sig figs

`M_"M" = color(green)("16.6 g/mol")`