Question

What is the molecular mass of a compound if 560mL have a mass of 1.10g at STP?

Answer 1

`M_r = 44.6`.

Explanation:

We can use the Ideal Gas Law to solve this problem.

`color(blue)(|bar(ul(color(white)(a/a)PV = nRT color(white)(a/a)|)))" "`

Since `n = "mass"/"molar mass" = m/M`, we can write the Ideal Gas Law as

`PV = m/MRT`

We can rearrange this to

`M = (mRT)/(PV)`

At STP, `P = "1 bar"` and `T = "0 °C"`.

∴ `M = ("1.10 g" × 8.314 × 10^"-2" color(red)(cancel(color(black)("bar·L·K"^"-1")))"mol"^"-1" × 273.15 color(red)(cancel(color(black)("K"))))/(1 color(red)(cancel(color(black)("bar"))) × 0.560 color(red)(cancel(color(black)("L")))) = "44.6 g/mol"`

∴ `M_r = 44.6`