Amount of subtance

(1)PV = nRT

You know this right?

(2)Moles = mass / mr

Therefore if we substitute (2) into (1)

PV = (Mass / Mr) x R x T

but we know Density = mass / Volume right?

Re-arrange said equation above and substitute for volume and you'll get the equation with variables you want.

Hint:

PV = nRT so nRT / P = V

So if we say that n = 1:
(1 x 8.31 x 323) / (1.01 x 10⁵) = 0.0266 m³ = 26.6 dm³

Now we know that 1 mole of gas will occupy 26.6 dm³ at 323 K and 1.01 x 10⁵ Pa:
n x 26.6 dm³ = V

Bear in mind that the equation for density is D= m / V

The next step is to manipulate n x 26.6 dm³ = V into an equation that equals density (as this will bring Mr - what we want to find out - into the equation):
V / n = 26.6
n / V = 1 / 26.6

To get n / V to become m / V (aka D), we multiply by Mr because Mr x n = m:
n x Mr / V = Mr / 26.6

And we can simply to:
m / V = Mr / 26.6

m / V is D so:
D = Mr / 26.6

As we know D, the only unknown in this equation is Mr so:
Mr = D x 26.6 = 1.655 x 26.6 = 44.0

Please tell me if you spot a mistake - I've checked it with the Chemsheets mark scheme but they can sometimes be a bit inconsistent.

It's good, but could be whittled down a little:

It's good, but could be whittled down a little:

PV=RT (for one mol)
V = RT/P = (8.31 x 323) / (1.01 x 10⁵) = 0.0266 m³ = 26.6 dm³

Density = m/V

mass of 1 mol = Density x V = 1.655 x 26.6 = 44.0

A gas has a density of 1.655gdm^-3 at 323k and 1.01 x 10^5 Pa.Calculate Mr

I know that we have to use

PV =nmr to find moles
and then us moles =mass/Mr
but how we will find Volume or Mass???

We have given a density
1.655 =mass/volume