An ideal gas at a temperature of 22 C is trapped in a metal cylinder of volume 0.2 m^3 at a pressure of 1.6x10^6 Pa. The gas has a molar mass of 4.3 x 10^(-2) kg mol^(-1). Calculate the density of the gas in the cylinder.

It's useful to start from the density formula and see what we need to find. The density is given by (rho) = m/V

We know the volume V, so we only need to find the mass m.

We are given the value for molar mass, and knowing that the number of moles, n, is given by: n=m/M, we can rearrange the equation and express the mass: m = nM

The only thing we need to find is the number of moles, which can be found from the ideal gas law:

PV = nRT

n = PV/(RT)

Substituting this into the equation for density gives us the final formula:

rho = MP/(RT) (Note that the volume V cancels out)

Now the only thing left is to substitute in the values and calculate the final answer.

We have:

M = 0.043 kg mol^-1

P = 1.6x10⁶ Pa

R = 8.31 J K^-1 mol^-1

T = 22 C = 295 K (don't forget to change to Kelvin scale for such problems, noting the units for ideal gas constant R)

The final answer is:

rho = 28.1 kg m^-3