Hi Julia,
Gas laws can at first be difficult to understand, but with a little practice they get much easier!
To calculate the density of a gas we first need to take the ideal gas law:
PV = nRT (P= pressure, V = volume, n = moles, R = ideal gas constant, T = temperature (in Kelvin!))
And convert it to a more useful equation for this question which is (I will derive it at the bottom if you would like to see that):
D = PM/RT (D = density, P = pressure, M = molecular mass, R = ideal gas constant, T = temperature (in Kelvin!))
With this adjusted equation, it is just a matter of plugging in some values to calculate the density! STP stands for standard temperature and pressure which is 1 atm and 0°C. But, remember, we need temperature in Kelvin (K) and K = C + 273. So STP is also 1 atm and 273 K.
First question:
Calculate the density (in g/L) of nitrogen dioxide gas at STP:
**use D = PM/RT.**
We are solving for D, P = 1atm (STP), M = molecular mass of nitrogen dioxide (NO2) which is 46g/mol (14g/mol for Nitrogen, 16g/mol per O), R = constant = 0.0821 L·atm/K·mol, T = 273 K (STP).
So, the answer is 2.05 g/L (all other units cancel out and you get units of mass over volume, or, density!)
Second question:
Then calculate the density at 1.01 atm and 27.6 ˚C.
Same process, use D = PM/RT, just make sure to remember to covert °C to Kelvin (K = C + 273). So the Temp we will use in the equation is 300.6 K, and the Pressure is 1.01 atm, all other variables are the same.
So, the answer is 1.88 g/L.
Derivation of D = PM/RT (feel free to ignore!)
PV=nRT (ideal gas law), let's rearrange for n (moles):
n = PV/RT
n, or moles, is defined as mass (m) / molar mass (M). So, if we plug in for n, we get:
m/M = PV/RT
Now that we have mass and molar mass in the equation, let's remember the definition of density = mass/volume. Next, we rearrange to get mass (m) over volume (V):
m/V = PM/RT
Since m/V is equal to density (D), we now have the desired equation D=PM/RT!
Feel free to ask any questions!