A sample of fluorine has a density of?

Question

A sample of fluorine gas has a density of  _____g/L at a pressure of 0.559 atm and a temperature of 44.0 °C. Assume ideal behavior.

Answer 1

Density is mass per unit volume. Since we're assuming ideal behavior, we can rearrange the ideal gas law to yield density.

PV = nRT

Since we know the identity of the gas, we can easily convert from n (moles of gas) to mass of gas. n will need to be in our numerator. Volume needs to be in the denominator. We can divide by V and RT from both sides:

PV / (VRT) = nRT / (VRT) = P / (RT) = n / V

Now we convert moles to mass using molar mass (g substance / mole substance):

n (GMM) / V = m / V = P * GMM / (RT)

Let's apply this:

molar mass of fluorine gas: 2 * atomic mass fluorine atom = 38.00 g / mol

density: m / V = (0.599 atm) (38.00 g F₂ / mol F₂ ) / [(0.08206 L * atm / K * mol ) (44 + 273 K) ]

m / V = (0.599 atm) (38.00 g F₂ / mol F₂ ) / [(0.08206 L * atm / K * mol ) (317 K) ] =

0.599 * 38.00 / (0,08206 * 317) g / L = 0.875 g / L

Would you expect this gas to sink or float with respect to room air under the same conditions? Show your calculations. (Hint: Look up the composition of air and use the idea of partial pressures to simplify your work.)