PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
We can rearrange this equation to solve for the density, which is defined as mass per unit volume:
density = mass/volume = (n * molar mass)/V
First, we need to convert the pressure from torr to atmospheres (atm):
7.00 x 10^2 torr * (1 atm / 760 torr) = 0.921 atm
Next, we need to convert the temperature from degrees Celsius (°C) to Kelvin (K):
27.0 °C + 273.15 = 300.15 K
Now, we can calculate the number of moles of fluorine gas using the ideal gas law:
n = PV/RT = (0.921 atm * V) / (0.08206 L atm/mol K * 300.15 K)
Since we don't know the volume, we'll leave it as V for now.
Finally, we can calculate the density:
density = (n * molar mass)/V = [(0.921 atm * V) / (0.08206 L atm/mol K * 300.15 K)] * (38.0 g/mol) / V
Simplifying the expression:
density = (1.458 g/L) * (0.921 atm / V)
Therefore, the density of fluorine gas at 7.00 x 10^2 torr and 27.0 °C is 1.458 g/L multiplied by the ratio of 0.921 atm to the volume in liters.
