Determine the specific mass of fluorine (F2) in g/cm³ in 20°C and 188 torr

Use PV = nRT and the conditions listed to determine the volume of F2.

Then specific mass = density = molar mass/volume in L = ?

To determine the specific mass of fluorine (F2) in g/cm³ at a given temperature and pressure, we need to use the ideal gas law equation, which relates the pressure, volume, number of moles, and temperature of a gas:

PV = nRT

where:
P = pressure (in units of force per unit area, such as torr)
V = volume (in units of cubic centimeters, cm³)
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in units of Kelvin, K)

In order to use this equation, we need to convert the given temperature and pressure to their necessary units.

Temperature:
The given temperature is in Celsius (°C), but we need to convert it to Kelvin (K). The conversion between Celsius and Kelvin is done by adding 273.15 to the Celsius temperature.

20°C + 273.15 = 293.15 K

Pressure:
The given pressure is in torr, but the ideal gas law equation uses units of atmosphere (atm). To convert torr to atm, we divide by 760 (since 760 torr = 1 atm).

188 torr / 760 torr/atm = 0.2474 atm

Now that we have converted the temperature to Kelvin and the pressure to atm, we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Let's plug in the values we have:

n = (0.2474 atm)(V) / (0.0821 L·atm/mol·K)(293.15 K)

Next, we need to determine the volume of F2 gas. To do this, we require the molar volume of an ideal gas at standard temperature and pressure (STP), which is defined as 1 mole of gas occupying 22.4 L at 0°C (273.15 K) and 1 atm. However, we currently have a different temperature and pressure.

Therefore, we can use the combined gas law equation:

(P1)(V1) / (T1) = (P2)(V2) / (T2)

where:
P1 = initial pressure (188 torr)
V1 = initial volume (unknown)
T1 = initial temperature (293.15 K)
P2 = final pressure (1 atm)
V2 = final volume (22.4 L)
T2 = final temperature (273.15 K)

Since we are solving for the volume (V1) of F2 gas, we can rearrange the equation:

V1 = (P2)(V2)(T1) / (P1)(T2)

Now we can calculate V1:

V1 = (1 atm)(22.4 L)(293.15 K) / (188 torr)(273.15 K)

After obtaining the value for V1, we can now substitute it back into the equation for the number of moles (n):

n = (0.2474 atm)(V1) / (0.0821 L·atm/mol·K)(293.15 K)

Finally, the specific mass (density) of fluorine (F2) in g/cm³ can be calculated by dividing the molar mass by the volume:

Specific mass of F2 (g/cm³) = (molar mass of F2 in g/mol) / (V1 in cm³)