Determine the molecular formula of phosphorus.

phosphorus gas has a density of 0.617 g/L at 70 and 200 Celsius ...

* at 790 torr not 70

70 what?

Use p*molar mass = density*R*T
Solve for molar mass, then
molar mass/30.97 = # P atoms/molecule.

To determine the molecular formula of phosphorus, we need to know its molar mass. Since you have provided the density of phosphorus gas at two different temperatures, we can use this information to calculate its molar mass.

To do this, we can utilize the ideal gas law, which states that the density (d) of a gas is related to its molar mass (M), temperature (T), and the gas constant (R) by the equation:

d = (M/R) * P/T

where P is the pressure.

First, we need to convert the temperature from Celsius to Kelvin by adding 273.15. This gives us:

70 Celsius = 273.15 + 70 = 343.15 K
200 Celsius = 273.15 + 200 = 473.15 K

Next, we can rearrange the equation to solve for the molar mass (M):

M = (d * R * T) / P

Now, we need the value of the gas constant (R). The ideal gas constant is usually given as 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K), depending on the units used for pressure.

For the given density, we have:
density = 0.617 g/L
pressure = P (we don't have the specific pressure value)

Now, let's calculate the molar mass of phosphorus at both temperatures:

At 70 Celsius (343.15 K):
M = (0.617 g/L * 0.0821 L·atm/(mol·K) * 343.15 K) / P

At 200 Celsius (473.15 K):
M = (0.617 g/L * 0.0821 L·atm/(mol·K) * 473.15 K) / P

By obtaining the molar mass of phosphorus using either of these equations, we can then compare it to the known molar mass of phosphorus (approximately 30.97 g/mol) to determine the molecular formula.