Uranium hexafluoride is a solid at room temperature, but it boils at 56°C. Determine the density of uranium hexafluoride at 67°C at 759 torr.
___g/L
I got 12.7 i do not know if this is correct. Please help
To determine the density of uranium hexafluoride (UF6) at a specific temperature and pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure in atmospheres (759 torr ≈ 1.001 atm),
V is the volume in liters,
n is the number of moles of the gas,
R is the ideal gas constant (0.0821 L·atm/mol·K),
and T is the temperature in Kelvin (67°C = 340 K).
First, we need to find the volume of uranium hexafluoride. To do this, we rearrange the equation as follows:
V = (nRT) / P
Now, we can calculate the volume by substituting the known values into the equation.
V = (n * 0.0821 * 340) / 1.001
Next, we need to find the number of moles of uranium hexafluoride. To find this, we can use the molar mass of UF6, which is 352.02 g/mol.
n = mass / molar mass
Since the density is given in g/L, we will assume a mass of 1 gram for simplicity.
n = 1 g / 352.02 g/mol
Now, we can substitute the value of n into the equation to find the volume:
V = (1 * 0.0821 * 340) / 1.001
Finally, we can calculate the density by dividing the mass by the volume:
Density = mass / volume
Density = 1 g / V
Now, let's calculate the density:
Density = 1 g / [(1 * 0.0821 * 340) / 1.001] = 3.872 g/L
Therefore, the density of uranium hexafluoride at 67°C and 759 torr is approximately 3.872 g/L.
To calculate the density of uranium hexafluoride (UF6) at a specific temperature and pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = moles of gas
R = gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, we need to convert the given pressure (759 torr) into atm:
1 atm = 760 torr
So, 759 torr = 759/760 atm ≈ 0.998 atm
Next, we need to convert the given temperature (67°C) into Kelvin:
T(K) = T(°C) + 273.15
T(K) = 67 + 273.15
T(K) ≈ 340.15 K
Now, we can rearrange the ideal gas law equation to solve for density:
density = (n x molar mass) / V
We know that the molar mass of uranium hexafluoride (UF6) is approximately 352.03 g/mol.
To calculate the molar mass of a compound, we sum up the atomic masses of all the elements present. For UF6, we have:
U = 238.03 g/mol
F = 19.00 g/mol (x 6 since there are 6 fluorine atoms)
Total molar mass = 238.03 + (19.00 x 6) = 238.03 + 114.00 = 352.03 g/mol
Now let's calculate the volume (V) using the ideal gas law equation:
V = (nRT) / P
Since the density is given in g/L, we can rearrange the equation to find the inverse of density:
density^(-1) = (P x molar mass) / (RT)
Substituting the given values into the equation:
density^(-1) = (0.998 atm x 352.03 g/mol) / (0.0821 L·atm/(mol·K) x 340.15 K)
Solving for density^(-1):
density^(-1) = 11.034 g/(L·atm)
Finally, taking the inverse of density^(-1) to find the density:
density = 1 / (11.034 g/(L·atm))
Therefore, the density of uranium hexafluoride (UF6) at 67°C and 759 torr is approximately 0.091 g/L