What is the density of PCl5 gas at STP?
molar mass PCl5/22.4 = density in g/L.
To find the density of PCl5 gas at STP (Standard Temperature and Pressure), we need to know the molar mass of PCl5 and apply the ideal gas law.
Step 1: Find the molar mass of PCl5.
The molar mass of P (Phosphorus) is 31.0 g/mol, and the molar mass of Cl (Chlorine) is 35.5 g/mol. PCl5 consists of one phosphorus atom and five chlorine atoms, so we can calculate the molar mass as follows:
Molar mass of PCl5 = (1 * Molar mass of P) + (5 * Molar mass of Cl)
= (1 * 31.0 g/mol) + (5 * 35.5 g/mol)
= 31.0 g/mol + 177.5 g/mol
= 208.5 g/mol
Step 2: Apply the ideal gas law to find the density.
The ideal gas law is given by the equation: PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 atm L/mol K)
T = temperature (in Kelvin)
At STP:
P = 1 atm
V = 22.4 L (molar volume at STP)
R = 0.0821 atm L/mol K
T = 273.15 K
Using the ideal gas law, we can find the number of moles of PCl5:
n = PV / RT
n = (1 atm) * (22.4 L) / ((0.0821 atm L/mol K) * (273.15 K))
n = 0.88 mol
Now, we can calculate the density:
Density = (mass of PCl5) / (volume of PCl5)
Density = [(n * molar mass of PCl5)] / (volume of PCl5)
Density = [(0.88 mol) * (208.5 g/mol)] / (22.4 L)
Density = 8.18 g/L
Therefore, the density of PCl5 gas at STP is approximately 8.18 g/L.
To find the density of PCl5 gas at Standard Temperature and Pressure (STP), we need to know the molar mass of PCl5 and use the ideal gas law.
1. Find the molar mass of PCl5:
- The molar mass of P (phosphorus) is approximately 30.97 g/mol.
- The molar mass of Cl (chlorine) is approximately 35.45 g/mol.
- Since there are 5 chlorine atoms in PCl5, the total molar mass of PCl5 is:
(30.97 g/mol) + (5 × 35.45 g/mol) = 208.42 g/mol
2. Use the ideal gas law, which states that PV = nRT, where:
- P is the pressure (atmospheres),
- V is the volume (liters),
- n is the number of moles of gas,
- R is the ideal gas constant (0.0821 L·atm/mol·K), and
- T is the temperature (Kelvin).
At STP, the temperature is 273.15 K and the pressure is 1 atmosphere.
3. Rearrange the ideal gas law to solve for density:
Density (ρ) = (molar mass) × (P / RT)
Plugging in the values:
Density (ρ) = (208.42 g/mol) × (1 atm) / (0.0821 L·atm/mol·K × 273.15 K)
4. Calculate the density:
Density (ρ) = 7.203 g/L
Therefore, the density of PCl5 gas at STP is approximately 7.203 g/L.