What is the density of NH3 at 400. torr and 35 ˚C?
To find the density of NH3 (ammonia) at 400. torr and 35 ˚C, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
First, let's convert the given pressure from torr to atm:
1 atm = 760 torr
So, 400. torr = 400. / 760 = 0.5263 atm
Next, let's convert the temperature from 35 ˚C to Kelvin:
T(K) = T(˚C) + 273.15
T(K) = 35 + 273.15 = 308.15 K
Now we need to determine the molar mass of NH3. N has a molar mass of 14.01 g/mol, and H has a molar mass of 1.01 g/mol. Since NH3 has three hydrogen atoms, its molar mass is:
(1 * 14.01 g/mol) + (3 * 1.01 g/mol) = 14.01 g/mol + 3.03 g/mol = 17.04 g/mol
Now we can rearrange the ideal gas law equation to solve for density:
density = (n * molar mass) / V
Since we are looking for density, which is mass/volume, we can rewrite the equation as:
density = (n * molar mass) / (V * molar mass)
Since we don't have the volume, we'll assume it to be 1 liter for simplicity. You can substitute the actual volume if it is given.
Now we need to find the number of moles (n) using the ideal gas law equation:
PV = nRT
n = (PV) / (RT)
Substituting the given values:
n = (0.5263 atm * 1 L) / (0.0821 L.atm/mol.K * 308.15 K)
n ≈ 0.02162 mol
Now we can calculate the density:
density = (0.02162 mol * 17.04 g/mol) / (1 L * 17.04 g/mol)
density ≈ 0.02162 g/L
Therefore, the density of NH3 at 400. torr and 35 ˚C is approximately 0.02162 g/L.
To calculate the density of NH3 at 400. torr and 35 ˚C, we need to use the ideal gas equation and the molar mass of NH3.
Step 1: Convert the pressure to standard atmospheric pressure
To convert the pressure from torr to atm, we divide by 760.
400. torr ÷ 760 = 0.526 atm
Step 2: Convert the temperature to Kelvin
To convert the temperature from ˚C to Kelvin, we add 273.15.
35 ˚C + 273.15 = 308.15 K
Step 3: Find the molar mass of NH3
The molar mass of NH3 (ammonia) is calculated by adding up the atomic masses of nitrogen and three hydrogen atoms.
Molar mass of NH3 = (1 × atomic mass of N) + (3 × atomic mass of H)
The atomic masses of N and H are approximately 14.01 g/mol and 1.01 g/mol, respectively.
Molar mass of NH3 = (1 × 14.01 g/mol) + (3 × 1.01 g/mol) = 17.03 g/mol
Step 4: Use the ideal gas equation to calculate density
The ideal gas equation is:
PV = nRT
where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature.
Since we want to find density (mass/volume) instead of moles, we can rearrange the equation:
PV = (m/M)RT
where m is the mass, M is the molar mass, and all other symbols remain the same.
The density, ρ, is given by:
ρ = m/V
To find density, we divide the mass by volume. Since we already have the molar mass (M), we need to find the number of moles (n) and volume (V).
We can calculate the number of moles using the ideal gas equation:
PV = nRT
n = PV / RT
Substituting the values:
n = (0.526 atm) × V / [(0.0821 L·atm/(mol·K)) × (308.15 K)]
Simplifying:
n = 0.01777 V
To find the volume, we need to assume a certain number of moles. For this calculation, we will assume 1 mole.
V = 1 moles / 0.01777 = 56.332 L
Now we can calculate the density:
ρ = m/V
ρ = (1 mole × 17.03 g/mol) / 56.332 L
ρ ≈ 0.302 g/L