The density of an unknown gas is 1.23 g/L in 330K and temperature 25.5 pressure kPa. What is the molar mass of the substance?
P*molar mass = density x RT
To determine the molar mass of the unknown gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (kPa)
V = volume (L)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (K)
First, let's convert the temperature from Celsius to Kelvin:
Temperature in Kelvin (T) = 330K
Next, let's convert the given pressure from kPa to Pa:
Pressure in Pascal (P) = 25.5 kPa × 1000 = 25500 Pa
Now, we rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (25500 Pa) × (V) / [(8.314 J/(mol·K)) × (330K)]
Since we know the density of the gas, we can rewrite the volume (V) as follows:
V = m / d
Where:
m = mass
d = density
Given that the density is 1.23 g/L, we can convert it to kg/m³ by dividing by 1000:
density (d) = 1.23 g/L / 1000 = 0.00123 kg/m³
Now, substitute this value for density in the volume equation:
V = m / d
V = (mass) / (density)
V = (m) / (0.00123 kg/m³)
Substitute this expression for V in the equation for n:
n = (25500 Pa) × (m) / [(8.314 J/(mol·K)) × (330K) × (0.00123 kg/m³)]
Since the mass (m) is given in grams, we need to convert it to kilograms:
mass (m) = 1.23 g × (1 kg / 1000 g) = 0.00123 kg
Now, substitute this expression for mass (m) in the equation for n:
n = (25500 Pa) × (0.00123 kg) / [(8.314 J/(mol·K)) × (330K) × (0.00123 kg/m³)]
Now, we can simplify this equation, canceling units:
n = (25500) × (0.00123) / [(8.314) × (330) × (0.00123)]
n ≈ 9.6072 × 10^(-5) mol
Finally, we determine the molar mass (M) using the equation:
M = molar mass / number of moles
M = (0.00123 kg) / (9.6072 × 10^(-5) mol)
M = 12.808 kg/mol
Therefore, the molar mass of the unknown gas is approximately 12.808 kg/mol.