Calculate the molar mass of a gas if 0.805g of this gas has a pressure of 4.00 bars at 305K in a 1 L. What is the gas density at this T and P, and what is the density at STP
gas density= mass/volume for the first case, both are given.
PV=nRT= mass/molmass*RT
solve for molmass, you are give all else
AT stp, you know T, P, n solve for new V
then gas density = mass/newvolume
Umm not clear... I don't understand at all.
To calculate the molar mass of a gas, we can use the ideal gas law, which states:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles of the gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Given:
Mass of gas (m) = 0.805g
Pressure (P) = 4.00 bar
Volume (V) = 1 L
Temperature (T) = 305 K
1. Convert pressure from bar to atmospheres (atm):
1 bar = 0.9869 atm (approximately)
4.00 bar = 4.00 x 0.9869 atm = 3.9476 atm (approximately)
2. Convert volume from liters (L) to m³:
1 L = 0.001 m³
1 m³ = 1000 L
1 L = 1 x 10⁻³ m³
So, volume (V) = 1 L = 1 x 10⁻³ m³
3. Rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (P x V) / (R x T)
To calculate the molar mass, we need the number of moles (n). For that, we need to know the ideal gas constant (R). The ideal gas constant is often represented as R = 0.0821 L·atm/mol·K.
4. Calculate the number of moles (n):
n = (3.9476 atm x 1 x 10⁻³ m³) / (0.0821 L·atm/mol·K x 305 K)
n ≈ 0.0001688 mol
5. Calculate molar mass (M):
Molar mass (M) = mass (m) / moles (n)
M = 0.805 g / 0.0001688 mol
M ≈ 4769.55 g/mol (rounded to four significant figures)
Therefore, the molar mass of the gas is approximately 4769.55 g/mol.
Now, let's calculate the gas density at this temperature and pressure and at standard temperature and pressure (STP).
Gas density is defined as mass per unit volume. So, to calculate the gas density, we need to divide the mass of the gas by its volume.
To calculate the gas density at the given temperature (305 K) and pressure (3.9476 atm):
Gas density at 305 K and 3.9476 atm = mass (m) / volume (V)
Gas density = 0.805 g / 1 L
Gas density at 305 K and 3.9476 atm ≈ 0.805 g/L (rounded to three significant figures)
Note: The unit of gas density can be different based on the units used for mass and volume.
Now, let's calculate the gas density at standard temperature and pressure (STP).
STP is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (1 atm).
To calculate the gas density at STP:
Gas density at STP = mass (m) / volume (V)
Gas density at STP = 0.805 g / 1 L
Gas density at STP ≈ 0.805 g/L (rounded to three significant figures)
Therefore, the gas density at the given temperature (305 K) and pressure (3.9476 atm) and at STP is approximately 0.805 g/L.