28cm3 of a gas weighs 0.4g at STP.Calculate the molecular mass of the gas.
well, 1 mole fills 22.4L
28cm^3 = 0.028L
So, you have .028/22.4 = 0.00125 moles (1/800 moles)
Thus, if the mol wt is x grams,
x/800 = 0.4
x = 320
To calculate the molecular mass of a gas, we can use the ideal gas equation, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
At standard temperature and pressure (STP), the pressure is 1 atmosphere (atm) and the temperature is 273.15 Kelvin (K).
First, we need to find the number of moles of the gas using the ideal gas equation. Rearranging the equation to solve for n, we get:
n = PV / RT
Given:
P = 1 atm
V = 28 cm^3 (convert to liters by dividing by 1000, since 1 L = 1000 cm^3)
T = 273.15 K
R = 0.0821 L·atm/(mol·K)
Converting the volume from cm^3 to liters:
V = 28 cm^3 / 1000 cm^3/L = 0.028 L
Substituting the values into the equation:
n = (1 atm) x (0.028 L) / (0.0821 L·atm/(mol·K)) x (273.15 K)
Simplifying:
n = 0.00108 mol
Now that we have the number of moles, we can calculate the molecular mass of the gas using the equation:
Molecular mass = Mass / Moles
Given:
Mass = 0.4 g
Moles = 0.00108 mol
Substituting the values into the equation:
Molecular mass = 0.4 g / 0.00108 mol
Simplifying:
Molecular mass ≈ 370.4 g/mol
Therefore, the molecular mass of the gas is approximately 370.4 g/mol.