The density of a gas is 2.0 grams per liter at STP. Its molar mass is approximately?
45 g
To find the molar mass of the gas, we can make use of the ideal gas law, which states that 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 STP (Standard Temperature and Pressure), the pressure is 1 atmosphere (atm) and the temperature is 273 Kelvin (K).
Since we know the density of the gas (2.0 grams per liter), we can convert it into grams per cubic meter (g/m^3) to match the units commonly used in the ideal gas law.
1 liter is equal to 0.001 cubic meters, so the density of the gas in g/m^3 is (2.0 grams per liter) * (1 liter / 0.001 cubic meters) = 2000 grams per cubic meter.
Now, let's plug the values into the ideal gas law:
PV = nRT
(1 atm) * (V) = (n) * (0.0821 L * atm / mol * K) * (273 K)
Simplifying:
V = (n) * (0.0821) * (273)
Since the volume is given in liters, we can replace V with 1 liter:
1 = (n) * (0.0821) * (273)
Solving for n (number of moles):
n = 1 / (0.0821 * 273)
n ≈ 0.0447 moles
The molar mass of the gas can be calculated using the formula:
Molar mass = mass / moles
Since we know the density of the gas is 2000 grams per cubic meter, we can calculate the mass of 1 cubic meter of the gas:
Mass = density * volume = 2000 g/m^3 * 1 m^3 = 2000 grams
Finally, we can calculate the molar mass:
Molar mass = mass / moles = 2000 grams / 0.0447 moles ≈ 44763 grams per mole
Therefore, the approximate molar mass of the gas is 44.7 grams per mole.
1 mole of a gas occupies 22.4 L at STP. So
2.0 g/L x 22.4 L = ?? g/mole