Final answer:
The molar mass of a gas sample weighing 6.80 g, exerting 0.950 atm of pressure at 225 K in a 3.00 L container is calculated to be 46.58 grams per mole using the ideal gas law.
Step-by-step explanation:
To calculate the molar mass of a gas given a sample of 6.80 g exerting 0.950 atm of pressure at 225 K in a 3.00 L container, we will apply the ideal gas law, which is PV=nRT. Here, P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles of gas, R is the ideal gas constant (0.0821 L·atm/K·mol), and T is the temperature in kelvins (K).
First, we solve for n (number of moles) using the ideal gas law:
(0.950 atm)(3.00 L) = n(0.0821 L·atm/K·mol)(225 K)
n = (0.950 × 3.00) / (0.0821 × 225)
n = 0.146 moles
Now that we have the moles, we calculate the molar mass (M) by dividing the mass of the gas by the number of moles:
M = mass of the gas / number of moles
M = 6.80 g / 0.146 mol
M = 46.58 g/mol
Here, we can conclude that the molar mass of the gas is 46.58 grams per mole.