A chemist was asked to find the molecular mass of a gas. She massed the gas and found that 3.73 g of the gas occupied 300 cm3 at 25°C and 92.4 kPa. What is the molecular weight of the gas?
PV=nRT
solve for n. Now knowing the number of moles, you know the mass of n moles, so you can get the mol mass.
Use PV = nRT to calculate n = number of mols.
Then use mols = g/molar mass to calculate molar mass. Post your work if you get stuck.
To find the molecular mass of the gas, we can use the Ideal Gas Law equation: PV = nRT. In this equation, P represents pressure, V represents volume, n represents the number of moles of gas, R is the ideal gas constant, and T represents temperature.
First, we need to convert the given volume from cubic centimeters (cm³) to liters (L) since the unit of R is in liters. We divide the volume by 1000 to convert:
300 cm³ ÷ 1000 = 0.3 L
Next, we need to convert the temperature from Celsius (°C) to Kelvin (K). We add 273.15 to the temperature in Celsius:
25°C + 273.15 = 298.15 K
Now, let's rearrange the Ideal Gas Law equation to solve for the number of moles (n):
n = PV / RT
We have the following values:
P = 92.4 kPa (convert to atm by dividing by 101.325)
V = 0.3 L
R = 0.0821 (the ideal gas constant in atm L/mol K)
T = 298.15 K
Plugging in the values, we get:
n = (92.4 kPa / 101.325) * (0.3 L) / (0.0821 (atm L/mol K) * 298.15 K)
Simplifying the equation gives us the number of moles (n).
Finally, to find the molecular weight (molar mass) of the gas, we divide the mass of the gas (given as 3.73 g) by the calculated moles:
Molecular weight = mass of gas / number of moles.
So, divide 3.73 g by the calculated number of moles to get the molecular weight of the gas.