The mass of an evacuated 255-mL flask is 143.187g. The mass of the flask filled with 267 torr of an unknown gas at 25 degrees Celsius is 143.289g. Calculate the molar mass of the unknown gas.

27.8

27.8 is right!

Use PV=nRT

This will give you the number of moles. 143.289-143.187 = 0.102 is the mass of n moles so 0.102/n is the molar mass or mass of one mole.

Well, calculating the molar mass of the unknown gas sounds like a gas-ty problem! But don't worry, I'll help you through it!

First, we need to find the mass of the gas in the flask. We can do that by subtracting the mass of the empty flask from the mass of the flask with the gas. So, we have:

Mass of gas = Mass of flask with gas - Mass of empty flask
Mass of gas = 143.289 g - 143.187 g
Mass of gas = 0.102 g

Now, let's use the ideal gas law to find the number of moles of the gas. The ideal gas law formula 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 in Kelvin.

To convert the volume from mL to L, we divide it by 1000: 255 mL ÷ 1000 = 0.255 L.

Now we can plug in the values into the ideal gas law equation:

(267 torr)(0.255 L) = n(0.08206 L•atm/(mol•K))(25 + 273.15 K)
68.085 L•torr = n(0.08206 L•atm/(mol•K))(298.15 K)

Okay, let's solve for n:

n = (68.085 L•torr) / [(0.08206 L•atm/(mol•K))(298.15 K)]
n ≈ 2.921 mol

Last but not yeast, we need to find the molar mass of the unknown gas by dividing the mass of the gas by the number of moles:

Molar mass = Mass of gas / Number of moles
Molar mass ≈ 0.102 g / 2.921 mol
Molar mass ≈ 0.035 g/mol

So, the molar mass of the unknown gas is approximately 0.035 g/mol.

To calculate the molar mass of the unknown gas, we need to use the ideal gas law equation, which is:

PV = nRT

Where:
P is the pressure of the gas (in this case, 267 torr)
V is the volume of the gas (in this case, 255 mL converted to liters by dividing by 1000)
n is the number of moles of the gas (which is what we want to find)
R is the ideal gas constant (you can use either 0.0821 L·atm/(mol·K) or 8.314 J/(mol·K))
T is the temperature of the gas in Kelvin (25 degrees Celsius converted to Kelvin by adding 273.15)

Step 1: Convert the volume from milliliters to liters:
Volume (V) = 255 mL / 1000 = 0.255 L

Step 2: Convert the Celsius temperature to Kelvin:
Temperature (T) = 25 + 273.15 = 298.15 K

Step 3: Plug the values into the ideal gas law equation and solve for n (the number of moles):
(267 torr) * (0.255 L) = n * (0.0821 L·atm/(mol·K)) * (298.15 K)

Step 4: Rearrange the equation to solve for n:
n = (267 torr * 0.255 L) / (0.0821 L·atm/(mol·K) * 298.15 K)

Step 5: Calculate the value of n:
n = 0.00889 mol

Step 6: Calculate the mass of the unknown gas using the molar mass (M) formula:
Mass (m) = n * M

Step 7: Rearrange the formula to solve for M:
M = (m) / (n)

Step 8: Calculate the mass difference of the flask:
Mass difference = Mass of the flask filled with gas – Mass of the evacuated flask
Mass difference = 143.289 g - 143.187 g = 0.102 g

Step 9: Calculate the molar mass:
Molar mass (M) = (Mass difference) / (n)

Molar mass (M) = 0.102 g / 0.00889 mol

Molar mass (M) ≈ 11.49 g/mol

Therefore, the molar mass of the unknown gas is approximately 11.49 g/mol.

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